LEO-II---2.3.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SWW349+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Oct  7 11:01:18 AM UTC 2026

% Result   : Theorem 119.26s 24.13s
% Output   : CNFRefutation 24.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :  129
% Syntax   : Number of formulae    : 1914 (1072 unt;   0 typ;   0 def)
%            Number of atoms       : 11360 (5078 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives : 39977 (5028   ~;3353   |;  60   &;31167   @)
%                                         ( 114 <=>; 255  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  534 ( 531 usr;  67 con; 0-10 aty)
%            Number of variables   : 8840 (   0   ^;8798   !;  42   ?;8840   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Big__Operators_Ocomm__monoid__add__class_Osetsum,type,
    c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).

thf(tp_c_Big__Operators_Ocomm__monoid__big,type,
    c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).

thf(tp_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod,type,
    c_Big__Operators_Ocomm__monoid__mult__class_Osetprod: $i > $i > $i ).

thf(tp_c_Big__Operators_Olattice_OInf__fin,type,
    c_Big__Operators_Olattice_OInf__fin: $i > $i > $i > $i ).

thf(tp_c_Big__Operators_Olattice_OSup__fin,type,
    c_Big__Operators_Olattice_OSup__fin: $i > $i > $i > $i ).

thf(tp_c_Big__Operators_Olattice__class_OInf__fin,type,
    c_Big__Operators_Olattice__class_OInf__fin: $i > $i > $i ).

thf(tp_c_Big__Operators_Olattice__class_OSup__fin,type,
    c_Big__Operators_Olattice__class_OSup__fin: $i > $i > $i ).

thf(tp_c_Big__Operators_Olinorder__class_OMax,type,
    c_Big__Operators_Olinorder__class_OMax: $i > $i > $i ).

thf(tp_c_Big__Operators_Olinorder__class_OMin,type,
    c_Big__Operators_Olinorder__class_OMin: $i > $i > $i ).

thf(tp_c_Big__Operators_Osemilattice__big,type,
    c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).

thf(tp_c_COMBB,type,
    c_COMBB: $i > $i > $i > $i ).

thf(tp_c_COMBC,type,
    c_COMBC: $i > $i > $i > $i ).

thf(tp_c_COMBI,type,
    c_COMBI: $i > $i ).

thf(tp_c_COMBK,type,
    c_COMBK: $i > $i > $i ).

thf(tp_c_COMBS,type,
    c_COMBS: $i > $i > $i > $i ).

thf(tp_c_Code__Numeral_OSuc__code__numeral,type,
    c_Code__Numeral_OSuc__code__numeral: $i > $i ).

thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case,type,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case: $i > $i > $i > $i > $i ).

thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__size,type,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size: $i > $i ).

thf(tp_c_Code__Numeral_Odiv__mod__code__numeral,type,
    c_Code__Numeral_Odiv__mod__code__numeral: $i > $i > $i ).

thf(tp_c_Code__Numeral_Oint__of,type,
    c_Code__Numeral_Oint__of: $i ).

thf(tp_c_Code__Numeral_Onat__of,type,
    c_Code__Numeral_Onat__of: $i ).

thf(tp_c_Code__Numeral_Onat__of__aux,type,
    c_Code__Numeral_Onat__of__aux: $i > $i > $i ).

thf(tp_c_Code__Numeral_Oof__nat,type,
    c_Code__Numeral_Oof__nat: $i ).

thf(tp_c_Code__Numeral_Osubtract__code__numeral,type,
    c_Code__Numeral_Osubtract__code__numeral: $i ).

thf(tp_c_Com_OArg,type,
    c_Com_OArg: $i ).

thf(tp_c_Com_ORes,type,
    c_Com_ORes: $i ).

thf(tp_c_Com_OWT,type,
    c_Com_OWT: $i ).

thf(tp_c_Com_OWT__bodies,type,
    c_Com_OWT__bodies: $o ).

thf(tp_c_Com_Obodies,type,
    c_Com_Obodies: $i ).

thf(tp_c_Com_Obody,type,
    c_Com_Obody: $i ).

thf(tp_c_Com_Ocom_OAss,type,
    c_Com_Ocom_OAss: $i > $i > $i ).

thf(tp_c_Com_Ocom_OBODY,type,
    c_Com_Ocom_OBODY: $i ).

thf(tp_c_Com_Ocom_OCall,type,
    c_Com_Ocom_OCall: $i > $i > $i > $i ).

thf(tp_c_Com_Ocom_OCond,type,
    c_Com_Ocom_OCond: $i > $i > $i > $i ).

thf(tp_c_Com_Ocom_OLocal,type,
    c_Com_Ocom_OLocal: $i > $i > $i > $i ).

thf(tp_c_Com_Ocom_OSKIP,type,
    c_Com_Ocom_OSKIP: $i ).

thf(tp_c_Com_Ocom_OSemi,type,
    c_Com_Ocom_OSemi: $i > $i > $i ).

thf(tp_c_Com_Ocom_OWhile,type,
    c_Com_Ocom_OWhile: $i > $i > $i ).

thf(tp_c_Com_Ocom_Ocom__case,type,
    c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Com_Ocom_Ocom__rec,type,
    c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Com_Ocom_Ocom__size,type,
    c_Com_Ocom_Ocom__size: $i > $i ).

thf(tp_c_Com_Ovname_OGlb,type,
    c_Com_Ovname_OGlb: $i > $i ).

thf(tp_c_Com_Ovname_OLoc,type,
    c_Com_Ovname_OLoc: $i > $i ).

thf(tp_c_Com_Ovname_Ovname__case,type,
    c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).

thf(tp_c_Com_Ovname_Ovname__rec,type,
    c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).

thf(tp_c_Com_Ovname_Ovname__size,type,
    c_Com_Ovname_Ovname__size: $i > $i ).

thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
    c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).

thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
    c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).

thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).

thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).

thf(tp_c_Divides_Oadjust,type,
    c_Divides_Oadjust: $i > $i ).

thf(tp_c_Divides_Odiv__class_Odiv,type,
    c_Divides_Odiv__class_Odiv: $i > $i > $i ).

thf(tp_c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).

thf(tp_c_Divides_Odivmod__int,type,
    c_Divides_Odivmod__int: $i > $i > $i ).

thf(tp_c_Divides_Odivmod__int__rel,type,
    c_Divides_Odivmod__int__rel: $i > $i > $i ).

thf(tp_c_Divides_Odivmod__nat,type,
    c_Divides_Odivmod__nat: $i > $i > $i ).

thf(tp_c_Divides_Odivmod__nat__rel,type,
    c_Divides_Odivmod__nat__rel: $i > $i > $i ).

thf(tp_c_Divides_OnegDivAlg,type,
    c_Divides_OnegDivAlg: $i > $i > $i ).

thf(tp_c_Divides_OnegDivAlg__rel,type,
    c_Divides_OnegDivAlg__rel: $i ).

thf(tp_c_Divides_OnegateSnd,type,
    c_Divides_OnegateSnd: $i ).

thf(tp_c_Divides_Opdivmod,type,
    c_Divides_Opdivmod: $i > $i > $i ).

thf(tp_c_Divides_OposDivAlg,type,
    c_Divides_OposDivAlg: $i > $i > $i ).

thf(tp_c_Divides_OposDivAlg__rel,type,
    c_Divides_OposDivAlg__rel: $i ).

thf(tp_c_Enum_Oall__n__lists,type,
    c_Enum_Oall__n__lists: $i > $i > $i > $o ).

thf(tp_c_Enum_Oenum__class_Oenum,type,
    c_Enum_Oenum__class_Oenum: $i > $i ).

thf(tp_c_Enum_Oenum__class_Oenum__all,type,
    c_Enum_Oenum__class_Oenum__all: $i > $i ).

thf(tp_c_Enum_Oenum__class_Oenum__ex,type,
    c_Enum_Oenum__class_Oenum__ex: $i > $i ).

thf(tp_c_Enum_Oenum__the,type,
    c_Enum_Oenum__the: $i > $i > $i ).

thf(tp_c_Enum_Oex__n__lists,type,
    c_Enum_Oex__n__lists: $i > $i > $i > $o ).

thf(tp_c_Enum_On__lists,type,
    c_Enum_On__lists: $i > $i > $i > $i ).

thf(tp_c_Enum_Oproduct,type,
    c_Enum_Oproduct: $i > $i > $i > $i > $i ).

thf(tp_c_Enum_Osublists,type,
    c_Enum_Osublists: $i > $i > $i ).

thf(tp_c_Equiv__Relations_Ocongruent,type,
    c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).

thf(tp_c_Equiv__Relations_Ocongruent2,type,
    c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_Equiv__Relations_Oequiv,type,
    c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).

thf(tp_c_Equiv__Relations_Oequivp,type,
    c_Equiv__Relations_Oequivp: $i > $i > $o ).

thf(tp_c_Equiv__Relations_Oquotient,type,
    c_Equiv__Relations_Oquotient: $i > $i ).

thf(tp_c_Finite__Set_Ocard,type,
    c_Finite__Set_Ocard: $i > $i ).

thf(tp_c_Finite__Set_Ofinite,type,
    c_Finite__Set_Ofinite: $i > $i ).

thf(tp_c_Finite__Set_Ofold,type,
    c_Finite__Set_Ofold: $i > $i > $i > $i ).

thf(tp_c_Finite__Set_Ofold1,type,
    c_Finite__Set_Ofold1: $i > $i > $i ).

thf(tp_c_Finite__Set_Ofold1Set,type,
    c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).

thf(tp_c_Finite__Set_Ofold__graph,type,
    c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Finite__Set_Ofold__image,type,
    c_Finite__Set_Ofold__image: $i > $i > $i > $i ).

thf(tp_c_Finite__Set_Ofolding,type,
    c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofolding__idem,type,
    c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofolding__image,type,
    c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofolding__image__simple,type,
    c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofolding__one,type,
    c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofolding__one__idem,type,
    c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).

thf(tp_c_Finite__Set_Ofun__left__comm__idem,type,
    c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).

thf(tp_c_FunDef_Oin__rel,type,
    c_FunDef_Oin__rel: $i > $i > $i > $i ).

thf(tp_c_FunDef_Omax__strict,type,
    c_FunDef_Omax__strict: $i ).

thf(tp_c_FunDef_Omax__weak,type,
    c_FunDef_Omax__weak: $i ).

thf(tp_c_FunDef_Omin__strict,type,
    c_FunDef_Omin__strict: $i ).

thf(tp_c_FunDef_Omin__weak,type,
    c_FunDef_Omin__weak: $i ).

thf(tp_c_FunDef_Opair__leq,type,
    c_FunDef_Opair__leq: $i ).

thf(tp_c_FunDef_Opair__less,type,
    c_FunDef_Opair__less: $i ).

thf(tp_c_FunDef_Oreduction__pair,type,
    c_FunDef_Oreduction__pair: $i > $i > $o ).

thf(tp_c_FunDef_Orp__inv__image,type,
    c_FunDef_Orp__inv__image: $i > $i > $i ).

thf(tp_c_Fun_Ocomp,type,
    c_Fun_Ocomp: $i > $i > $i > $i > $i ).

thf(tp_c_Fun_Ofun__upd,type,
    c_Fun_Ofun__upd: $i > $i > $i ).

thf(tp_c_Fun_Oid,type,
    c_Fun_Oid: $i > $i ).

thf(tp_c_Fun_Oinj__on,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

thf(tp_c_Fun_Ooverride__on,type,
    c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Fun_Othe__inv__into,type,
    c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).

thf(tp_c_Groups_Oabs__class_Oabs,type,
    c_Groups_Oabs__class_Oabs: $i > $i ).

thf(tp_c_Groups_Ominus__class_Ominus,type,
    c_Groups_Ominus__class_Ominus: $i > $i ).

thf(tp_c_Groups_Oone__class_Oone,type,
    c_Groups_Oone__class_Oone: $i > $i ).

thf(tp_c_Groups_Oplus__class_Oplus,type,
    c_Groups_Oplus__class_Oplus: $i > $i ).

thf(tp_c_Groups_Osgn__class_Osgn,type,
    c_Groups_Osgn__class_Osgn: $i > $i > $i ).

thf(tp_c_Groups_Otimes__class_Otimes,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

thf(tp_c_Groups_Ouminus__class_Ouminus,type,
    c_Groups_Ouminus__class_Ouminus: $i > $i ).

thf(tp_c_Groups_Ozero__class_Ozero,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

thf(tp_c_HOL_OAll,type,
    c_HOL_OAll: $i > $i ).

thf(tp_c_HOL_OEx,type,
    c_HOL_OEx: $i > $i ).

thf(tp_c_HOL_OLet,type,
    c_HOL_OLet: $i > $i > $i ).

thf(tp_c_HOL_OThe,type,
    c_HOL_OThe: $i > $i > $i ).

thf(tp_c_HOL_Obool_Obool__size,type,
    c_HOL_Obool_Obool__size: $i > $i ).

thf(tp_c_Hilbert__Choice_OEps,type,
    c_Hilbert__Choice_OEps: $i > $i > $i ).

thf(tp_c_Hilbert__Choice_OGreatest,type,
    c_Hilbert__Choice_OGreatest: $i > $i ).

thf(tp_c_Hilbert__Choice_OGreatestM,type,
    c_Hilbert__Choice_OGreatestM: $i > $i > $i > $i ).

thf(tp_c_Hilbert__Choice_OLeastM,type,
    c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).

thf(tp_c_Hoare__Mirabelle_OMGT,type,
    c_Hoare__Mirabelle_OMGT: $i > $i ).

thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
    c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).

thf(tp_c_Hoare__Mirabelle_Ohoare__valids,type,
    c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).

thf(tp_c_Hoare__Mirabelle_Opeek__and,type,
    c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).

thf(tp_c_Hoare__Mirabelle_Ostate__not__singleton,type,
    c_Hoare__Mirabelle_Ostate__not__singleton: $o ).

thf(tp_c_Hoare__Mirabelle_Otriple_Otriple,type,
    c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).

thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__case,type,
    c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).

thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__rec,type,
    c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).

thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__size,type,
    c_Hoare__Mirabelle_Otriple_Otriple__size: $i > $i > $i > $i ).

thf(tp_c_Hoare__Mirabelle_Otriple__valid,type,
    c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).

thf(tp_c_If,type,
    c_If: $i > $i ).

thf(tp_c_Inductive_Ocomplete__lattice__class_Ogfp,type,
    c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).

thf(tp_c_Inductive_Ocomplete__lattice__class_Olfp,type,
    c_Inductive_Ocomplete__lattice__class_Olfp: $i > $i > $i ).

thf(tp_c_Int_OAbs__Integ,type,
    c_Int_OAbs__Integ: $i ).

thf(tp_c_Int_OBit0,type,
    c_Int_OBit0: $i > $i ).

thf(tp_c_Int_OBit1,type,
    c_Int_OBit1: $i > $i ).

thf(tp_c_Int_OInteg,type,
    c_Int_OInteg: $i ).

thf(tp_c_Int_OMin,type,
    c_Int_OMin: $i ).

thf(tp_c_Int_OPls,type,
    c_Int_OPls: $i ).

thf(tp_c_Int_ORep__Integ,type,
    c_Int_ORep__Integ: $i ).

thf(tp_c_Int_Oint__ge__less__than,type,
    c_Int_Oint__ge__less__than: $i > $i ).

thf(tp_c_Int_Oint__ge__less__than2,type,
    c_Int_Oint__ge__less__than2: $i > $i ).

thf(tp_c_Int_Ointrel,type,
    c_Int_Ointrel: $i ).

thf(tp_c_Int_Oiszero,type,
    c_Int_Oiszero: $i > $i > $o ).

thf(tp_c_Int_Onat,type,
    c_Int_Onat: $i ).

thf(tp_c_Int_Onat__aux,type,
    c_Int_Onat__aux: $i > $i > $i ).

thf(tp_c_Int_Onumber__class_Onumber__of,type,
    c_Int_Onumber__class_Onumber__of: $i > $i ).

thf(tp_c_Int_Opred,type,
    c_Int_Opred: $i > $i ).

thf(tp_c_Int_Oring__1__class_OInts,type,
    c_Int_Oring__1__class_OInts: $i > $i ).

thf(tp_c_Int_Oring__1__class_Oof__int,type,
    c_Int_Oring__1__class_Oof__int: $i > $i ).

thf(tp_c_Int_Osucc,type,
    c_Int_Osucc: $i > $i ).

thf(tp_c_Lattices_Osemilattice__inf__class_Oinf,type,
    c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).

thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
    c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).

thf(tp_c_Lazy__Sequence_Oanamorph,type,
    c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i > $i ).

thf(tp_c_Lazy__Sequence_Ohb__not__seq,type,
    c_Lazy__Sequence_Ohb__not__seq: $i > $i ).

thf(tp_c_List_Oappend,type,
    c_List_Oappend: $i > $i ).

thf(tp_c_List_Obutlast,type,
    c_List_Obutlast: $i > $i > $i ).

thf(tp_c_List_Oconcat,type,
    c_List_Oconcat: $i > $i > $i ).

thf(tp_c_List_Odistinct,type,
    c_List_Odistinct: $i > $i ).

thf(tp_c_List_Odrop,type,
    c_List_Odrop: $i > $i ).

thf(tp_c_List_OdropWhile,type,
    c_List_OdropWhile: $i > $i > $i > $i ).

thf(tp_c_List_Oembed__list,type,
    c_List_Oembed__list: $i > $i ).

thf(tp_c_List_Ofilter,type,
    c_List_Ofilter: $i > $i > $i ).

thf(tp_c_List_Ofoldl,type,
    c_List_Ofoldl: $i > $i > $i > $i > $i ).

thf(tp_c_List_Ofoldr,type,
    c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).

thf(tp_c_List_Ohd,type,
    c_List_Ohd: $i > $i ).

thf(tp_c_List_Oinsert,type,
    c_List_Oinsert: $i > $i > $i > $i ).

thf(tp_c_List_Olast,type,
    c_List_Olast: $i > $i > $i ).

thf(tp_c_List_Olenlex,type,
    c_List_Olenlex: $i > $i > $i ).

thf(tp_c_List_Olex,type,
    c_List_Olex: $i > $i > $i ).

thf(tp_c_List_Olexn,type,
    c_List_Olexn: $i > $i > $i ).

thf(tp_c_List_Olexord,type,
    c_List_Olexord: $i > $i > $i ).

thf(tp_c_List_Olinorder__class_Oinsort__insert__key,type,
    c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).

thf(tp_c_List_Olinorder__class_Oinsort__key,type,
    c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).

thf(tp_c_List_Olinorder__class_Osort__key,type,
    c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).

thf(tp_c_List_Olinorder__class_Osorted,type,
    c_List_Olinorder__class_Osorted: $i > $i > $o ).

thf(tp_c_List_Olinorder__class_Osorted__list__of__set,type,
    c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).

thf(tp_c_List_Olist_OCons,type,
    c_List_Olist_OCons: $i > $i ).

thf(tp_c_List_Olist_ONil,type,
    c_List_Olist_ONil: $i > $i ).

thf(tp_c_List_Olist_Olist__case,type,
    c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).

thf(tp_c_List_Olist_Olist__size,type,
    c_List_Olist_Olist__size: $i > $i > $i > $i ).

thf(tp_c_List_Olist__all2,type,
    c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).

thf(tp_c_List_Olist__ex,type,
    c_List_Olist__ex: $i > $i > $i > $o ).

thf(tp_c_List_Olist__update,type,
    c_List_Olist__update: $i > $i > $i ).

thf(tp_c_List_Olistrel,type,
    c_List_Olistrel: $i > $i > $i ).

thf(tp_c_List_Olistrel1,type,
    c_List_Olistrel1: $i > $i > $i ).

thf(tp_c_List_Olistrelp,type,
    c_List_Olistrelp: $i > $i > $i > $i > $o ).

thf(tp_c_List_Olists,type,
    c_List_Olists: $i > $i > $i ).

thf(tp_c_List_Olistset,type,
    c_List_Olistset: $i > $i > $i ).

thf(tp_c_List_Olistsp,type,
    c_List_Olistsp: $i > $i > $i ).

thf(tp_c_List_Omap,type,
    c_List_Omap: $i > $i > $i ).

thf(tp_c_List_Omap__filter,type,
    c_List_Omap__filter: $i > $i > $i > $i > $i ).

thf(tp_c_List_Omaps,type,
    c_List_Omaps: $i > $i > $i > $i > $i ).

thf(tp_c_List_Omeasures,type,
    c_List_Omeasures: $i > $i > $i ).

thf(tp_c_List_Omonoid__add__class_Olistsum,type,
    c_List_Omonoid__add__class_Olistsum: $i > $i ).

thf(tp_c_List_Onat__list,type,
    c_List_Onat__list: $i > $o ).

thf(tp_c_List_Onth,type,
    c_List_Onth: $i > $i ).

thf(tp_c_List_Opartition,type,
    c_List_Opartition: $i > $i > $i > $i ).

thf(tp_c_List_Oremdups,type,
    c_List_Oremdups: $i > $i > $i ).

thf(tp_c_List_Oremove1,type,
    c_List_Oremove1: $i > $i > $i > $i ).

thf(tp_c_List_OremoveAll,type,
    c_List_OremoveAll: $i > $i > $i ).

thf(tp_c_List_Oreturn__list,type,
    c_List_Oreturn__list: $i > $i ).

thf(tp_c_List_Orev,type,
    c_List_Orev: $i > $i ).

thf(tp_c_List_Orotate,type,
    c_List_Orotate: $i > $i > $i ).

thf(tp_c_List_Orotate1,type,
    c_List_Orotate1: $i > $i ).

thf(tp_c_List_Oset,type,
    c_List_Oset: $i > $i ).

thf(tp_c_List_Oset__Cons,type,
    c_List_Oset__Cons: $i > $i > $i > $i ).

thf(tp_c_List_Osublist,type,
    c_List_Osublist: $i > $i > $i > $i ).

thf(tp_c_List_Otake,type,
    c_List_Otake: $i > $i ).

thf(tp_c_List_OtakeWhile,type,
    c_List_OtakeWhile: $i > $i > $i > $i ).

thf(tp_c_List_Otl,type,
    c_List_Otl: $i > $i ).

thf(tp_c_List_Otranspose,type,
    c_List_Otranspose: $i > $i > $i ).

thf(tp_c_List_Otranspose__rel,type,
    c_List_Otranspose__rel: $i > $i ).

thf(tp_c_List_Oupt,type,
    c_List_Oupt: $i > $i > $i ).

thf(tp_c_List_Oupto,type,
    c_List_Oupto: $i > $i > $i ).

thf(tp_c_List_Oupto__rel,type,
    c_List_Oupto__rel: $i ).

thf(tp_c_List_Ozip,type,
    c_List_Ozip: $i > $i > $i ).

thf(tp_c_Map_Odom,type,
    c_Map_Odom: $i > $i > $i > $i ).

thf(tp_c_Map_Omap__add,type,
    c_Map_Omap__add: $i > $i > $i > $i > $i ).

thf(tp_c_Map_Omap__comp,type,
    c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Map_Omap__le,type,
    c_Map_Omap__le: $i > $i > $i > $i > $o ).

thf(tp_c_Map_Omap__of,type,
    c_Map_Omap__of: $i > $i > $i ).

thf(tp_c_Map_Omap__upds,type,
    c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Map_Oran,type,
    c_Map_Oran: $i > $i > $i > $i ).

thf(tp_c_Map_Orestrict__map,type,
    c_Map_Orestrict__map: $i > $i > $i > $i > $i ).

thf(tp_c_Nat_OSuc,type,
    c_Nat_OSuc: $i ).

thf(tp_c_Nat_Ocompow,type,
    c_Nat_Ocompow: $i > $i > $i ).

thf(tp_c_Nat_Ofunpow,type,
    c_Nat_Ofunpow: $i > $i ).

thf(tp_c_Nat_Onat_Onat__case,type,
    c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).

thf(tp_c_Nat_Onat_Onat__rec,type,
    c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).

thf(tp_c_Nat_Onat_Onat__size,type,
    c_Nat_Onat_Onat__size: $i > $i ).

thf(tp_c_Nat_Osemiring__1__class_ONats,type,
    c_Nat_Osemiring__1__class_ONats: $i > $i ).

thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).

thf(tp_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
    c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).

thf(tp_c_Nat_Osize__class_Osize,type,
    c_Nat_Osize__class_Osize: $i > $i ).

thf(tp_c_Nat__Numeral_Oneg,type,
    c_Nat__Numeral_Oneg: $i ).

thf(tp_c_Nat__Transfer_Ois__nat,type,
    c_Nat__Transfer_Ois__nat: $i > $o ).

thf(tp_c_Nat__Transfer_Onat__set,type,
    c_Nat__Transfer_Onat__set: $i > $o ).

thf(tp_c_Nat__Transfer_Otransfer__morphism,type,
    c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).

thf(tp_c_Nat__Transfer_Otsub,type,
    c_Nat__Transfer_Otsub: $i > $i > $i ).

thf(tp_c_Natural_Oevalc,type,
    c_Natural_Oevalc: $i > $i ).

thf(tp_c_Natural_Oevaln,type,
    c_Natural_Oevaln: $i ).

thf(tp_c_Natural_Ogetlocs,type,
    c_Natural_Ogetlocs: $i ).

thf(tp_c_Natural_Onewlocs,type,
    c_Natural_Onewlocs: $i ).

thf(tp_c_Natural_Osetlocs,type,
    c_Natural_Osetlocs: $i ).

thf(tp_c_Natural_Oupdate,type,
    c_Natural_Oupdate: $i ).

thf(tp_c_New__DSequence_Opos__not__seq,type,
    c_New__DSequence_Opos__not__seq: $i > $i ).

thf(tp_c_New__Random__Sequence_Opos__not__random__dseq,type,
    c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_OAbs__Frac,type,
    c_Nitpick_OAbs__Frac: $i > $i > $i ).

thf(tp_c_Nitpick_OFrac,type,
    c_Nitpick_OFrac: $i ).

thf(tp_c_Nitpick_Ocard_H,type,
    c_Nitpick_Ocard_H: $i > $i > $i ).

thf(tp_c_Nitpick_Ofold__graph_H,type,
    c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_Nitpick_Ofrac,type,
    c_Nitpick_Ofrac: $i > $i > $i > $i ).

thf(tp_c_Nitpick_Oint__gcd,type,
    c_Nitpick_Oint__gcd: $i ).

thf(tp_c_Nitpick_Oint__lcm,type,
    c_Nitpick_Oint__lcm: $i > $i > $i ).

thf(tp_c_Nitpick_Onat__gcd,type,
    c_Nitpick_Onat__gcd: $i > $i > $i ).

thf(tp_c_Nitpick_Onat__gcd__rel,type,
    c_Nitpick_Onat__gcd__rel: $i ).

thf(tp_c_Nitpick_Onat__lcm,type,
    c_Nitpick_Onat__lcm: $i > $i > $i ).

thf(tp_c_Nitpick_Onorm__frac,type,
    c_Nitpick_Onorm__frac: $i > $i > $i ).

thf(tp_c_Nitpick_Onorm__frac__rel,type,
    c_Nitpick_Onorm__frac__rel: $i ).

thf(tp_c_Nitpick_Onumber__of__frac,type,
    c_Nitpick_Onumber__of__frac: $i > $i > $i ).

thf(tp_c_Nitpick_Oone__frac,type,
    c_Nitpick_Oone__frac: $i > $i ).

thf(tp_c_Nitpick_Opair__box_OPairBox,type,
    c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Opair__box_Opair__box__case,type,
    c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Opair__box_Opair__box__rec,type,
    c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Opair__box_Opair__box__size,type,
    c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Oprod,type,
    c_Nitpick_Oprod: $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Orefl_H,type,
    c_Nitpick_Orefl_H: $i > $i > $o ).

thf(tp_c_Nitpick_Osetsum_H,type,
    c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).

thf(tp_c_Nitpick_Ounknown,type,
    c_Nitpick_Ounknown: $i > $o ).

thf(tp_c_Nitpick_Owf_H,type,
    c_Nitpick_Owf_H: $i > $i > $o ).

thf(tp_c_Nitpick_Ozero__frac,type,
    c_Nitpick_Ozero__frac: $i > $i ).

thf(tp_c_Option_Obind,type,
    c_Option_Obind: $i > $i > $i ).

thf(tp_c_Option_Ois__none,type,
    c_Option_Ois__none: $i > $i > $o ).

thf(tp_c_Option_Omap,type,
    c_Option_Omap: $i > $i > $i ).

thf(tp_c_Option_Ooption_ONone,type,
    c_Option_Ooption_ONone: $i > $i ).

thf(tp_c_Option_Ooption_OSome,type,
    c_Option_Ooption_OSome: $i > $i ).

thf(tp_c_Option_Ooption_Ooption__case,type,
    c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i ).

thf(tp_c_Option_Ooption_Ooption__rec,type,
    c_Option_Ooption_Ooption__rec: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Option_Ooption_Ooption__size,type,
    c_Option_Ooption_Ooption__size: $i > $i > $i > $i ).

thf(tp_c_Option_Oset,type,
    c_Option_Oset: $i > $i > $i ).

thf(tp_c_Option_Othe,type,
    c_Option_Othe: $i > $i ).

thf(tp_c_Orderings_Obot__class_Obot,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

thf(tp_c_Orderings_Oord_Omax,type,
    c_Orderings_Oord_Omax: $i > $i > $i ).

thf(tp_c_Orderings_Oord_Omin,type,
    c_Orderings_Oord_Omin: $i > $i > $i ).

thf(tp_c_Orderings_Oord__class_OLeast,type,
    c_Orderings_Oord__class_OLeast: $i > $i > $i ).

thf(tp_c_Orderings_Oord__class_Oless,type,
    c_Orderings_Oord__class_Oless: $i > $i ).

thf(tp_c_Orderings_Oord__class_Oless__eq,type,
    c_Orderings_Oord__class_Oless__eq: $i > $i ).

thf(tp_c_Orderings_Oord__class_Omax,type,
    c_Orderings_Oord__class_Omax: $i > $i ).

thf(tp_c_Orderings_Oord__class_Omin,type,
    c_Orderings_Oord__class_Omin: $i > $i ).

thf(tp_c_Orderings_Oorder__class_Omono,type,
    c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).

thf(tp_c_Orderings_Otop__class_Otop,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

thf(tp_c_Partial__Function_Oflat__lub,type,
    c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).

thf(tp_c_Power_Opower_Opower,type,
    c_Power_Opower_Opower: $i > $i > $i > $i ).

thf(tp_c_Power_Opower__class_Opower,type,
    c_Power_Opower__class_Opower: $i > $i ).

thf(tp_c_Predicate_ODomainP,type,
    c_Predicate_ODomainP: $i > $i > $i > $i ).

thf(tp_c_Predicate_OPowp,type,
    c_Predicate_OPowp: $i > $i > $i ).

thf(tp_c_Predicate_ORangeP,type,
    c_Predicate_ORangeP: $i > $i > $i > $i ).

thf(tp_c_Predicate_Opred__comp,type,
    c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_Predicate_Oreflp,type,
    c_Predicate_Oreflp: $i > $i > $o ).

thf(tp_c_Product__Type_OPair,type,
    c_Product__Type_OPair: $i > $i > $i ).

thf(tp_c_Product__Type_OSigma,type,
    c_Product__Type_OSigma: $i > $i > $i ).

thf(tp_c_Product__Type_Oapfst,type,
    c_Product__Type_Oapfst: $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Oapsnd,type,
    c_Product__Type_Oapsnd: $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Ofst,type,
    c_Product__Type_Ofst: $i > $i > $i ).

thf(tp_c_Product__Type_Omap__pair,type,
    c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Oprod_Oprod__case,type,
    c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).

thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
    c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Oprod_Oprod__size,type,
    c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Oscomp,type,
    c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).

thf(tp_c_Product__Type_Osnd,type,
    c_Product__Type_Osnd: $i > $i > $i ).

thf(tp_c_Random_Oinc__shift,type,
    c_Random_Oinc__shift: $i > $i > $i ).

thf(tp_c_Random_Oiterate,type,
    c_Random_Oiterate: $i > $i > $i > $i > $i ).

thf(tp_c_Random_Olog,type,
    c_Random_Olog: $i > $i > $i ).

thf(tp_c_Random_Ominus__shift,type,
    c_Random_Ominus__shift: $i > $i > $i > $i ).

thf(tp_c_Random_Opick,type,
    c_Random_Opick: $i > $i > $i ).

thf(tp_c_Random_Orange,type,
    c_Random_Orange: $i > $i ).

thf(tp_c_Random_Oselect,type,
    c_Random_Oselect: $i > $i > $i ).

thf(tp_c_Random_Oselect__weight,type,
    c_Random_Oselect__weight: $i > $i > $i ).

thf(tp_c_Recdef_Osame__fst,type,
    c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).

thf(tp_c_Relation_ODomain,type,
    c_Relation_ODomain: $i > $i > $i ).

thf(tp_c_Relation_OField,type,
    c_Relation_OField: $i > $i ).

thf(tp_c_Relation_OId,type,
    c_Relation_OId: $i > $i ).

thf(tp_c_Relation_OId__on,type,
    c_Relation_OId__on: $i > $i > $i ).

thf(tp_c_Relation_OImage,type,
    c_Relation_OImage: $i > $i > $i > $i ).

thf(tp_c_Relation_ORange,type,
    c_Relation_ORange: $i > $i > $i ).

thf(tp_c_Relation_Oconverse,type,
    c_Relation_Oconverse: $i > $i > $i ).

thf(tp_c_Relation_Oinv__image,type,
    c_Relation_Oinv__image: $i > $i > $i ).

thf(tp_c_Relation_Oirrefl,type,
    c_Relation_Oirrefl: $i > $i > $o ).

thf(tp_c_Relation_Orefl__on,type,
    c_Relation_Orefl__on: $i > $i > $i > $o ).

thf(tp_c_Relation_Orel__comp,type,
    c_Relation_Orel__comp: $i > $i > $i > $i ).

thf(tp_c_Relation_Osingle__valued,type,
    c_Relation_Osingle__valued: $i > $i > $i > $o ).

thf(tp_c_Relation_Ototal__on,type,
    c_Relation_Ototal__on: $i > $i > $i > $o ).

thf(tp_c_Rings_Oinverse__class_Odivide,type,
    c_Rings_Oinverse__class_Odivide: $i > $i ).

thf(tp_c_SMT_Oz3div,type,
    c_SMT_Oz3div: $i > $i > $i ).

thf(tp_c_SMT_Oz3mod,type,
    c_SMT_Oz3mod: $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OatLeast,type,
    c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OatLeastAtMost,type,
    c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OatLeastLessThan,type,
    c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OatMost,type,
    c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OgreaterThan,type,
    c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OgreaterThanAtMost,type,
    c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OgreaterThanLessThan,type,
    c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord_OlessThan,type,
    c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord__class_OatLeast,type,
    c_SetInterval_Oord__class_OatLeast: $i > $i ).

thf(tp_c_SetInterval_Oord__class_OatLeastAtMost,type,
    c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord__class_OatLeastLessThan,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).

thf(tp_c_SetInterval_Oord__class_OatMost,type,
    c_SetInterval_Oord__class_OatMost: $i > $i ).

thf(tp_c_SetInterval_Oord__class_OgreaterThan,type,
    c_SetInterval_Oord__class_OgreaterThan: $i > $i ).

thf(tp_c_SetInterval_Oord__class_OgreaterThanAtMost,type,
    c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord__class_OgreaterThanLessThan,type,
    c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).

thf(tp_c_SetInterval_Oord__class_OlessThan,type,
    c_SetInterval_Oord__class_OlessThan: $i > $i ).

thf(tp_c_Set_OBall,type,
    c_Set_OBall: $i > $i ).

thf(tp_c_Set_OCollect,type,
    c_Set_OCollect: $i > $i ).

thf(tp_c_Set_OPow,type,
    c_Set_OPow: $i > $i ).

thf(tp_c_Set_Oimage,type,
    c_Set_Oimage: $i > $i > $i > $i ).

thf(tp_c_Set_Oinsert,type,
    c_Set_Oinsert: $i > $i ).

thf(tp_c_Set_Othe__elem,type,
    c_Set_Othe__elem: $i > $i > $i ).

thf(tp_c_Set_Ovimage,type,
    c_Set_Ovimage: $i > $i > $i > $i ).

thf(tp_c_Smallcheck_Ofull__small_H,type,
    c_Smallcheck_Ofull__small_H: $i > $i > $i > $i ).

thf(tp_c_Smallcheck_Ofull__small__class_Ofull__small,type,
    c_Smallcheck_Ofull__small__class_Ofull__small: $i > $i > $i > $i ).

thf(tp_c_Smallcheck_Oorelse,type,
    c_Smallcheck_Oorelse: $i > $i > $i > $i ).

thf(tp_c_Smallcheck_Osmall_H,type,
    c_Smallcheck_Osmall_H: $i > $i > $i > $i ).

thf(tp_c_Smallcheck_Osmall_H__rel,type,
    c_Smallcheck_Osmall_H__rel: $i ).

thf(tp_c_Smallcheck_Osmall__class_Osmall,type,
    c_Smallcheck_Osmall__class_Osmall: $i > $i ).

thf(tp_c_Sum__Type_OPlus,type,
    c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).

thf(tp_c_Sum__Type_Osum_Osum__case,type,
    c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Transitive__Closure_Ortrancl,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(tp_c_Transitive__Closure_Otrancl,type,
    c_Transitive__Closure_Otrancl: $i > $i > $i ).

thf(tp_c_Typedef_Otype__definition,type,
    c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).

thf(tp_c_Wellfounded_Oacc,type,
    c_Wellfounded_Oacc: $i > $i > $i ).

thf(tp_c_Wellfounded_Oaccp,type,
    c_Wellfounded_Oaccp: $i > $i > $i ).

thf(tp_c_Wellfounded_Oacyclic,type,
    c_Wellfounded_Oacyclic: $i > $i > $o ).

thf(tp_c_Wellfounded_Ofinite__psubset,type,
    c_Wellfounded_Ofinite__psubset: $i > $i ).

thf(tp_c_Wellfounded_Oless__than,type,
    c_Wellfounded_Oless__than: $i ).

thf(tp_c_Wellfounded_Olex__prod,type,
    c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).

thf(tp_c_Wellfounded_Omax__ext,type,
    c_Wellfounded_Omax__ext: $i > $i > $i ).

thf(tp_c_Wellfounded_Omax__extp,type,
    c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).

thf(tp_c_Wellfounded_Omeasure,type,
    c_Wellfounded_Omeasure: $i > $i ).

thf(tp_c_Wellfounded_Omin__ext,type,
    c_Wellfounded_Omin__ext: $i > $i > $i ).

thf(tp_c_Wellfounded_Omlex__prod,type,
    c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).

thf(tp_c_Wellfounded_Opred__nat,type,
    c_Wellfounded_Opred__nat: $i ).

thf(tp_c_Wellfounded_Owf,type,
    c_Wellfounded_Owf: $i > $i > $o ).

thf(tp_c_Wellfounded_OwfP,type,
    c_Wellfounded_OwfP: $i > $i > $o ).

thf(tp_c_fFalse,type,
    c_fFalse: $i ).

thf(tp_c_fNot,type,
    c_fNot: $i ).

thf(tp_c_fTrue,type,
    c_fTrue: $i ).

thf(tp_c_fconj,type,
    c_fconj: $i ).

thf(tp_c_fdisj,type,
    c_fdisj: $i ).

thf(tp_c_fequal,type,
    c_fequal: $i ).

thf(tp_c_fimplies,type,
    c_fimplies: $i ).

thf(tp_c_member,type,
    c_member: $i > $i ).

thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
    class_Complete__Lattice_Ocomplete__lattice: $i > $o ).

thf(tp_class_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

thf(tp_class_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $i > $o ).

thf(tp_class_Enum_Oenum,type,
    class_Enum_Oenum: $i > $o ).

thf(tp_class_Fields_Ofield,type,
    class_Fields_Ofield: $i > $o ).

thf(tp_class_Fields_Ofield__inverse__zero,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

thf(tp_class_Fields_Olinordered__field,type,
    class_Fields_Olinordered__field: $i > $o ).

thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

thf(tp_class_Finite__Set_Ofinite,type,
    class_Finite__Set_Ofinite: $i > $o ).

thf(tp_class_Groups_Oab__group__add,type,
    class_Groups_Oab__group__add: $i > $o ).

thf(tp_class_Groups_Oab__semigroup__add,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

thf(tp_class_Groups_Oab__semigroup__mult,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

thf(tp_class_Groups_Oabs__if,type,
    class_Groups_Oabs__if: $i > $o ).

thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

thf(tp_class_Groups_Ocancel__semigroup__add,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

thf(tp_class_Groups_Ocomm__monoid__add,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

thf(tp_class_Groups_Ocomm__monoid__mult,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

thf(tp_class_Groups_Ogroup__add,type,
    class_Groups_Ogroup__add: $i > $o ).

thf(tp_class_Groups_Olinordered__ab__group__add,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

thf(tp_class_Groups_Olinordered__ab__semigroup__add,type,
    class_Groups_Olinordered__ab__semigroup__add: $i > $o ).

thf(tp_class_Groups_Ominus,type,
    class_Groups_Ominus: $i > $o ).

thf(tp_class_Groups_Omonoid__add,type,
    class_Groups_Omonoid__add: $i > $o ).

thf(tp_class_Groups_Omonoid__mult,type,
    class_Groups_Omonoid__mult: $i > $o ).

thf(tp_class_Groups_Oone,type,
    class_Groups_Oone: $i > $o ).

thf(tp_class_Groups_Oordered__ab__group__add,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(tp_class_Groups_Oordered__comm__monoid__add,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

thf(tp_class_Groups_Osemigroup__add,type,
    class_Groups_Osemigroup__add: $i > $o ).

thf(tp_class_Groups_Osgn__if,type,
    class_Groups_Osgn__if: $i > $o ).

thf(tp_class_Groups_Ouminus,type,
    class_Groups_Ouminus: $i > $o ).

thf(tp_class_Groups_Ozero,type,
    class_Groups_Ozero: $i > $o ).

thf(tp_class_HOL_Oequal,type,
    class_HOL_Oequal: $i > $o ).

thf(tp_class_Int_Onumber,type,
    class_Int_Onumber: $i > $o ).

thf(tp_class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

thf(tp_class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $i > $o ).

thf(tp_class_Lattices_Oab__semigroup__idem__mult,type,
    class_Lattices_Oab__semigroup__idem__mult: $i > $o ).

thf(tp_class_Lattices_Oboolean__algebra,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

thf(tp_class_Lattices_Obounded__lattice,type,
    class_Lattices_Obounded__lattice: $i > $o ).

thf(tp_class_Lattices_Obounded__lattice__bot,type,
    class_Lattices_Obounded__lattice__bot: $i > $o ).

thf(tp_class_Lattices_Obounded__lattice__top,type,
    class_Lattices_Obounded__lattice__top: $i > $o ).

thf(tp_class_Lattices_Odistrib__lattice,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

thf(tp_class_Lattices_Olattice,type,
    class_Lattices_Olattice: $i > $o ).

thf(tp_class_Lattices_Osemilattice__inf,type,
    class_Lattices_Osemilattice__inf: $i > $o ).

thf(tp_class_Lattices_Osemilattice__sup,type,
    class_Lattices_Osemilattice__sup: $i > $o ).

thf(tp_class_Nat_Osemiring__char__0,type,
    class_Nat_Osemiring__char__0: $i > $o ).

thf(tp_class_Orderings_Obot,type,
    class_Orderings_Obot: $i > $o ).

thf(tp_class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

thf(tp_class_Orderings_Oord,type,
    class_Orderings_Oord: $i > $o ).

thf(tp_class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

thf(tp_class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

thf(tp_class_Orderings_Otop,type,
    class_Orderings_Otop: $i > $o ).

thf(tp_class_Orderings_Owellorder,type,
    class_Orderings_Owellorder: $i > $o ).

thf(tp_class_Power_Opower,type,
    class_Power_Opower: $i > $o ).

thf(tp_class_Rings_Ocomm__ring__1,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

thf(tp_class_Rings_Ocomm__semiring,type,
    class_Rings_Ocomm__semiring: $i > $o ).

thf(tp_class_Rings_Ocomm__semiring__1,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

thf(tp_class_Rings_Odivision__ring,type,
    class_Rings_Odivision__ring: $i > $o ).

thf(tp_class_Rings_Odivision__ring__inverse__zero,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

thf(tp_class_Rings_Oidom,type,
    class_Rings_Oidom: $i > $o ).

thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

thf(tp_class_Rings_Olinordered__idom,type,
    class_Rings_Olinordered__idom: $i > $o ).

thf(tp_class_Rings_Olinordered__ring,type,
    class_Rings_Olinordered__ring: $i > $o ).

thf(tp_class_Rings_Olinordered__ring__strict,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

thf(tp_class_Rings_Olinordered__semidom,type,
    class_Rings_Olinordered__semidom: $i > $o ).

thf(tp_class_Rings_Olinordered__semiring,type,
    class_Rings_Olinordered__semiring: $i > $o ).

thf(tp_class_Rings_Olinordered__semiring__1,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

thf(tp_class_Rings_Olinordered__semiring__strict,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

thf(tp_class_Rings_Omult__zero,type,
    class_Rings_Omult__zero: $i > $o ).

thf(tp_class_Rings_Ono__zero__divisors,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

thf(tp_class_Rings_Oordered__cancel__semiring,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

thf(tp_class_Rings_Oordered__comm__semiring,type,
    class_Rings_Oordered__comm__semiring: $i > $o ).

thf(tp_class_Rings_Oordered__ring,type,
    class_Rings_Oordered__ring: $i > $o ).

thf(tp_class_Rings_Oordered__ring__abs,type,
    class_Rings_Oordered__ring__abs: $i > $o ).

thf(tp_class_Rings_Oordered__semiring,type,
    class_Rings_Oordered__semiring: $i > $o ).

thf(tp_class_Rings_Oring,type,
    class_Rings_Oring: $i > $o ).

thf(tp_class_Rings_Oring__1,type,
    class_Rings_Oring__1: $i > $o ).

thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

thf(tp_class_Rings_Oring__no__zero__divisors,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

thf(tp_class_Rings_Osemiring,type,
    class_Rings_Osemiring: $i > $o ).

thf(tp_class_Rings_Osemiring__0,type,
    class_Rings_Osemiring__0: $i > $o ).

thf(tp_class_Rings_Osemiring__1,type,
    class_Rings_Osemiring__1: $i > $o ).

thf(tp_class_Rings_Ozero__neq__one,type,
    class_Rings_Ozero__neq__one: $i > $o ).

thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

thf(tp_class_Smallcheck_Osmall,type,
    class_Smallcheck_Osmall: $i > $o ).

thf(tp_hAPP,type,
    hAPP: $i > $i > $i ).

thf(tp_hBOOL,type,
    hBOOL: $i > $o ).

thf(tp_sK10_SY1406,type,
    sK10_SY1406: $i > $i > $i > $i ).

thf(tp_sK11_SY1219,type,
    sK11_SY1219: $i > $i > $i ).

thf(tp_sK12_SY1392,type,
    sK12_SY1392: $i > $i > $i > $i ).

thf(tp_sK13_SY1665,type,
    sK13_SY1665: $i > $i > $i > $i ).

thf(tp_sK14_SY1115,type,
    sK14_SY1115: $i > $i > $i > $i > $i ).

thf(tp_sK15_SY1224,type,
    sK15_SY1224: $i > $i > $i > $i > $i ).

thf(tp_sK16_SY1547,type,
    sK16_SY1547: $i > $i > $i > $i > $i ).

thf(tp_sK17_SY1286,type,
    sK17_SY1286: $i > $i > $i > $i ).

thf(tp_sK18_SY1584,type,
    sK18_SY1584: $i > $i > $i > $i > $i > $i ).

thf(tp_sK19_SY1503,type,
    sK19_SY1503: $i > $i > $i > $i > $i ).

thf(tp_sK1_SY817,type,
    sK1_SY817: $i > $i ).

thf(tp_sK20_SY1503,type,
    sK20_SY1503: $i > $i > $i > $i > $i ).

thf(tp_sK21_SY1507,type,
    sK21_SY1507: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK22_SY1662,type,
    sK22_SY1662: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK23_SY1478,type,
    sK23_SY1478: $i > $i > $i > $i > $i ).

thf(tp_sK24_SY1478,type,
    sK24_SY1478: $i > $i > $i > $i > $i ).

thf(tp_sK2_SY1178,type,
    sK2_SY1178: $i > $i > $i ).

thf(tp_sK3_SY1374,type,
    sK3_SY1374: $i > $i > $i > $i ).

thf(tp_sK4_SY1487,type,
    sK4_SY1487: $i > $i > $i > $i > $i ).

thf(tp_sK5_SY762,type,
    sK5_SY762: $i > $i > $i ).

thf(tp_sK6_SY1342,type,
    sK6_SY1342: $i > $i > $i > $i ).

thf(tp_sK7_SY1351,type,
    sK7_SY1351: $i > $i > $i > $i ).

thf(tp_sK8_SY1659,type,
    sK8_SY1659: $i > $i > $i ).

thf(tp_sK9_SY1403,type,
    sK9_SY1403: $i > $i > $i > $i ).

thf(tp_tc_Code__Evaluation_Oterm,type,
    tc_Code__Evaluation_Oterm: $i ).

thf(tp_tc_Code__Numeral_Ocode__numeral,type,
    tc_Code__Numeral_Ocode__numeral: $i ).

thf(tp_tc_Com_Ocom,type,
    tc_Com_Ocom: $i ).

thf(tp_tc_Com_Oloc,type,
    tc_Com_Oloc: $i ).

thf(tp_tc_Com_Opname,type,
    tc_Com_Opname: $i ).

thf(tp_tc_Com_Ostate,type,
    tc_Com_Ostate: $i ).

thf(tp_tc_Com_Ovname,type,
    tc_Com_Ovname: $i ).

thf(tp_tc_HOL_Obool,type,
    tc_HOL_Obool: $i ).

thf(tp_tc_Hoare__Mirabelle_Otriple,type,
    tc_Hoare__Mirabelle_Otriple: $i > $i ).

thf(tp_tc_Int_Oint,type,
    tc_Int_Oint: $i ).

thf(tp_tc_Lazy__Sequence_Olazy__sequence,type,
    tc_Lazy__Sequence_Olazy__sequence: $i > $i ).

thf(tp_tc_List_Olist,type,
    tc_List_Olist: $i > $i ).

thf(tp_tc_Nat_Onat,type,
    tc_Nat_Onat: $i ).

thf(tp_tc_Nitpick_Opair__box,type,
    tc_Nitpick_Opair__box: $i > $i > $i ).

thf(tp_tc_Option_Ooption,type,
    tc_Option_Ooption: $i > $i ).

thf(tp_tc_Product__Type_Ounit,type,
    tc_Product__Type_Ounit: $i ).

thf(tp_tc_fun,type,
    tc_fun: $i > $i > $i ).

thf(tp_tc_prod,type,
    tc_prod: $i > $i > $i ).

thf(tp_tc_sum,type,
    tc_sum: $i > $i > $i ).

thf(tp_v_Z,type,
    v_Z: $i ).

thf(tp_v_c,type,
    v_c: $i ).

thf(tp_v_s_H,type,
    v_s_H: $i ).

thf(1,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
      | ~ ( hBOOL @ V_P_2 )
      | ( hBOOL @ V_Q_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).

thf(2,axiom,
    ! [V_P_2: $i,V_Q_2: $i] :
      ( ~ ( hBOOL @ V_Q_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).

thf(3,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ( hBOOL @ V_P_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).

thf(4,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
      | ( hBOOL @ V_P_2 )
      | ( hBOOL @ V_Q_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).

thf(5,axiom,
    ! [V_P_2: $i,V_Q_2: $i] :
      ( ~ ( hBOOL @ V_Q_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).

thf(6,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ V_P_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).

thf(7,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
      | ( hBOOL @ V_Q_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).

thf(8,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
      | ( hBOOL @ V_P_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).

thf(9,axiom,
    ! [V_Q_2: $i,V_P_2: $i] :
      ( ~ ( hBOOL @ V_P_2 )
      | ~ ( hBOOL @ V_Q_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).

thf(10,axiom,
    ! [V_P_2: $i] :
      ( ~ ~ ( hBOOL @ V_P_2 )
      | ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).

thf(11,axiom,
    ! [V_P_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
      | ~ ( hBOOL @ V_P_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).

thf(12,axiom,
    hBOOL @ c_fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).

thf(13,axiom,
    ~ ( hBOOL @ c_fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).

thf(14,axiom,
    ! [V_y_2: $i,V_x_2: $i] :
      ( ( V_x_2 != V_y_2 )
      | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

thf(15,axiom,
    ! [V_y_2: $i,V_x_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
      | ( V_x_2 = V_y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

thf(16,axiom,
    ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
      = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).

thf(17,axiom,
    ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
      = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).

thf(18,axiom,
    ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
      = ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).

thf(19,axiom,
    ! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
      = V_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).

thf(20,axiom,
    ! [V_P: $i,T_a: $i] :
      ( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
      = V_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

thf(296,axiom,
    ! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
      ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).

thf(333,axiom,
    ! [V_r_2: $i,T_a: $i,T_b: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
      = V_r_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).

thf(451,axiom,
    ! [V_y_2: $i,V_x_2: $i] :
      ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
        = ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
    <=> ( V_x_2 = V_y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

thf(452,axiom,
    ! [V_l_2: $i,V_k_2: $i] :
      ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
        = ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
    <=> ( V_k_2 = V_l_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

thf(470,axiom,
    ! [V_m_2: $i,V_n_2: $i] :
      ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
        = ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
    <=> ( V_n_2 = V_m_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

thf(810,axiom,
    ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
        = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
    <=> ( V_xs_2 = V_ys_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

thf(811,axiom,
    ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
        = V_ys_2 )
    <=> ( V_xs_2
        = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).

thf(812,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
      = V_xs ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).

thf(1153,axiom,
    ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
        = V_zs )
     => ( ( V_ys
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
       => ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).

thf(1154,axiom,
    ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
    <=> ( V_ys_2 = V_zs_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).

thf(1155,axiom,
    ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
    <=> ( V_ys_2 = V_zs_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).

thf(1156,axiom,
    ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
    <=> ? [B_us: $i] :
          ( ( ( V_xs_2
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
            & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
              = V_ts_2 ) )
          | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
              = V_zs_2 )
            & ( V_ys_2
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

thf(1157,axiom,
    ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
      = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).

thf(1269,axiom,
    ! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
      ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
     => ( ( V_ca_2
          = ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
       => ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).

thf(1272,axiom,
    ! [T_a: $i,V_P_2: $i] :
      ( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
    <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).

thf(1273,axiom,
    ! [T_a: $i,V_P_2: $i] :
      ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
     => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).

thf(1274,axiom,
    ! [T_a: $i,B_P: $i] :
      ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
     => ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).

thf(1275,axiom,
    ! [T_a: $i,V_x_2: $i,V_P_2: $i] :
      ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
     => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).

thf(1346,axiom,
    ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
      ( ( V_i != V_i_H )
     => ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
        = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).

thf(1347,axiom,
    ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
      = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).

thf(1401,axiom,
    ! [V_x: $i,T_a: $i,V_xs: $i] :
      ( V_xs
     != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).

thf(1402,axiom,
    ! [V_xs: $i,V_x: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
     != V_xs ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).

thf(1403,axiom,
    ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
    <=> ( ( V_a_2 = V_a_H_2 )
        & ( V_list_2 = V_list_H_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).

thf(1548,axiom,
    ! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
    <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).

thf(1549,axiom,
    ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
     => ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).

thf(1590,axiom,
    ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
      ( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
    <=> ? [B_b: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).

thf(1600,axiom,
    ! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
       => ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).

thf(1604,axiom,
    ! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
    <=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).

thf(1605,axiom,
    ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
     => ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).

thf(1626,axiom,
    ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
      = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).

thf(1652,axiom,
    ! [V_x_1: $i,T_a: $i] :
      ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
      = V_x_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).

thf(1653,axiom,
    ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
      ( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
     => ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).

thf(1654,axiom,
    ! [V_x: $i,T_a: $i] :
      ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
      = V_x ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).

thf(1725,axiom,
    ! [V_P_2: $i,T_a: $i] :
      ( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
      = V_P_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).

thf(1750,axiom,
    ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
      ( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
     => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
        = ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

thf(1878,axiom,
    ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
      ( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
     => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
        = V_x_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).

thf(2139,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
      ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
     => ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
          = ( hAPP @ V_Rep_2 @ V_y_2 ) )
      <=> ( V_x_2 = V_y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).

thf(2140,axiom,
    ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
      ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
     => ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
        = V_x_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).

thf(2187,axiom,
    ! [V_y_2: $i,V_x_2: $i] :
      ( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
        = ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
    <=> ( V_x_2 = V_y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).

thf(2499,axiom,
    ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
      ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
       => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).

thf(2500,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
      ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
       => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).

thf(2501,axiom,
    ! [V_x_2: $i,V_R_2: $i,T_a: $i] :
      ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
     => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).

thf(2502,axiom,
    ! [V_R_2: $i,T_a: $i] :
      ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
    <=> ! [B_x: $i,B_y: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
        <=> ( ( hAPP @ V_R_2 @ B_x )
            = ( hAPP @ V_R_2 @ B_y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).

thf(2852,axiom,
    ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
    <=> ! [B_x: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).

thf(2853,axiom,
    ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
    <=> ! [B_x: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).

thf(2854,axiom,
    ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
       => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).

thf(2855,axiom,
    ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
     => ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
       => ( V_qr = V_qr_H ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).

thf(2898,axiom,
    ! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
      ( ( V_p_2 = V_q_2 )
     => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).

thf(2899,axiom,
    ! [T_b: $i,T_a: $i,V_P_2: $i] :
      ( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
    <=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).

thf(2900,axiom,
    ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
    <=> ( ( V_a_2 = V_a_H_2 )
        & ( V_b_2 = V_b_H_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).

thf(2901,axiom,
    ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
     => ~ ( ( V_a = V_a_H )
         => ( V_b != V_b_H ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).

thf(3785,axiom,
    ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
    <=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).

thf(4811,axiom,
    ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
      ( ( V_a_2 = V_b_2 )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
       => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).

thf(4812,axiom,
    ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
      ( ( V_x_2 = V_y_2 )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
      <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).

thf(4813,axiom,
    ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
      ( ( V_A_2 = V_B_2 )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
      <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).

thf(4816,axiom,
    ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
    <=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

thf(4822,axiom,
    ! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
      ( ( V_A_2 = V_B_2 )
     => ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
         => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
       => ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).

thf(4824,axiom,
    ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
      ( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
        = ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
     => ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
        = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).

thf(4829,axiom,
    ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
      ( ( V_s_2 = V_t_2 )
     => ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
        = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).

thf(4877,axiom,
    ! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
     => ! [B_v: $i] :
          ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
          = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).

thf(4878,axiom,
    ! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
     => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
        = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).

thf(4879,axiom,
    ! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
        = V_ca_2 )
     => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
        = ( hAPP @ V_ca_2 @ V_v_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

thf(4880,axiom,
    ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
      = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).

thf(4881,axiom,
    ! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
      = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).

thf(4905,axiom,
    ! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
      ( ( ( hAPP @ V_f_2 @ V_x_2 )
        = V_y_2 )
     => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
        = V_f_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

thf(4906,axiom,
    ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
      ( ( V_z_2 != V_x_2 )
     => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
        = ( hAPP @ V_f_2 @ V_z_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).

thf(4907,axiom,
    ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
      ( ( V_a_2 != V_ca_2 )
     => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

thf(4908,axiom,
    ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
      ( ( ( V_z_2 = V_x_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
          = V_y_2 ) )
      & ( ( V_z_2 != V_x_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
          = ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).

thf(4909,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
      = V_y_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).

thf(4910,axiom,
    ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

thf(4911,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
        = V_f_2 )
    <=> ( ( hAPP @ V_f_2 @ V_x_2 )
        = V_y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).

thf(4917,axiom,
    ! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
      ( ( ( V_x_2 = V_a_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
          = V_b_2 ) )
      & ( ( V_x_2 != V_a_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
          = ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).

thf(4918,axiom,
    ! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
      = V_f_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).

thf(4927,axiom,
    ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
      = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).

thf(4939,axiom,
    ! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
    <=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
        & ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_peek__and__def) ).

thf(4962,axiom,
    ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
    <=> ( ( V_y_2 = V_x_2 )
        | ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).

thf(4963,axiom,
    ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

thf(4964,axiom,
    ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).

thf(5028,axiom,
    ! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
    <=> ( ( V_fun1_2 = V_fun1_H_2 )
        & ( V_com_2 = V_com_H_2 )
        & ( V_fun2_2 = V_fun2_H_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).

thf(5040,axiom,
    ! [V_nat_H_2: $i,V_nat_2: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
        = ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
    <=> ( V_nat_2 = V_nat_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

thf(5041,axiom,
    ! [V_y: $i,V_x: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ V_x )
        = ( hAPP @ c_Nat_OSuc @ V_y ) )
     => ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

thf(5045,axiom,
    ! [V_n: $i] :
      ( ( hAPP @ c_Nat_OSuc @ V_n )
     != V_n ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(5046,axiom,
    ! [V_n: $i] :
      ( V_n
     != ( hAPP @ c_Nat_OSuc @ V_n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(5056,axiom,
    ! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
        = ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
    <=> ( V_a_2 = V_a_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Oinject) ).

thf(5080,axiom,
    ! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
       => ? [B_n: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
            & ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__max2) ).

thf(5085,axiom,
    ! [V_t: $i,V_s: $i,V_c: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
     => ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__evaln) ).

thf(5135,axiom,
    ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
     => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).

thf(5136,axiom,
    ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
    <=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).

thf(5142,axiom,
    ! [V_pname_H_2: $i,V_pname_2: $i] :
      ( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
        = ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
    <=> ( V_pname_2 = V_pname_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).

thf(5191,axiom,
    ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
     => ( ( ( V_t_2 = V_s_2 )
         => ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
       => ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
           => ! [B_s1: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
               => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).

thf(5192,axiom,
    ! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
     => ~ ! [B_s1: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
           => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).

thf(5208,axiom,
    ! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
    <=> ? [B_s1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).

thf(5209,axiom,
    ! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
    <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
        | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).

thf(5210,axiom,
    ! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
    <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
        | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
          & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).

thf(5211,axiom,
    ! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
    <=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
       => ? [B_s1: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
            & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).

thf(5212,axiom,
    ! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
    <=> ( ( ( V_a5_2 = V_a2_2 )
          & ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
        | ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
          & ? [B_s1: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).

thf(5213,axiom,
    ! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).

thf(5214,axiom,
    ! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
      ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
       => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).

thf(5215,axiom,
    ! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
     => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).

thf(5216,axiom,
    ! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
     => ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
       => ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
           => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).

thf(5217,axiom,
    ! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
      ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
       => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).

thf(5218,axiom,
    ! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
      ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
       => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).

thf(5219,axiom,
    ! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
       => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSemi) ).

thf(5220,axiom,
    ! [V_t: $i,V_s: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
     => ( V_t = V_s ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).

thf(5221,axiom,
    ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSkip) ).

thf(5224,axiom,
    ! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
     => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
       => ( V_u = V_t ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).

thf(5225,axiom,
    ! [V_g_2: $i,V_f_2: $i] :
      ( ! [B_x: $i] :
          ( ( hAPP @ V_f_2 @ B_x )
          = ( hAPP @ V_g_2 @ B_x ) )
     => ( V_f_2 = V_g_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

thf(5226,axiom,
    ! [B_Z_H: $i] :
      ( ! [B_s1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
         => ( B_Z_H = B_s1 ) )
     => ( B_Z_H = v_s_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(5228,conjecture,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(5229,negated_conjecture,
    ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5228]) ).

thf(5230,plain,
    ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5229]) ).

thf(5231,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
          | ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(5232,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i] :
          ( ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(5233,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(5234,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_P_2 )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(5235,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i] :
          ( ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(5236,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(5237,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(5238,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_P_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(5239,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ V_P_2 )
          | ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(5240,plain,
    ( ( ! [V_P_2: $i] :
          ( ~ ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(5241,plain,
    ( ( ! [V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
          | ~ ( hBOOL @ V_P_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(5242,plain,
    ( ( hBOOL @ c_fTrue )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(5243,plain,
    ( ( ~ ( hBOOL @ c_fFalse ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(5244,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( V_x_2 != V_y_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(5245,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
          | ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(5246,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(5247,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(5248,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(5249,plain,
    ( ( ! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
          = V_P ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(5250,plain,
    ( ( ! [V_P: $i,T_a: $i] :
          ( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
          = V_P ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(5251,plain,
    ( ( ! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
          ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[296]) ).

thf(5252,plain,
    ( ( ! [V_r_2: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
          = V_r_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[333]) ).

thf(5253,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
            = ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
        <=> ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[451]) ).

thf(5254,plain,
    ( ( ! [V_l_2: $i,V_k_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
            = ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
        <=> ( V_k_2 = V_l_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[452]) ).

thf(5255,plain,
    ( ( ! [V_m_2: $i,V_n_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
            = ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
        <=> ( V_n_2 = V_m_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[470]) ).

thf(5256,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
            = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
        <=> ( V_xs_2 = V_ys_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[810]) ).

thf(5257,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
            = V_ys_2 )
        <=> ( V_xs_2
            = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[811]) ).

thf(5258,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
          = V_xs ) )
    = $true ),
    inference(unfold_def,[status(thm)],[812]) ).

thf(5259,plain,
    ( ( ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
            = V_zs )
         => ( ( V_ys
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
           => ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1153]) ).

thf(5260,plain,
    ( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1154]) ).

thf(5261,plain,
    ( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1155]) ).

thf(5262,plain,
    ( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
        <=> ? [B_us: $i] :
              ( ( ( V_xs_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
                & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
                  = V_ts_2 ) )
              | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
                  = V_zs_2 )
                & ( V_ys_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1156]) ).

thf(5263,plain,
    ( ( ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1157]) ).

thf(5264,plain,
    ( ( ! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
          ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
         => ( ( V_ca_2
              = ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
           => ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1269]) ).

thf(5265,plain,
    ( ( ! [T_a: $i,V_P_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
        <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1272]) ).

thf(5266,plain,
    ( ( ! [T_a: $i,V_P_2: $i] :
          ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
         => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1273]) ).

thf(5267,plain,
    ( ( ! [T_a: $i,B_P: $i] :
          ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
         => ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1274]) ).

thf(5268,plain,
    ( ( ! [T_a: $i,V_x_2: $i,V_P_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
         => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1275]) ).

thf(5269,plain,
    ( ( ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
          ( ( V_i != V_i_H )
         => ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1346]) ).

thf(5270,plain,
    ( ( ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1347]) ).

thf(5271,plain,
    ( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
          ( V_xs
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1401]) ).

thf(5272,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
         != V_xs ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1402]) ).

thf(5273,plain,
    ( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
        <=> ( ( V_a_2 = V_a_H_2 )
            & ( V_list_2 = V_list_H_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1403]) ).

thf(5274,plain,
    ( ( ! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
        <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1548]) ).

thf(5275,plain,
    ( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1549]) ).

thf(5276,plain,
    ( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
        <=> ? [B_b: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1590]) ).

thf(5277,plain,
    ( ( ! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
           => ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1600]) ).

thf(5278,plain,
    ( ( ! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
        <=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1604]) ).

thf(5279,plain,
    ( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1605]) ).

thf(5280,plain,
    ( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
          = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1626]) ).

thf(5281,plain,
    ( ( ! [V_x_1: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
          = V_x_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1652]) ).

thf(5282,plain,
    ( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
          ( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
         => ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1653]) ).

thf(5283,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
          = V_x ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1654]) ).

thf(5284,plain,
    ( ( ! [V_P_2: $i,T_a: $i] :
          ( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
          = V_P_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1725]) ).

thf(5285,plain,
    ( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
            = ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1750]) ).

thf(5286,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
          ( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
            = V_x_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1878]) ).

thf(5287,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
         => ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
              = ( hAPP @ V_Rep_2 @ V_y_2 ) )
          <=> ( V_x_2 = V_y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2139]) ).

thf(5288,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
         => ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
            = V_x_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2140]) ).

thf(5289,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
            = ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
        <=> ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2187]) ).

thf(5290,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
           => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
             => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2499]) ).

thf(5291,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2500]) ).

thf(5292,plain,
    ( ( ! [V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2501]) ).

thf(5293,plain,
    ( ( ! [V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
        <=> ! [B_x: $i,B_y: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
            <=> ( ( hAPP @ V_R_2 @ B_x )
                = ( hAPP @ V_R_2 @ B_y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2502]) ).

thf(5294,plain,
    ( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
        <=> ! [B_x: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
             => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2852]) ).

thf(5295,plain,
    ( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
        <=> ! [B_x: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
             => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2853]) ).

thf(5296,plain,
    ( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
           => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2854]) ).

thf(5297,plain,
    ( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
         => ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
           => ( V_qr = V_qr_H ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2855]) ).

thf(5298,plain,
    ( ( ! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
          ( ( V_p_2 = V_q_2 )
         => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2898]) ).

thf(5299,plain,
    ( ( ! [T_b: $i,T_a: $i,V_P_2: $i] :
          ( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
        <=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2899]) ).

thf(5300,plain,
    ( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
        <=> ( ( V_a_2 = V_a_H_2 )
            & ( V_b_2 = V_b_H_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2900]) ).

thf(5301,plain,
    ( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
         => ~ ( ( V_a = V_a_H )
             => ( V_b != V_b_H ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2901]) ).

thf(5302,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
        <=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3785]) ).

thf(5303,plain,
    ( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
          ( ( V_a_2 = V_b_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4811]) ).

thf(5304,plain,
    ( ( ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
          ( ( V_x_2 = V_y_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4812]) ).

thf(5305,plain,
    ( ( ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
          ( ( V_A_2 = V_B_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4813]) ).

thf(5306,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
        <=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4816]) ).

thf(5307,plain,
    ( ( ! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
          ( ( V_A_2 = V_B_2 )
         => ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
             => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
           => ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4822]) ).

thf(5308,plain,
    ( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
          ( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
            = ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
            = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4824]) ).

thf(5309,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
          ( ( V_s_2 = V_t_2 )
         => ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
            = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4829]) ).

thf(5310,plain,
    ( ( ! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
         => ! [B_v: $i] :
              ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
              = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4877]) ).

thf(5311,plain,
    ( ( ! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4878]) ).

thf(5312,plain,
    ( ( ! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = V_ca_2 )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_ca_2 @ V_v_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4879]) ).

thf(5313,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
          = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4880]) ).

thf(5314,plain,
    ( ( ! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
          = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4881]) ).

thf(5315,plain,
    ( ( ! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
          ( ( ( hAPP @ V_f_2 @ V_x_2 )
            = V_y_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4905]) ).

thf(5316,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
          ( ( V_z_2 != V_x_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
            = ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4906]) ).

thf(5317,plain,
    ( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
          ( ( V_a_2 != V_ca_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4907]) ).

thf(5318,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
          ( ( ( V_z_2 = V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
              = V_y_2 ) )
          & ( ( V_z_2 != V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
              = ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4908]) ).

thf(5319,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
          = V_y_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4909]) ).

thf(5320,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4910]) ).

thf(5321,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 )
        <=> ( ( hAPP @ V_f_2 @ V_x_2 )
            = V_y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4911]) ).

thf(5322,plain,
    ( ( ! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
          ( ( ( V_x_2 = V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
              = V_b_2 ) )
          & ( ( V_x_2 != V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
              = ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4917]) ).

thf(5323,plain,
    ( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
          = V_f_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4918]) ).

thf(5324,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
          = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4927]) ).

thf(5325,plain,
    ( ( ! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
        <=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
            & ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4939]) ).

thf(5326,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
        <=> ( ( V_y_2 = V_x_2 )
            | ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4962]) ).

thf(5327,plain,
    ( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4963]) ).

thf(5328,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4964]) ).

thf(5329,plain,
    ( ( ! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
        <=> ( ( V_fun1_2 = V_fun1_H_2 )
            & ( V_com_2 = V_com_H_2 )
            & ( V_fun2_2 = V_fun2_H_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5028]) ).

thf(5330,plain,
    ( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
            = ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
        <=> ( V_nat_2 = V_nat_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5040]) ).

thf(5331,plain,
    ( ( ! [V_y: $i,V_x: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ V_x )
            = ( hAPP @ c_Nat_OSuc @ V_y ) )
         => ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5041]) ).

thf(5332,plain,
    ( ( ! [V_n: $i] :
          ( ( hAPP @ c_Nat_OSuc @ V_n )
         != V_n ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5045]) ).

thf(5333,plain,
    ( ( ! [V_n: $i] :
          ( V_n
         != ( hAPP @ c_Nat_OSuc @ V_n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5046]) ).

thf(5334,plain,
    ( ( ! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
            = ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
        <=> ( V_a_2 = V_a_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5056]) ).

thf(5335,plain,
    ( ( ! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
           => ? [B_n: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
                & ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5080]) ).

thf(5336,plain,
    ( ( ! [V_t: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
         => ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5085]) ).

thf(5337,plain,
    ( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5135]) ).

thf(5338,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
        <=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5136]) ).

thf(5339,plain,
    ( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
          ( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
            = ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
        <=> ( V_pname_2 = V_pname_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5142]) ).

thf(5340,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
         => ( ( ( V_t_2 = V_s_2 )
             => ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
           => ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
               => ! [B_s1: $i] :
                    ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
                   => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5191]) ).

thf(5341,plain,
    ( ( ! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
         => ~ ! [B_s1: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
               => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5192]) ).

thf(5342,plain,
    ( ( ! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
        <=> ? [B_s1: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5208]) ).

thf(5343,plain,
    ( ( ! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
        <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
            | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5209]) ).

thf(5344,plain,
    ( ( ! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
        <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
            | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5210]) ).

thf(5345,plain,
    ( ( ! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
        <=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
           => ? [B_s1: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
                & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5211]) ).

thf(5346,plain,
    ( ( ! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
        <=> ( ( ( V_a5_2 = V_a2_2 )
              & ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
            | ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ? [B_s1: $i] :
                  ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
                  & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5212]) ).

thf(5347,plain,
    ( ( ! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5213]) ).

thf(5348,plain,
    ( ( ! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
           => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
             => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5214]) ).

thf(5349,plain,
    ( ( ! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5215]) ).

thf(5350,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
         => ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
             => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
           => ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
               => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5216]) ).

thf(5351,plain,
    ( ( ! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5217]) ).

thf(5352,plain,
    ( ( ! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5218]) ).

thf(5353,plain,
    ( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5219]) ).

thf(5354,plain,
    ( ( ! [V_t: $i,V_s: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
         => ( V_t = V_s ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5220]) ).

thf(5355,plain,
    ( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5221]) ).

thf(5356,plain,
    ( ( ! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
           => ( V_u = V_t ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5224]) ).

thf(5357,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i] :
          ( ! [B_x: $i] :
              ( ( hAPP @ V_f_2 @ B_x )
              = ( hAPP @ V_g_2 @ B_x ) )
         => ( V_f_2 = V_g_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5225]) ).

thf(5358,plain,
    ( ( ! [B_Z_H: $i] :
          ( ! [B_s1: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
             => ( B_Z_H = B_s1 ) )
         => ( B_Z_H = v_s_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5226]) ).

thf(5359,plain,
    ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5230]) ).

thf(5360,plain,
    ( ( ! [B_Z_H: $i] :
          ( ! [B_s1: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
             => ( B_Z_H = B_s1 ) )
         => ( B_Z_H = v_s_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[5358]) ).

thf(5361,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i] :
          ( ! [B_x: $i] :
              ( ( hAPP @ V_f_2 @ B_x )
              = ( hAPP @ V_g_2 @ B_x ) )
         => ( V_f_2 = V_g_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5357]) ).

thf(5362,plain,
    ( ( ! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
           => ( V_u = V_t ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5356]) ).

thf(5363,plain,
    ( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
    = $true ),
    inference(copy,[status(thm)],[5355]) ).

thf(5364,plain,
    ( ( ! [V_t: $i,V_s: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
         => ( V_t = V_s ) ) )
    = $true ),
    inference(copy,[status(thm)],[5354]) ).

thf(5365,plain,
    ( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5353]) ).

thf(5366,plain,
    ( ( ! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5352]) ).

thf(5367,plain,
    ( ( ! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5351]) ).

thf(5368,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
         => ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
             => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
           => ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
               => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5350]) ).

thf(5369,plain,
    ( ( ! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5349]) ).

thf(5370,plain,
    ( ( ! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
           => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
             => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5348]) ).

thf(5371,plain,
    ( ( ! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[5347]) ).

thf(5372,plain,
    ( ( ! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
        <=> ( ( ( V_a5_2 = V_a2_2 )
              & ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
            | ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ? [B_s1: $i] :
                  ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
                  & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5346]) ).

thf(5373,plain,
    ( ( ! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
        <=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
           => ? [B_s1: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
                & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5345]) ).

thf(5374,plain,
    ( ( ! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
        <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
            | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5344]) ).

thf(5375,plain,
    ( ( ! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
        <=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
            | ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5343]) ).

thf(5376,plain,
    ( ( ! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
        <=> ? [B_s1: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5342]) ).

thf(5377,plain,
    ( ( ! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
         => ~ ! [B_s1: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
               => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5341]) ).

thf(5378,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
         => ( ( ( V_t_2 = V_s_2 )
             => ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
           => ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
               => ! [B_s1: $i] :
                    ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
                   => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5340]) ).

thf(5379,plain,
    ( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
          ( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
            = ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
        <=> ( V_pname_2 = V_pname_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5339]) ).

thf(5380,plain,
    ( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
        <=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5338]) ).

thf(5381,plain,
    ( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5337]) ).

thf(5382,plain,
    ( ( ! [V_t: $i,V_s: $i,V_c: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
         => ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5336]) ).

thf(5383,plain,
    ( ( ! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
           => ? [B_n: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
                & ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5335]) ).

thf(5384,plain,
    ( ( ! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
            = ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
        <=> ( V_a_2 = V_a_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5334]) ).

thf(5385,plain,
    ( ( ! [V_n: $i] :
          ( V_n
         != ( hAPP @ c_Nat_OSuc @ V_n ) ) )
    = $true ),
    inference(copy,[status(thm)],[5333]) ).

thf(5386,plain,
    ( ( ! [V_n: $i] :
          ( ( hAPP @ c_Nat_OSuc @ V_n )
         != V_n ) )
    = $true ),
    inference(copy,[status(thm)],[5332]) ).

thf(5387,plain,
    ( ( ! [V_y: $i,V_x: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ V_x )
            = ( hAPP @ c_Nat_OSuc @ V_y ) )
         => ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5331]) ).

thf(5388,plain,
    ( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
            = ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
        <=> ( V_nat_2 = V_nat_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5330]) ).

thf(5389,plain,
    ( ( ! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
        <=> ( ( V_fun1_2 = V_fun1_H_2 )
            & ( V_com_2 = V_com_H_2 )
            & ( V_fun2_2 = V_fun2_H_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5329]) ).

thf(5390,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5328]) ).

thf(5391,plain,
    ( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5327]) ).

thf(5392,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
        <=> ( ( V_y_2 = V_x_2 )
            | ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5326]) ).

thf(5393,plain,
    ( ( ! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
        <=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
            & ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5325]) ).

thf(5394,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
          = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5324]) ).

thf(5395,plain,
    ( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
          = V_f_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5323]) ).

thf(5396,plain,
    ( ( ! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
          ( ( ( V_x_2 = V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
              = V_b_2 ) )
          & ( ( V_x_2 != V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
              = ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5322]) ).

thf(5397,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 )
        <=> ( ( hAPP @ V_f_2 @ V_x_2 )
            = V_y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5321]) ).

thf(5398,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5320]) ).

thf(5399,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
          = V_y_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5319]) ).

thf(5400,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
          ( ( ( V_z_2 = V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
              = V_y_2 ) )
          & ( ( V_z_2 != V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
              = ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5318]) ).

thf(5401,plain,
    ( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
          ( ( V_a_2 != V_ca_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5317]) ).

thf(5402,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
          ( ( V_z_2 != V_x_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
            = ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5316]) ).

thf(5403,plain,
    ( ( ! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
          ( ( ( hAPP @ V_f_2 @ V_x_2 )
            = V_y_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5315]) ).

thf(5404,plain,
    ( ( ! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
          = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5314]) ).

thf(5405,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
          = ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5313]) ).

thf(5406,plain,
    ( ( ! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = V_ca_2 )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_ca_2 @ V_v_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5312]) ).

thf(5407,plain,
    ( ( ! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5311]) ).

thf(5408,plain,
    ( ( ! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
         => ! [B_v: $i] :
              ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
              = ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5310]) ).

thf(5409,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
          ( ( V_s_2 = V_t_2 )
         => ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
            = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5309]) ).

thf(5410,plain,
    ( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
          ( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
            = ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
            = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5308]) ).

thf(5411,plain,
    ( ( ! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
          ( ( V_A_2 = V_B_2 )
         => ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
             => ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
           => ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5307]) ).

thf(5412,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
        <=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5306]) ).

thf(5413,plain,
    ( ( ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
          ( ( V_A_2 = V_B_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5305]) ).

thf(5414,plain,
    ( ( ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
          ( ( V_x_2 = V_y_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
          <=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5304]) ).

thf(5415,plain,
    ( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
          ( ( V_a_2 = V_b_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5303]) ).

thf(5416,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
        <=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5302]) ).

thf(5417,plain,
    ( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
         => ~ ( ( V_a = V_a_H )
             => ( V_b != V_b_H ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5301]) ).

thf(5418,plain,
    ( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
        <=> ( ( V_a_2 = V_a_H_2 )
            & ( V_b_2 = V_b_H_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5300]) ).

thf(5419,plain,
    ( ( ! [T_b: $i,T_a: $i,V_P_2: $i] :
          ( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
        <=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5299]) ).

thf(5420,plain,
    ( ( ! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
          ( ( V_p_2 = V_q_2 )
         => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5298]) ).

thf(5421,plain,
    ( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
         => ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
           => ( V_qr = V_qr_H ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5297]) ).

thf(5422,plain,
    ( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
           => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5296]) ).

thf(5423,plain,
    ( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
        <=> ! [B_x: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
             => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5295]) ).

thf(5424,plain,
    ( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
        <=> ! [B_x: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
             => ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5294]) ).

thf(5425,plain,
    ( ( ! [V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
        <=> ! [B_x: $i,B_y: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
            <=> ( ( hAPP @ V_R_2 @ B_x )
                = ( hAPP @ V_R_2 @ B_y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5293]) ).

thf(5426,plain,
    ( ( ! [V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5292]) ).

thf(5427,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5291]) ).

thf(5428,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
           => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
             => ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5290]) ).

thf(5429,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
            = ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
        <=> ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5289]) ).

thf(5430,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
         => ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
            = V_x_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5288]) ).

thf(5431,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
         => ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
              = ( hAPP @ V_Rep_2 @ V_y_2 ) )
          <=> ( V_x_2 = V_y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5287]) ).

thf(5432,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
          ( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
            = V_x_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5286]) ).

thf(5433,plain,
    ( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
          ( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
            = ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5285]) ).

thf(5434,plain,
    ( ( ! [V_P_2: $i,T_a: $i] :
          ( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
          = V_P_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5284]) ).

thf(5435,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
          = V_x ) )
    = $true ),
    inference(copy,[status(thm)],[5283]) ).

thf(5436,plain,
    ( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
          ( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
         => ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5282]) ).

thf(5437,plain,
    ( ( ! [V_x_1: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
          = V_x_1 ) )
    = $true ),
    inference(copy,[status(thm)],[5281]) ).

thf(5438,plain,
    ( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
          = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5280]) ).

thf(5439,plain,
    ( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5279]) ).

thf(5440,plain,
    ( ( ! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
        <=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5278]) ).

thf(5441,plain,
    ( ( ! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
           => ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5277]) ).

thf(5442,plain,
    ( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
        <=> ? [B_b: $i] :
              ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
              & ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5276]) ).

thf(5443,plain,
    ( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
         => ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5275]) ).

thf(5444,plain,
    ( ( ! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
          ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
        <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5274]) ).

thf(5445,plain,
    ( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
        <=> ( ( V_a_2 = V_a_H_2 )
            & ( V_list_2 = V_list_H_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5273]) ).

thf(5446,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
         != V_xs ) )
    = $true ),
    inference(copy,[status(thm)],[5272]) ).

thf(5447,plain,
    ( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
          ( V_xs
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ) )
    = $true ),
    inference(copy,[status(thm)],[5271]) ).

thf(5448,plain,
    ( ( ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5270]) ).

thf(5449,plain,
    ( ( ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
          ( ( V_i != V_i_H )
         => ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5269]) ).

thf(5450,plain,
    ( ( ! [T_a: $i,V_x_2: $i,V_P_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
         => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5268]) ).

thf(5451,plain,
    ( ( ! [T_a: $i,B_P: $i] :
          ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
         => ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5267]) ).

thf(5452,plain,
    ( ( ! [T_a: $i,V_P_2: $i] :
          ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
         => ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5266]) ).

thf(5453,plain,
    ( ( ! [T_a: $i,V_P_2: $i] :
          ( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
        <=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5265]) ).

thf(5454,plain,
    ( ( ! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
          ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
         => ( ( V_ca_2
              = ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
           => ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5264]) ).

thf(5455,plain,
    ( ( ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5263]) ).

thf(5456,plain,
    ( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
        <=> ? [B_us: $i] :
              ( ( ( V_xs_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
                & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
                  = V_ts_2 ) )
              | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
                  = V_zs_2 )
                & ( V_ys_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5262]) ).

thf(5457,plain,
    ( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5261]) ).

thf(5458,plain,
    ( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5260]) ).

thf(5459,plain,
    ( ( ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
            = V_zs )
         => ( ( V_ys
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
           => ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5259]) ).

thf(5460,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
          = V_xs ) )
    = $true ),
    inference(copy,[status(thm)],[5258]) ).

thf(5461,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
            = V_ys_2 )
        <=> ( V_xs_2
            = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5257]) ).

thf(5462,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
            = ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
        <=> ( V_xs_2 = V_ys_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5256]) ).

thf(5463,plain,
    ( ( ! [V_m_2: $i,V_n_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
            = ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
        <=> ( V_n_2 = V_m_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5255]) ).

thf(5464,plain,
    ( ( ! [V_l_2: $i,V_k_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
            = ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
        <=> ( V_k_2 = V_l_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5254]) ).

thf(5465,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
            = ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
        <=> ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5253]) ).

thf(5466,plain,
    ( ( ! [V_r_2: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
          = V_r_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5252]) ).

thf(5467,plain,
    ( ( ! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
          ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5251]) ).

thf(5468,plain,
    ( ( ! [V_P: $i,T_a: $i] :
          ( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
          = V_P ) )
    = $true ),
    inference(copy,[status(thm)],[5250]) ).

thf(5469,plain,
    ( ( ! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
          ( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
          = V_P ) )
    = $true ),
    inference(copy,[status(thm)],[5249]) ).

thf(5470,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5248]) ).

thf(5471,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5247]) ).

thf(5472,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
          = ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5246]) ).

thf(5473,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
          | ( V_x_2 = V_y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5245]) ).

thf(5474,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i] :
          ( ( V_x_2 != V_y_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5244]) ).

thf(5475,plain,
    ( ( ~ ( hBOOL @ c_fFalse ) )
    = $true ),
    inference(copy,[status(thm)],[5243]) ).

thf(5476,plain,
    ( ( hBOOL @ c_fTrue )
    = $true ),
    inference(copy,[status(thm)],[5242]) ).

thf(5477,plain,
    ( ( ! [V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
          | ~ ( hBOOL @ V_P_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5241]) ).

thf(5478,plain,
    ( ( ! [V_P_2: $i] :
          ( ~ ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5240]) ).

thf(5479,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ V_P_2 )
          | ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5239]) ).

thf(5480,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_P_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5238]) ).

thf(5481,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5237]) ).

thf(5482,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5236]) ).

thf(5483,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i] :
          ( ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5235]) ).

thf(5484,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
          | ( hBOOL @ V_P_2 )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5234]) ).

thf(5485,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ( hBOOL @ V_P_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5233]) ).

thf(5486,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i] :
          ( ~ ( hBOOL @ V_Q_2 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5232]) ).

thf(5487,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
          | ~ ( hBOOL @ V_P_2 )
          | ( hBOOL @ V_Q_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5231]) ).

thf(5488,plain,
    ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[5359]) ).

thf(5489,plain,
    ( ( ! [SX0: $i] :
          ( SX0
         != ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5385]) ).

thf(5490,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
                    | ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
                      | ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5393]) ).

thf(5491,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX4 ) @ SX3 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX4 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5365]) ).

thf(5492,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX0 ) @ SX0 ) )
                | ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
                | ~ ! [SX3: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX0 ) @ SX3 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
                    | ~ ! [SX3: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX0 ) @ SX3 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5373]) ).

thf(5493,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ( SX5 != SX4 )
          | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SX3 @ SX2 @ SX1 ) @ SX0 ) @ SX5 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SX3 @ SX2 @ SX1 ) @ SX0 ) @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5420]) ).

thf(5494,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ! [SX3: $i] :
                  ~ ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
          | ( SX1
           != ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) )
          | ( hBOOL @ ( hAPP @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5454]) ).

thf(5495,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX5 ) @ SX4 ) @ SX3 )
                 != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX2 ) @ SX1 ) @ SX0 ) )
                | ~ ( ~ ~ ( ( SX5 != SX2 )
                          | ( SX4 != SX1 ) )
                    | ( SX3 != SX0 ) ) )
            | ~ ( ~ ~ ( ~ ~ ( ( SX5 != SX2 )
                            | ( SX4 != SX1 ) )
                      | ( SX3 != SX0 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX5 ) @ SX4 ) @ SX3 )
                  = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5389]) ).

thf(5496,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( ( SX5 != SX4 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ SX2 ) @ SX5 ) @ SX1 ) ) @ SX4 ) @ SX0 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SX3 @ SX2 ) @ SX4 ) @ SX0 ) ) @ SX5 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5449]) ).

thf(5497,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ~ ( ~ ( ( SX5 != SX4 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 ) @ SX1 ) @ SX4 ) @ SX0 ) @ SX5 )
                  = SX0 ) )
            | ~ ( ~ ( ( SX5 != SX4 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 ) @ SX1 ) @ SX4 ) @ SX0 ) @ SX5 )
                  = ( hAPP @ SX1 @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5400]) ).

thf(5498,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 != SX0 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5474]) ).

thf(5499,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
                | ~ ( ( SX0 != SX1 )
                    | ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
                    | ~ ~ ! [SX4: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) )
            | ~ ( ~ ( ~ ( ( SX0 != SX1 )
                        | ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
                    | ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
                        | ~ ~ ! [SX4: $i] :
                                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
                                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5372]) ).

thf(5500,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ SX1 )
           != ( hAPP @ c_Nat_OSuc @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5387]) ).

thf(5501,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
          ( ( ( hAPP @ SX10 @ ( hAPP @ SX9 @ SX8 ) )
           != ( hAPP @ SX7 @ ( hAPP @ SX6 @ SX5 ) ) )
          | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX4 @ SX3 @ SX2 @ SX10 ) @ SX9 ) @ SX8 )
            = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SX1 @ SX3 @ SX0 @ SX7 ) @ SX6 ) @ SX5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5410]) ).

thf(5502,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
          | ~ ! [SX4: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5377]) ).

thf(5503,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
                 != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) )
                | ~ ( ( SX3 != SX1 )
                    | ( SX2 != SX0 ) ) )
            | ~ ( ~ ~ ( ( SX3 != SX1 )
                      | ( SX2 != SX0 ) )
                | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
                  = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5418]) ).

thf(5504,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ SX6 @ SX5 @ SX4 @ SX3 ) @ SX2 )
           != SX1 )
          | ( ( hAPP @ SX3 @ ( hAPP @ SX2 @ SX0 ) )
            = ( hAPP @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5406]) ).

thf(5505,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX0 ) @ SX1 ) )
                | ( SX2 = SX0 ) )
            | ~ ( ( SX2 != SX0 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5458]) ).

thf(5506,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX2 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX0 ) )
                | ~ ! [SX5: $i] :
                      ~ ( ~ ( ( SX3
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX5 ) )
                            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX2 )
                             != SX0 ) )
                        | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX5 )
                             != SX1 )
                            | ( SX2
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX0 ) ) ) ) )
            | ~ ( ~ ~ ! [SX5: $i] :
                        ~ ( ~ ( ( SX3
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX5 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX2 )
                               != SX0 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX5 )
                               != SX1 )
                              | ( SX2
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX5 ) @ SX0 ) ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX3 ) @ SX2 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5456]) ).

thf(5507,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( SX3 != SX2 )
          | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5411]) ).

thf(5508,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
          | ( hBOOL @ ( hAPP @ SX2 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5450]) ).

thf(5509,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5465]) ).

thf(5510,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ( SX6 != SX5 )
          | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 )
            = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5409]) ).

thf(5511,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( ( SX6 != SX5 ) )
          | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ SX2 ) @ SX6 ) @ SX1 ) ) @ SX5 ) @ SX0 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ SX2 ) @ SX5 ) @ SX0 ) ) @ SX6 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5401]) ).

thf(5512,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
                | ( SX2 = SX0 )
                | ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
            | ~ ( ~ ( ( SX2 = SX0 )
                    | ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5392]) ).

thf(5513,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX0 ) ) @ SX1 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5369]) ).

thf(5514,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
         != SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5446]) ).

thf(5515,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX4 @ SX2 ) ) @ SX1 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX4 @ SX2 ) ) @ SX3 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5370]) ).

thf(5516,plain,
    ( ( ! [SX0: $i] :
          ( ( hAPP @ c_Nat_OSuc @ SX0 )
         != SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5386]) ).

thf(5517,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
          | ~ ( ( SX0 != SX1 )
              | ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
              | ! [SX4: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5378]) ).

thf(5518,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
                | ! [SX3: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
                    | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
            | ~ ( ~ ! [SX3: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5424]) ).

thf(5519,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( c_Predicate_Oreflp @ SX2 @ SX1 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5436]) ).

thf(5520,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
                | ~ ! [SX7: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) ) )
            | ~ ( ~ ~ ! [SX7: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) )
                | ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5442]) ).

thf(5521,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5422]) ).

thf(5522,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SX1 )
                 != ( hAPP @ c_Nat_OSuc @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Nat_OSuc @ SX1 )
                  = ( hAPP @ c_Nat_OSuc @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5388]) ).

thf(5523,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
                | ! [SX3: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
                    | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
            | ~ ( ~ ! [SX3: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5423]) ).

thf(5524,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ( ( hAPP @ SX4 @ SX3 )
           != SX2 )
          | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX1 @ SX0 ) @ SX4 ) @ SX3 ) @ SX2 )
            = SX4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5403]) ).

thf(5525,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( ( SX5 != SX4 ) )
          | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 ) @ SX1 ) @ SX4 ) @ SX0 ) @ SX5 )
            = ( hAPP @ SX1 @ SX5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5402]) ).

thf(5526,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( SX3 != SX2 )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5413]) ).

thf(5527,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
                 != SX0 )
                | ( SX1
                  = ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) ) )
            | ~ ( ( SX1
                 != ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) )
                | ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
                  = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5461]) ).

thf(5528,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 )
                | ! [SX2: $i,SX3: $i] :
                    ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
                          | ( ( hAPP @ SX0 @ SX2 )
                            = ( hAPP @ SX0 @ SX3 ) ) )
                      | ~ ( ( ( hAPP @ SX0 @ SX2 )
                           != ( hAPP @ SX0 @ SX3 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
            | ~ ( ~ ! [SX2: $i,SX3: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
                            | ( ( hAPP @ SX0 @ SX2 )
                              = ( hAPP @ SX0 @ SX3 ) ) )
                        | ~ ( ( ( hAPP @ SX0 @ SX2 )
                             != ( hAPP @ SX0 @ SX3 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) )
                | ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5425]) ).

thf(5529,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
                | ~ ! [SX4: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) ) )
            | ~ ( ~ ~ ! [SX4: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) )
                | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5440]) ).

thf(5530,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SX2 ) @ SX1 )
                 != ( hAPP @ ( c_Option_Ooption_OSome @ SX2 ) @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ ( c_Option_Ooption_OSome @ SX2 ) @ SX1 )
                  = ( hAPP @ ( c_Option_Ooption_OSome @ SX2 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5384]) ).

thf(5531,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( c_Typedef_Otype__definition @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 )
          | ~ ( ~ ( ( ( hAPP @ SX4 @ SX1 )
                   != ( hAPP @ SX4 @ SX0 ) )
                  | ( SX1 = SX0 ) )
              | ~ ( ( SX1 != SX0 )
                  | ( ( hAPP @ SX4 @ SX1 )
                    = ( hAPP @ SX4 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5431]) ).

thf(5532,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( c_Finite__Set_Ofolding__one__idem @ SX3 @ SX2 @ SX1 )
          | ( ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX0 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5432]) ).

thf(5533,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ SX7 @ SX6 @ SX5 @ SX4 ) @ SX3 )
           != ( hAPP @ ( c_Fun_Ocomp @ SX2 @ SX6 @ SX5 @ SX1 ) @ SX0 ) )
          | ! [SX8: $i] :
              ( ( hAPP @ SX4 @ ( hAPP @ SX3 @ SX8 ) )
              = ( hAPP @ SX1 @ ( hAPP @ SX0 @ SX8 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5408]) ).

thf(5534,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
            | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
                    | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5375]) ).

thf(5535,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( c_Equiv__Relations_Oequivp @ SX2 @ SX1 )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5426]) ).

thf(5536,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) )
                | ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5412]) ).

thf(5537,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) )
          | ~ ! [SX3: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5382]) ).

thf(5538,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX1 @ SX0 @ SX4 ) @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5443]) ).

thf(5539,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( c_Typedef_Otype__definition @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
          | ( ( hAPP @ SX2 @ ( hAPP @ SX3 @ SX0 ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5430]) ).

thf(5540,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SX4 @ SX3 @ SX2 )
          | ( ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
            = ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5433]) ).

thf(5541,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX4 ) @ SX3 )
           != SX2 )
          | ( SX1
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX3 ) @ SX0 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX4 ) @ SX1 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX5 ) @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5459]) ).

thf(5542,plain,
    ( ( ! [SX0: $i] :
          ( ~ ! [SX1: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ( SX0 = v_s_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5360]) ).

thf(5543,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX7 @ SX6 ) @ SX5 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX5 ) @ SX3 ) )
          | ( c_Predicate_Opred__comp @ SX2 @ SX1 @ SX0 @ SX7 @ SX4 @ SX6 @ SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5441]) ).

thf(5544,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX0 @ SX2 ) ) @ SX3 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5366]) ).

thf(5545,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) )
                | ~ ! [SX3: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) ) )
            | ~ ( ~ ~ ! [SX3: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5380]) ).

thf(5546,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ~ ( ~ ( ( SX5 != SX4 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 ) @ SX1 ) @ SX4 ) @ SX0 ) @ SX5 )
                  = SX0 ) )
            | ~ ( ~ ( ( SX5 != SX4 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 ) @ SX1 ) @ SX4 ) @ SX0 ) @ SX5 )
                  = ( hAPP @ SX1 @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5396]) ).

thf(5547,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 )
                 != SX2 )
                | ( ( hAPP @ SX2 @ SX1 )
                  = SX0 ) )
            | ~ ( ( ( hAPP @ SX2 @ SX1 )
                 != SX0 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SX4 @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 )
                  = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5397]) ).

thf(5548,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( SX3 != SX2 )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5414]) ).

thf(5549,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX1 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SX3 ) @ SX2 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5457]) ).

thf(5550,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( SX3 != SX2 )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5415]) ).

thf(5551,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ( hAPP @ SX1 @ SX2 )
                = ( hAPP @ SX0 @ SX2 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5361]) ).

thf(5552,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5381]) ).

thf(5553,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
                | ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) )
            | ~ ( ~ ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) )
                | ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5419]) ).

thf(5554,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5421]) ).

thf(5555,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5364]) ).

thf(5556,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX2 @ SX0 ) ) @ SX3 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5367]) ).

thf(5557,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ! [SX2: $i] :
                  ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
          | ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5452]) ).

thf(5558,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
                | ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5416]) ).

thf(5559,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
            | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
                    | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5374]) ).

thf(5560,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SX1 )
                 != ( hAPP @ c_Com_Ocom_OBODY @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Com_Ocom_OBODY @ SX1 )
                  = ( hAPP @ c_Com_Ocom_OBODY @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5379]) ).

thf(5561,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX3 ) @ SX2 )
           != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX5 @ SX4 ) @ SX1 ) @ SX0 ) )
          | ~ ( ( SX3 != SX1 )
              | ( SX2 != SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5417]) ).

thf(5562,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( c_Equiv__Relations_Oequivp @ SX4 @ SX3 )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5428]) ).

thf(5563,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX1 @ SX0 @ SX4 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5439]) ).

thf(5564,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ! [SX2: $i] :
                  ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
          | ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5451]) ).

thf(5565,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX3 ) @ SX2 )
                 != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX1 ) @ SX0 ) )
                | ~ ( ( SX3 != SX1 )
                    | ( SX2 != SX0 ) ) )
            | ~ ( ~ ~ ( ( SX3 != SX1 )
                      | ( SX2 != SX0 ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX3 ) @ SX2 )
                  = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX4 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5445]) ).

thf(5566,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5362]) ).

thf(5567,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( SX2
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5447]) ).

thf(5568,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( c_Equiv__Relations_Oequivp @ SX3 @ SX2 )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5427]) ).

thf(5569,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SX1 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5464]) ).

thf(5570,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) )
                | ~ ! [SX2: $i] :
                      ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
            | ~ ( ~ ~ ! [SX2: $i] :
                        ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
                | ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5453]) ).

thf(5571,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SX1 )
                 != ( hAPP @ c_Code__Numeral_Oof__nat @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SX1 )
                  = ( hAPP @ c_Code__Numeral_Oof__nat @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5463]) ).

thf(5572,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
                 != ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ ( c_List_Orev @ SX2 ) @ SX1 )
                  = ( hAPP @ ( c_List_Orev @ SX2 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5462]) ).

thf(5573,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
                | ~ ! [SX4: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) )
            | ~ ( ~ ~ ! [SX4: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) )
                | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5444]) ).

thf(5574,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
                | ~ ! [SX4: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) ) )
            | ~ ( ~ ~ ! [SX4: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5376]) ).

thf(5575,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SX1 )
                 != ( hAPP @ c_Int_ORep__Integ @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ c_Int_ORep__Integ @ SX1 )
                  = ( hAPP @ c_Int_ORep__Integ @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5429]) ).

thf(5576,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5368]) ).

thf(5577,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ SX8 @ SX7 @ SX6 @ SX5 ) @ SX4 )
           != ( hAPP @ ( c_Fun_Ocomp @ SX3 @ SX7 @ SX6 @ SX2 ) @ SX1 ) )
          | ( ( hAPP @ SX5 @ ( hAPP @ SX4 @ SX0 ) )
            = ( hAPP @ SX2 @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5407]) ).

thf(5578,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX7 ) @ SX6 ) @ SX5 ) @ SX4 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
          | ~ ! [SX8: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX7 ) @ SX6 ) @ SX8 ) @ SX4 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX8 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5383]) ).

thf(5579,plain,
    ! [SV1: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV1 ) @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5363]) ).

thf(5580,plain,
    ! [SV2: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV2 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5371]) ).

thf(5581,plain,
    ! [SV3: $i] :
      ( ( ! [SY529: $i,SY530: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY530 ) @ SY529 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY530 ) @ SY529 ) @ SV3 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY530 ) @ SY529 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5390]) ).

thf(5582,plain,
    ! [SV4: $i] :
      ( ( ! [SY531: $i,SY532: $i,SY533: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY533 ) @ SY532 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY533 ) @ SY531 ) @ SV4 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY533 ) @ SY531 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY533 ) @ SY532 ) @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5391]) ).

thf(5583,plain,
    ! [SV5: $i] :
      ( ( ! [SY534: $i,SY535: $i,SY536: $i,SY537: $i,SY538: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY538 @ SY537 @ SY536 @ SY535 ) @ SY534 ) @ SV5 )
            = ( hAPP @ SY535 @ ( hAPP @ SY534 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5394]) ).

thf(5584,plain,
    ! [SV6: $i] :
      ( ( ! [SY539: $i,SY540: $i,SY541: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY541 @ SY540 ) @ SY539 ) @ SV6 ) @ ( hAPP @ SY539 @ SV6 ) )
            = SY539 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5395]) ).

thf(5585,plain,
    ! [SV7: $i] :
      ( ( ! [SY542: $i,SY543: $i,SY544: $i,SY545: $i,SY546: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY546 @ SY545 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY546 @ SY545 ) @ SY544 ) @ SY543 ) @ SY542 ) ) @ SY543 ) @ SV7 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY546 @ SY545 ) @ SY544 ) @ SY543 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5398]) ).

thf(5586,plain,
    ! [SV8: $i] :
      ( ( ! [SY547: $i,SY548: $i,SY549: $i,SY550: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY550 @ SY549 ) @ SY548 ) @ SY547 ) @ SV8 ) @ SY547 )
            = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5399]) ).

thf(5587,plain,
    ! [SV9: $i] :
      ( ( ! [SY551: $i,SY552: $i,SY553: $i,SY554: $i,SY555: $i,SY556: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY556 @ SY555 @ SY554 @ SY553 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY552 @ SY556 @ SY554 @ SY551 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SY552 @ SY555 @ SY554 @ ( hAPP @ ( c_Fun_Ocomp @ SY556 @ SY555 @ SY552 @ SY553 ) @ SY551 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5404]) ).

thf(5588,plain,
    ! [SV10: $i] :
      ( ( ! [SY557: $i,SY558: $i,SY559: $i,SY560: $i,SY561: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY561 @ SY560 @ SY559 @ SY558 ) @ SY557 ) @ SV10 )
            = ( hAPP @ SY558 @ ( hAPP @ SY557 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5405]) ).

thf(5589,plain,
    ! [SV11: $i] :
      ( ( ! [SY562: $i] :
            ( ( hAPP @ ( c_Set_OCollect @ SY562 ) @ SV11 )
            = SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5434]) ).

thf(5590,plain,
    ! [SV12: $i] :
      ( ( ! [SY563: $i] :
            ( ( hAPP @ ( c_Fun_Oid @ SY563 ) @ SV12 )
            = SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5435]) ).

thf(5591,plain,
    ! [SV13: $i] :
      ( ( ! [SY564: $i] :
            ( ( hAPP @ ( c_Fun_Oid @ SY564 ) @ SV13 )
            = SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5437]) ).

thf(5592,plain,
    ! [SV14: $i] :
      ( ( ! [SY565: $i,SY566: $i,SY567: $i,SY568: $i,SY569: $i,SY570: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY570 @ SY569 @ SY568 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY570 @ SY567 @ SY569 ) @ SY566 ) @ SY565 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY570 @ SY567 @ SY568 ) @ SY566 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY567 @ SY569 @ SY568 ) @ SY565 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5438]) ).

thf(5593,plain,
    ! [SV15: $i] :
      ( ( ! [SY571: $i,SY572: $i,SY573: $i,SY574: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY574 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY574 @ SY573 ) @ SY572 ) @ SY571 ) ) @ SY572 ) @ SV15 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY574 @ SY573 ) @ SY572 ) @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5448]) ).

thf(5594,plain,
    ! [SV16: $i] :
      ( ( ! [SY575: $i,SY576: $i,SY577: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY577 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY577 ) @ SY576 ) @ SY575 ) ) @ SV16 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY577 ) @ SY576 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY577 ) @ SY575 ) @ SV16 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5455]) ).

thf(5595,plain,
    ! [SV17: $i] :
      ( ( ! [SY578: $i] :
            ( ( hAPP @ ( c_List_Orev @ SY578 ) @ ( hAPP @ ( c_List_Orev @ SY578 ) @ SV17 ) )
            = SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5460]) ).

thf(5596,plain,
    ! [SV18: $i] :
      ( ( ! [SY579: $i,SY580: $i] :
            ( ( hAPP @ ( c_Relation_Oconverse @ SY580 @ SY579 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY579 @ SY580 ) @ SV18 ) )
            = SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5466]) ).

thf(5597,plain,
    ! [SV19: $i] :
      ( ( ! [SY581: $i,SY582: $i,SY583: $i] :
            ( ( hAPP @ SY583 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY582 @ SY582 ) @ SY581 ) @ SY583 ) @ SV19 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY582 @ SY582 ) @ SY581 ) @ SY583 ) @ ( hAPP @ SY583 @ SV19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5467]) ).

thf(5598,plain,
    ! [SV20: $i] :
      ( ( ! [SY584: $i] :
            ( ( hAPP @ ( c_COMBI @ SY584 ) @ SV20 )
            = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5468]) ).

thf(5599,plain,
    ! [SV21: $i] :
      ( ( ! [SY585: $i,SY586: $i,SY587: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY587 @ SY586 ) @ SY585 ) @ SV21 )
            = SY585 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5469]) ).

thf(5600,plain,
    ! [SV22: $i] :
      ( ( ! [SY588: $i,SY589: $i,SY590: $i,SY591: $i,SY592: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY592 @ SY591 @ SY590 ) @ SY589 ) @ SY588 ) @ SV22 )
            = ( hAPP @ SY589 @ ( hAPP @ SY588 @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5470]) ).

thf(5601,plain,
    ! [SV23: $i] :
      ( ( ! [SY593: $i,SY594: $i,SY595: $i,SY596: $i,SY597: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY597 @ SY596 @ SY595 ) @ SY594 ) @ SY593 ) @ SV23 )
            = ( hAPP @ ( hAPP @ SY594 @ SV23 ) @ SY593 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5471]) ).

thf(5602,plain,
    ! [SV24: $i] :
      ( ( ! [SY598: $i,SY599: $i,SY600: $i,SY601: $i,SY602: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY602 @ SY601 @ SY600 ) @ SY599 ) @ SY598 ) @ SV24 )
            = ( hAPP @ ( hAPP @ SY599 @ SV24 ) @ ( hAPP @ SY598 @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5472]) ).

thf(5603,plain,
    ! [SV25: $i] :
      ( ( ! [SY603: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY603 ) @ SV25 ) )
            | ( SY603 = SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5473]) ).

thf(5604,plain,
    ( ( hBOOL @ c_fFalse )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5475]) ).

thf(5605,plain,
    ! [SV26: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
        | ~ ( hBOOL @ SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5477]) ).

thf(5606,plain,
    ! [SV27: $i] :
      ( ( ~ ~ ( hBOOL @ SV27 )
        | ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5478]) ).

thf(5607,plain,
    ! [SV28: $i] :
      ( ( ! [SY604: $i] :
            ( ~ ( hBOOL @ SY604 )
            | ~ ( hBOOL @ SV28 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY604 ) @ SV28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5479]) ).

thf(5608,plain,
    ! [SV29: $i] :
      ( ( ! [SY605: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY605 ) @ SV29 ) )
            | ( hBOOL @ SY605 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5480]) ).

thf(5609,plain,
    ! [SV30: $i] :
      ( ( ! [SY606: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY606 ) @ SV30 ) )
            | ( hBOOL @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5481]) ).

thf(5610,plain,
    ! [SV31: $i] :
      ( ( ! [SY607: $i] :
            ( ~ ( hBOOL @ SY607 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY607 ) @ SV31 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5482]) ).

thf(5611,plain,
    ! [SV32: $i] :
      ( ( ! [SY608: $i] :
            ( ~ ( hBOOL @ SY608 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SY608 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5483]) ).

thf(5612,plain,
    ! [SV33: $i] :
      ( ( ! [SY609: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY609 ) @ SV33 ) )
            | ( hBOOL @ SY609 )
            | ( hBOOL @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5484]) ).

thf(5613,plain,
    ! [SV34: $i] :
      ( ( ! [SY610: $i] :
            ( ( hBOOL @ SY610 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY610 ) @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5485]) ).

thf(5614,plain,
    ! [SV35: $i] :
      ( ( ! [SY611: $i] :
            ( ~ ( hBOOL @ SY611 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SY611 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5486]) ).

thf(5615,plain,
    ! [SV36: $i] :
      ( ( ! [SY612: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY612 ) @ SV36 ) )
            | ~ ( hBOOL @ SY612 )
            | ( hBOOL @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5487]) ).

thf(5616,plain,
    ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5488]) ).

thf(5617,plain,
    ! [SV37: $i] :
      ( ( SV37
       != ( hAPP @ c_Nat_OSuc @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5489]) ).

thf(5618,plain,
    ! [SV38: $i] :
      ( ( ! [SY613: $i,SY614: $i,SY615: $i,SY616: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY616 @ SY615 @ SY614 ) @ SY613 ) @ SV38 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY615 @ SY613 ) @ SV38 ) )
                      | ~ ( hBOOL @ ( hAPP @ SY614 @ SV38 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY615 @ SY613 ) @ SV38 ) )
                        | ~ ( hBOOL @ ( hAPP @ SY614 @ SV38 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY616 @ SY615 @ SY614 ) @ SY613 ) @ SV38 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5490]) ).

thf(5619,plain,
    ! [SV39: $i] :
      ( ( ! [SY617: $i,SY618: $i,SY619: $i,SY620: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY620 ) @ SY619 ) @ SY618 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY617 ) @ SY618 ) @ SV39 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY620 @ SY617 ) ) @ SY619 ) @ SV39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5491]) ).

thf(5620,plain,
    ! [SV40: $i] :
      ( ( ! [SY621: $i,SY622: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY622 @ SY621 ) ) @ SV40 ) @ SV40 ) )
                  | ~ ( hBOOL @ ( hAPP @ SY622 @ SV40 ) )
                  | ~ ! [SY623: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY621 ) @ SV40 ) @ SY623 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY622 @ SY621 ) ) @ SY623 ) @ SV40 ) ) ) )
              | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY622 @ SV40 ) )
                      | ~ ! [SY624: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY621 ) @ SV40 ) @ SY624 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY622 @ SY621 ) ) @ SY624 ) @ SV40 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY622 @ SY621 ) ) @ SV40 ) @ SV40 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5492]) ).

thf(5621,plain,
    ! [SV41: $i] :
      ( ( ! [SY625: $i,SY626: $i,SY627: $i,SY628: $i,SY629: $i] :
            ( ( SY629 != SY628 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY627 @ SY626 @ SY625 ) @ SV41 ) @ SY629 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY627 @ SY626 @ SY625 ) @ SV41 ) @ SY628 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5493]) ).

thf(5622,plain,
    ! [SV42: $i] :
      ( ( ! [SY630: $i,SY631: $i] :
            ( ~ ~ ! [SX3: $i] :
                    ~ ( hBOOL @ ( hAPP @ SY631 @ SX3 ) )
            | ( SY630
             != ( c_Hilbert__Choice_OEps @ SV42 @ SY631 ) )
            | ( hBOOL @ ( hAPP @ SY631 @ SY630 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5494]) ).

thf(5623,plain,
    ! [SV43: $i] :
      ( ( ! [SY633: $i,SY634: $i,SY635: $i,SY636: $i,SY637: $i,SY638: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY638 ) @ SY637 ) @ SY636 ) @ SY635 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY638 ) @ SY634 ) @ SY633 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SY637 != SY634 )
                            | ( SY636 != SY633 ) )
                      | ( SY635 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY637 != SY634 )
                              | ( SY636 != SY633 ) )
                        | ( SY635 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY638 ) @ SY637 ) @ SY636 ) @ SY635 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY638 ) @ SY634 ) @ SY633 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5495]) ).

thf(5624,plain,
    ! [SV44: $i] :
      ( ( ! [SY639: $i,SY640: $i,SY641: $i,SY642: $i,SY643: $i] :
            ( ~ ( ( SY643 != SY642 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY641 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY641 @ SY640 ) @ SY643 ) @ SY639 ) ) @ SY642 ) @ SV44 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY641 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY641 @ SY640 ) @ SY642 ) @ SV44 ) ) @ SY643 ) @ SY639 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5496]) ).

thf(5625,plain,
    ! [SV45: $i] :
      ( ( ! [SY644: $i,SY645: $i,SY646: $i,SY647: $i,SY648: $i] :
            ~ ( ~ ( ( SY648 != SY647 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY646 @ SY645 ) @ SY644 ) @ SY647 ) @ SV45 ) @ SY648 )
                    = SV45 ) )
              | ~ ( ~ ( ( SY648 != SY647 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY646 @ SY645 ) @ SY644 ) @ SY647 ) @ SV45 ) @ SY648 )
                    = ( hAPP @ SY644 @ SY648 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5497]) ).

thf(5626,plain,
    ! [SV46: $i] :
      ( ( ! [SY649: $i] :
            ( ( SY649 != SV46 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY649 ) @ SV46 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5498]) ).

thf(5627,plain,
    ! [SV47: $i] :
      ( ( ! [SY650: $i,SY651: $i,SY652: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY652 @ SY651 ) ) @ SY650 ) @ SV47 ) )
                  | ~ ( ( SV47 != SY650 )
                      | ~ ~ ( hBOOL @ ( hAPP @ SY652 @ SY650 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY652 @ SY650 ) )
                      | ~ ~ ! [SY653: $i] :
                              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY651 ) @ SY650 ) @ SY653 ) )
                                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY652 @ SY651 ) ) @ SY653 ) @ SV47 ) ) ) ) )
              | ~ ( ~ ( ~ ( ( SV47 != SY650 )
                          | ~ ~ ( hBOOL @ ( hAPP @ SY652 @ SY650 ) ) )
                      | ~ ( ~ ( hBOOL @ ( hAPP @ SY652 @ SY650 ) )
                          | ~ ~ ! [SY654: $i] :
                                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY651 ) @ SY650 ) @ SY654 ) )
                                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY652 @ SY651 ) ) @ SY654 ) @ SV47 ) ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY652 @ SY651 ) ) @ SY650 ) @ SV47 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5499]) ).

thf(5628,plain,
    ! [SV48: $i] :
      ( ( ! [SY655: $i] :
            ( ( ( hAPP @ c_Nat_OSuc @ SY655 )
             != ( hAPP @ c_Nat_OSuc @ SV48 ) )
            | ( SY655 = SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5500]) ).

thf(5629,plain,
    ! [SV49: $i] :
      ( ( ! [SY656: $i,SY657: $i,SY658: $i,SY659: $i,SY660: $i,SY661: $i,SY662: $i,SY663: $i,SY664: $i,SY665: $i] :
            ( ( ( hAPP @ SY665 @ ( hAPP @ SY664 @ SY663 ) )
             != ( hAPP @ SY662 @ ( hAPP @ SY661 @ SY660 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY659 @ SY658 @ SY657 @ SY665 ) @ SY664 ) @ SY663 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY656 @ SY658 @ SV49 @ SY662 ) @ SY661 ) @ SY660 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5501]) ).

thf(5630,plain,
    ! [SV50: $i] :
      ( ( ! [SY666: $i,SY667: $i,SY668: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY668 @ SY667 ) ) @ SY666 ) @ SV50 ) )
            | ~ ! [SY669: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY668 ) @ SY666 ) @ SY669 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY667 ) @ SY669 ) @ SV50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5502]) ).

thf(5631,plain,
    ! [SV51: $i] :
      ( ( ! [SY670: $i,SY671: $i,SY672: $i,SY673: $i,SY674: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY674 @ SY673 ) @ SY672 ) @ SY671 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY674 @ SY673 ) @ SY670 ) @ SV51 ) )
                  | ~ ( ( SY672 != SY670 )
                      | ( SY671 != SV51 ) ) )
              | ~ ( ~ ~ ( ( SY672 != SY670 )
                        | ( SY671 != SV51 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY674 @ SY673 ) @ SY672 ) @ SY671 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY674 @ SY673 ) @ SY670 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5503]) ).

thf(5632,plain,
    ! [SV52: $i] :
      ( ( ! [SY675: $i,SY676: $i,SY677: $i,SY678: $i,SY679: $i,SY680: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY680 @ SY679 @ SY678 @ SY677 ) @ SY676 )
             != SY675 )
            | ( ( hAPP @ SY677 @ ( hAPP @ SY676 @ SV52 ) )
              = ( hAPP @ SY675 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5504]) ).

thf(5633,plain,
    ! [SV53: $i] :
      ( ( ! [SY681: $i,SY682: $i,SY683: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SY682 ) @ SY681 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SV53 ) @ SY681 ) )
                  | ( SY682 = SV53 ) )
              | ~ ( ( SY682 != SV53 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SY682 ) @ SY681 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SV53 ) @ SY681 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5505]) ).

thf(5634,plain,
    ! [SV54: $i] :
      ( ( ! [SY684: $i,SY685: $i,SY686: $i,SY687: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY686 ) @ SY685 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY684 ) @ SV54 ) )
                  | ~ ! [SY688: $i] :
                        ~ ( ~ ( ( SY686
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY684 ) @ SY688 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY688 ) @ SY685 )
                               != SV54 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY686 ) @ SY688 )
                               != SY684 )
                              | ( SY685
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY688 ) @ SV54 ) ) ) ) )
              | ~ ( ~ ~ ! [SY689: $i] :
                          ~ ( ~ ( ( SY686
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY684 ) @ SY689 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY689 ) @ SY685 )
                                 != SV54 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY686 ) @ SY689 )
                                 != SY684 )
                                | ( SY685
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY689 ) @ SV54 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY686 ) @ SY685 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY687 ) @ SY684 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5506]) ).

thf(5635,plain,
    ! [SV55: $i] :
      ( ( ! [SY690: $i,SY691: $i,SY692: $i] :
            ( ( SY692 != SY691 )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY690 ) @ SV55 ) @ SY692 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY690 ) @ SV55 ) @ SY691 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY690 ) @ SV55 ) @ SY692 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY690 ) @ SV55 ) @ SY691 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5507]) ).

thf(5636,plain,
    ! [SV56: $i] :
      ( ( ! [SY693: $i,SY694: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY694 @ SY693 ) )
            | ( hBOOL @ ( hAPP @ SY694 @ ( c_Hilbert__Choice_OEps @ SV56 @ SY694 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5508]) ).

thf(5637,plain,
    ! [SV57: $i] :
      ( ( ! [SY695: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY695 )
                   != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
                  | ( SY695 = SV57 ) )
              | ~ ( ( SY695 != SV57 )
                  | ( ( hAPP @ c_Code__Numeral_Onat__of @ SY695 )
                    = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5509]) ).

thf(5638,plain,
    ! [SV58: $i] :
      ( ( ! [SY696: $i,SY697: $i,SY698: $i,SY699: $i,SY700: $i,SY701: $i] :
            ( ( SY701 != SY700 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY699 @ SY698 @ SY697 @ SY696 @ SV58 ) @ SY701 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY699 @ SY698 @ SY697 @ SY696 @ SV58 ) @ SY700 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5510]) ).

thf(5639,plain,
    ! [SV59: $i] :
      ( ( ! [SY702: $i,SY703: $i,SY704: $i,SY705: $i,SY706: $i,SY707: $i] :
            ( ~ ( ( SY707 != SY706 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY705 @ SY704 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY705 @ SY704 ) @ SY703 ) @ SY707 ) @ SY702 ) ) @ SY706 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY705 @ SY704 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY705 @ SY704 ) @ SY703 ) @ SY706 ) @ SV59 ) ) @ SY707 ) @ SY702 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5511]) ).

thf(5640,plain,
    ! [SV60: $i] :
      ( ( ! [SY708: $i,SY709: $i,SY710: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY710 ) @ SY709 ) @ SY708 ) @ SV60 ) )
                  | ( SY709 = SV60 )
                  | ( hBOOL @ ( hAPP @ SY708 @ SV60 ) ) )
              | ~ ( ~ ( ( SY709 = SV60 )
                      | ( hBOOL @ ( hAPP @ SY708 @ SV60 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY710 ) @ SY709 ) @ SY708 ) @ SV60 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5512]) ).

thf(5641,plain,
    ! [SV61: $i] :
      ( ( ! [SY711: $i,SY712: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY712 @ SY711 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY712 @ SV61 ) ) @ SY711 ) @ SY711 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5513]) ).

thf(5642,plain,
    ! [SV62: $i] :
      ( ( ! [SY713: $i,SY714: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY714 ) @ SY713 ) @ SV62 )
           != SV62 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5514]) ).

thf(5643,plain,
    ! [SV63: $i] :
      ( ( ! [SY715: $i,SY716: $i,SY717: $i,SY718: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY718 @ SY717 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY716 ) @ SY717 ) @ SY715 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY718 @ SY716 ) ) @ SY715 ) @ SV63 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY718 @ SY716 ) ) @ SY717 ) @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5515]) ).

thf(5644,plain,
    ! [SV64: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ SV64 )
       != SV64 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5516]) ).

thf(5645,plain,
    ! [SV65: $i] :
      ( ( ! [SY719: $i,SY720: $i,SY721: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY721 @ SY720 ) ) @ SY719 ) @ SV65 ) )
            | ~ ( ( SV65 != SY719 )
                | ( hBOOL @ ( hAPP @ SY721 @ SY719 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY721 @ SY719 ) )
                | ! [SY722: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY720 ) @ SY719 ) @ SY722 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY721 @ SY720 ) ) @ SY722 ) @ SV65 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5517]) ).

thf(5646,plain,
    ! [SV66: $i] :
      ( ( ! [SY723: $i,SY724: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY724 @ SY723 ) @ SV66 ) )
                  | ! [SY725: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY723 @ SY725 ) @ SV66 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY724 @ SY723 ) @ SY725 ) ) ) )
              | ~ ( ~ ! [SY726: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY723 @ SY726 ) @ SV66 ) )
                        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY724 @ SY723 ) @ SY726 ) ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY724 @ SY723 ) @ SV66 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5518]) ).

thf(5647,plain,
    ! [SV67: $i] :
      ( ( ! [SY727: $i,SY728: $i] :
            ( ~ ( c_Predicate_Oreflp @ SY728 @ SY727 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY727 @ SV67 ) @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5519]) ).

thf(5648,plain,
    ! [SV68: $i] :
      ( ( ! [SY729: $i,SY730: $i,SY731: $i,SY732: $i,SY733: $i,SY734: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY734 @ SY733 @ SY732 @ SY731 @ SY730 @ SY729 @ SV68 )
                  | ~ ! [SY735: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY731 @ SY729 ) @ SY735 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY730 @ SY735 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY736: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY731 @ SY729 ) @ SY736 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY730 @ SY736 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY734 @ SY733 @ SY732 @ SY731 @ SY730 @ SY729 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5520]) ).

thf(5649,plain,
    ! [SV69: $i] :
      ( ( ! [SY737: $i,SY738: $i,SY739: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY739 @ SY738 ) @ SY737 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY738 @ SV69 ) @ SY737 ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY739 @ SY738 ) @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5521]) ).

thf(5650,plain,
    ! [SV70: $i] :
      ( ( ! [SY740: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY740 )
                   != ( hAPP @ c_Nat_OSuc @ SV70 ) )
                  | ( SY740 = SV70 ) )
              | ~ ( ( SY740 != SV70 )
                  | ( ( hAPP @ c_Nat_OSuc @ SY740 )
                    = ( hAPP @ c_Nat_OSuc @ SV70 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5522]) ).

thf(5651,plain,
    ! [SV71: $i] :
      ( ( ! [SY741: $i,SY742: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY742 @ SY741 ) @ SV71 ) )
                  | ! [SY743: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY741 @ SY743 ) @ SV71 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY742 @ SY741 ) @ SY743 ) ) ) )
              | ~ ( ~ ! [SY744: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY741 @ SY744 ) @ SV71 ) )
                        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY742 @ SY741 ) @ SY744 ) ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY742 @ SY741 ) @ SV71 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5523]) ).

thf(5652,plain,
    ! [SV72: $i] :
      ( ( ! [SY745: $i,SY746: $i,SY747: $i,SY748: $i] :
            ( ( ( hAPP @ SY748 @ SY747 )
             != SY746 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY745 @ SV72 ) @ SY748 ) @ SY747 ) @ SY746 )
              = SY748 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5524]) ).

thf(5653,plain,
    ! [SV73: $i] :
      ( ( ! [SY749: $i,SY750: $i,SY751: $i,SY752: $i,SY753: $i] :
            ( ~ ( ( SY753 != SY752 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY751 @ SY750 ) @ SY749 ) @ SY752 ) @ SV73 ) @ SY753 )
              = ( hAPP @ SY749 @ SY753 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5525]) ).

thf(5654,plain,
    ! [SV74: $i] :
      ( ( ! [SY754: $i,SY755: $i,SY756: $i] :
            ( ( SY756 != SY755 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY754 ) @ SV74 ) @ SY756 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY754 ) @ SV74 ) @ SY755 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY754 ) @ SV74 ) @ SY755 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY754 ) @ SV74 ) @ SY756 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5526]) ).

thf(5655,plain,
    ! [SV75: $i] :
      ( ( ! [SY757: $i,SY758: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY758 ) @ SY757 )
                   != SV75 )
                  | ( SY757
                    = ( hAPP @ ( c_List_Orev @ SY758 ) @ SV75 ) ) )
              | ~ ( ( SY757
                   != ( hAPP @ ( c_List_Orev @ SY758 ) @ SV75 ) )
                  | ( ( hAPP @ ( c_List_Orev @ SY758 ) @ SY757 )
                    = SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5527]) ).

thf(5656,plain,
    ! [SV76: $i] :
      ( ( ! [SY759: $i] :
            ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SY759 @ SV76 )
                  | ! [SY760: $i,SY761: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                            | ( ( hAPP @ SV76 @ SY760 )
                              = ( hAPP @ SV76 @ SY761 ) ) )
                        | ~ ( ( ( hAPP @ SV76 @ SY760 )
                             != ( hAPP @ SV76 @ SY761 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
              | ~ ( ~ ! [SY762: $i,SY763: $i] :
                        ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                              | ( ( hAPP @ SV76 @ SY762 )
                                = ( hAPP @ SV76 @ SY763 ) ) )
                          | ~ ( ( ( hAPP @ SV76 @ SY762 )
                               != ( hAPP @ SV76 @ SY763 ) )
                              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) )
                  | ( c_Equiv__Relations_Oequivp @ SY759 @ SV76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5528]) ).

thf(5657,plain,
    ! [SV77: $i] :
      ( ( ! [SY764: $i,SY765: $i,SY766: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY766 @ SY765 @ SY764 ) @ SV77 ) )
                  | ~ ! [SY767: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY764 @ SY767 ) @ SV77 ) ) )
              | ~ ( ~ ~ ! [SY768: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY764 @ SY768 ) @ SV77 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY766 @ SY765 @ SY764 ) @ SV77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5529]) ).

thf(5658,plain,
    ! [SV78: $i] :
      ( ( ! [SY769: $i,SY770: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY770 ) @ SY769 )
                   != ( hAPP @ ( c_Option_Ooption_OSome @ SY770 ) @ SV78 ) )
                  | ( SY769 = SV78 ) )
              | ~ ( ( SY769 != SV78 )
                  | ( ( hAPP @ ( c_Option_Ooption_OSome @ SY770 ) @ SY769 )
                    = ( hAPP @ ( c_Option_Ooption_OSome @ SY770 ) @ SV78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5530]) ).

thf(5659,plain,
    ! [SV79: $i] :
      ( ( ! [SY771: $i,SY772: $i,SY773: $i,SY774: $i,SY775: $i,SY776: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY776 @ SY775 @ SY774 @ SY773 @ SY772 )
            | ~ ( ~ ( ( ( hAPP @ SY774 @ SY771 )
                     != ( hAPP @ SY774 @ SV79 ) )
                    | ( SY771 = SV79 ) )
                | ~ ( ( SY771 != SV79 )
                    | ( ( hAPP @ SY774 @ SY771 )
                      = ( hAPP @ SY774 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5531]) ).

thf(5660,plain,
    ! [SV80: $i] :
      ( ( ! [SY777: $i,SY778: $i,SY779: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY779 @ SY778 @ SY777 )
            | ( ( hAPP @ ( hAPP @ SY778 @ SV80 ) @ SV80 )
              = SV80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5532]) ).

thf(5661,plain,
    ! [SV81: $i] :
      ( ( ! [SY780: $i,SY781: $i,SY782: $i,SY783: $i,SY784: $i,SY785: $i,SY786: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY786 @ SY785 @ SY784 @ SY783 ) @ SY782 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY781 @ SY785 @ SY784 @ SY780 ) @ SV81 ) )
            | ! [SY787: $i] :
                ( ( hAPP @ SY783 @ ( hAPP @ SY782 @ SY787 ) )
                = ( hAPP @ SY780 @ ( hAPP @ SV81 @ SY787 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5533]) ).

thf(5662,plain,
    ! [SV82: $i] :
      ( ( ! [SY788: $i,SY789: $i,SY790: $i,SY791: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY791 @ SY790 @ SY789 ) ) @ SY788 ) @ SV82 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY791 @ SY788 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY790 ) @ SY788 ) @ SV82 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY791 @ SY788 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY789 ) @ SY788 ) @ SV82 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY791 @ SY788 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY790 ) @ SY788 ) @ SV82 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY791 @ SY788 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY789 ) @ SY788 ) @ SV82 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY791 @ SY790 @ SY789 ) ) @ SY788 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5534]) ).

thf(5663,plain,
    ! [SV83: $i] :
      ( ( ! [SY792: $i,SY793: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY793 @ SY792 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY792 @ SV83 ) @ SV83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5535]) ).

thf(5664,plain,
    ! [SV84: $i] :
      ( ( ! [SY794: $i,SY795: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY795 ) @ SY794 ) @ SV84 ) )
                  | ( hBOOL @ ( hAPP @ SV84 @ SY794 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV84 @ SY794 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY795 ) @ SY794 ) @ SV84 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5536]) ).

thf(5665,plain,
    ! [SV85: $i] :
      ( ( ! [SY796: $i,SY797: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY797 ) @ SY796 ) @ SV85 ) )
            | ~ ! [SY798: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY797 ) @ SY796 ) @ SY798 ) @ SV85 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5537]) ).

thf(5666,plain,
    ! [SV86: $i] :
      ( ( ! [SY799: $i,SY800: $i,SY801: $i,SY802: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY802 @ SY801 ) @ SY800 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY799 @ SV86 @ SY802 ) @ SY801 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5538]) ).

thf(5667,plain,
    ! [SV87: $i] :
      ( ( ! [SY803: $i,SY804: $i,SY805: $i,SY806: $i,SY807: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY807 @ SY806 @ SY805 @ SY804 @ SY803 )
            | ( ( hAPP @ SY804 @ ( hAPP @ SY805 @ SV87 ) )
              = SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5539]) ).

thf(5668,plain,
    ! [SV88: $i] :
      ( ( ! [SY808: $i,SY809: $i,SY810: $i,SY811: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY811 @ SY810 @ SY809 )
            | ( ( hAPP @ ( hAPP @ SY809 @ SY808 ) @ ( hAPP @ ( hAPP @ SY809 @ SY808 ) @ SV88 ) )
              = ( hAPP @ ( hAPP @ SY809 @ SY808 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5540]) ).

thf(5669,plain,
    ! [SV89: $i] :
      ( ( ! [SY812: $i,SY813: $i,SY814: $i,SY815: $i,SY816: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY816 ) @ SY815 ) @ SY814 )
             != SY813 )
            | ( SY812
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY816 ) @ SY814 ) @ SV89 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY816 ) @ SY815 ) @ SY812 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY816 ) @ SY813 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5541]) ).

thf(5670,plain,
    ! [SV90: $i] :
      ( ( ~ ! [SY817: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY817 ) )
              | ( SV90 = SY817 ) )
        | ( SV90 = v_s_H ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5542]) ).

thf(5671,plain,
    ! [SV91: $i] :
      ( ( ! [SY818: $i,SY819: $i,SY820: $i,SY821: $i,SY822: $i,SY823: $i,SY824: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY824 @ SY823 ) @ SY822 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY821 @ SY822 ) @ SY820 ) )
            | ( c_Predicate_Opred__comp @ SY819 @ SY818 @ SV91 @ SY824 @ SY821 @ SY823 @ SY820 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5543]) ).

thf(5672,plain,
    ! [SV92: $i] :
      ( ( ! [SY825: $i,SY826: $i,SY827: $i,SY828: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY828 @ SY827 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY826 ) @ SY827 ) @ SY825 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY828 @ SV92 @ SY826 ) ) @ SY827 ) @ SY825 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5544]) ).

thf(5673,plain,
    ! [SV93: $i] :
      ( ( ! [SY829: $i,SY830: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY830 ) @ SY829 ) @ SV93 ) )
                  | ~ ! [SY831: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY830 ) @ SY829 ) @ SY831 ) @ SV93 ) ) )
              | ~ ( ~ ~ ! [SY832: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY830 ) @ SY829 ) @ SY832 ) @ SV93 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY830 ) @ SY829 ) @ SV93 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5545]) ).

thf(5674,plain,
    ! [SV94: $i] :
      ( ( ! [SY833: $i,SY834: $i,SY835: $i,SY836: $i,SY837: $i] :
            ~ ( ~ ( ( SY837 != SY836 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY835 @ SY834 ) @ SY833 ) @ SY836 ) @ SV94 ) @ SY837 )
                    = SV94 ) )
              | ~ ( ~ ( ( SY837 != SY836 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY835 @ SY834 ) @ SY833 ) @ SY836 ) @ SV94 ) @ SY837 )
                    = ( hAPP @ SY833 @ SY837 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5546]) ).

thf(5675,plain,
    ! [SV95: $i] :
      ( ( ! [SY838: $i,SY839: $i,SY840: $i,SY841: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY841 @ SY840 ) @ SY839 ) @ SY838 ) @ SV95 )
                   != SY839 )
                  | ( ( hAPP @ SY839 @ SY838 )
                    = SV95 ) )
              | ~ ( ( ( hAPP @ SY839 @ SY838 )
                   != SV95 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY841 @ SY840 ) @ SY839 ) @ SY838 ) @ SV95 )
                    = SY839 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5547]) ).

thf(5676,plain,
    ! [SV96: $i] :
      ( ( ! [SY842: $i,SY843: $i,SY844: $i] :
            ( ( SY844 != SY843 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY842 ) @ SY844 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY842 ) @ SY843 ) @ SV96 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY842 ) @ SY843 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY842 ) @ SY844 ) @ SV96 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5548]) ).

thf(5677,plain,
    ! [SV97: $i] :
      ( ( ! [SY845: $i,SY846: $i,SY847: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY847 ) @ SY846 ) @ SY845 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY847 ) @ SY846 ) @ SV97 ) )
                  | ( SY845 = SV97 ) )
              | ~ ( ( SY845 != SV97 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY847 ) @ SY846 ) @ SY845 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY847 ) @ SY846 ) @ SV97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5549]) ).

thf(5678,plain,
    ! [SV98: $i] :
      ( ( ! [SY848: $i,SY849: $i,SY850: $i] :
            ( ( SY850 != SY849 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY848 ) @ SY849 ) @ SV98 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY848 ) @ SY850 ) @ SV98 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5550]) ).

thf(5679,plain,
    ! [SV99: $i] :
      ( ( ! [SY851: $i] :
            ( ~ ! [SY852: $i] :
                  ( ( hAPP @ SY851 @ SY852 )
                  = ( hAPP @ SV99 @ SY852 ) )
            | ( SY851 = SV99 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5551]) ).

thf(5680,plain,
    ! [SV100: $i] :
      ( ( ! [SY853: $i,SY854: $i,SY855: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY855 ) @ SY854 ) @ SY853 ) @ SV100 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY855 ) @ SY854 ) @ SV100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5552]) ).

thf(5681,plain,
    ! [SV101: $i] :
      ( ( ! [SY856: $i,SY857: $i] :
            ~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY857 @ SX3 ) )
                  | ! [SY859: $i,SY860: $i] : ( hBOOL @ ( hAPP @ SY857 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY856 @ SV101 ) @ SY859 ) @ SY860 ) ) ) )
              | ~ ( ~ ! [SY861: $i,SY862: $i] : ( hBOOL @ ( hAPP @ SY857 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY856 @ SV101 ) @ SY861 ) @ SY862 ) ) )
                  | ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY857 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5553]) ).

thf(5682,plain,
    ! [SV102: $i] :
      ( ( ! [SY864: $i,SY865: $i,SY866: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY866 @ SY865 ) @ SY864 ) )
            | ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY866 @ SY865 ) @ SV102 ) )
            | ( SY864 = SV102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5554]) ).

thf(5683,plain,
    ! [SV103: $i] :
      ( ( ! [SY867: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SY867 ) @ SV103 ) )
            | ( SV103 = SY867 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5555]) ).

thf(5684,plain,
    ! [SV104: $i] :
      ( ( ! [SY868: $i,SY869: $i,SY870: $i,SY871: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY871 @ SY870 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY869 ) @ SY870 ) @ SY868 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY871 @ SY869 @ SV104 ) ) @ SY870 ) @ SY868 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5556]) ).

thf(5685,plain,
    ! [SV105: $i] :
      ( ( ! [SY872: $i] :
            ( ~ ~ ! [SX2: $i] :
                    ~ ( hBOOL @ ( hAPP @ SY872 @ SX2 ) )
            | ( hBOOL @ ( hAPP @ SY872 @ ( c_Hilbert__Choice_OEps @ SV105 @ SY872 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5557]) ).

thf(5686,plain,
    ! [SV106: $i] :
      ( ( ! [SY874: $i,SY875: $i,SY876: $i,SY877: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY877 @ SY876 @ SY875 ) @ SY874 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP @ SY874 @ ( hAPP @ SY875 @ SV106 ) ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SY874 @ ( hAPP @ SY875 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY877 @ SY876 @ SY875 ) @ SY874 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5558]) ).

thf(5687,plain,
    ! [SV107: $i] :
      ( ( ! [SY878: $i,SY879: $i,SY880: $i,SY881: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY881 @ SY880 @ SY879 ) ) @ SY878 ) @ SV107 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY881 @ SY878 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY880 ) @ SY878 ) @ SV107 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY881 @ SY878 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY879 ) @ SY878 ) @ SV107 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY881 @ SY878 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY880 ) @ SY878 ) @ SV107 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY881 @ SY878 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY879 ) @ SY878 ) @ SV107 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY881 @ SY880 @ SY879 ) ) @ SY878 ) @ SV107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5559]) ).

thf(5688,plain,
    ! [SV108: $i] :
      ( ( ! [SY882: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SY882 )
                   != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
                  | ( SY882 = SV108 ) )
              | ~ ( ( SY882 != SV108 )
                  | ( ( hAPP @ c_Com_Ocom_OBODY @ SY882 )
                    = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5560]) ).

thf(5689,plain,
    ! [SV109: $i] :
      ( ( ! [SY883: $i,SY884: $i,SY885: $i,SY886: $i,SY887: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY887 @ SY886 ) @ SY885 ) @ SY884 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY887 @ SY886 ) @ SY883 ) @ SV109 ) )
            | ~ ( ( SY885 != SY883 )
                | ( SY884 != SV109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5561]) ).

thf(5690,plain,
    ! [SV110: $i] :
      ( ( ! [SY888: $i,SY889: $i,SY890: $i,SY891: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY891 @ SY890 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY890 @ SY889 ) @ SY888 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY890 @ SY888 ) @ SV110 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY890 @ SY889 ) @ SV110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5562]) ).

thf(5691,plain,
    ! [SV111: $i] :
      ( ( ! [SY892: $i,SY893: $i,SY894: $i,SY895: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY895 @ SY894 ) @ SY893 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY892 @ SV111 @ SY895 ) @ SY893 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5563]) ).

thf(5692,plain,
    ! [SV112: $i] :
      ( ( ! [SY896: $i] :
            ( ~ ~ ! [SX2: $i] :
                    ~ ( hBOOL @ ( hAPP @ SY896 @ SX2 ) )
            | ( hBOOL @ ( hAPP @ SY896 @ ( c_Hilbert__Choice_OEps @ SV112 @ SY896 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5564]) ).

thf(5693,plain,
    ! [SV113: $i] :
      ( ( ! [SY898: $i,SY899: $i,SY900: $i,SY901: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY901 ) @ SY900 ) @ SY899 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY901 ) @ SY898 ) @ SV113 ) )
                  | ~ ( ( SY900 != SY898 )
                      | ( SY899 != SV113 ) ) )
              | ~ ( ~ ~ ( ( SY900 != SY898 )
                        | ( SY899 != SV113 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY901 ) @ SY900 ) @ SY899 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY901 ) @ SY898 ) @ SV113 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5565]) ).

thf(5694,plain,
    ! [SV114: $i] :
      ( ( ! [SY902: $i,SY903: $i,SY904: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY904 ) @ SY903 ) @ SY902 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY904 ) @ SY903 ) @ SV114 ) )
            | ( SV114 = SY902 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5566]) ).

thf(5695,plain,
    ! [SV115: $i] :
      ( ( ! [SY905: $i,SY906: $i] :
            ( SY906
           != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY905 ) @ SV115 ) @ SY906 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5567]) ).

thf(5696,plain,
    ! [SV116: $i] :
      ( ( ! [SY907: $i,SY908: $i,SY909: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY909 @ SY908 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY908 @ SY907 ) @ SV116 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY908 @ SV116 ) @ SY907 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5568]) ).

thf(5697,plain,
    ! [SV117: $i] :
      ( ( ! [SY910: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY910 )
                   != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
                  | ( SY910 = SV117 ) )
              | ~ ( ( SY910 != SV117 )
                  | ( ( hAPP @ c_Code__Numeral_Onat__of @ SY910 )
                    = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5569]) ).

thf(5698,plain,
    ! [SV118: $i] :
      ( ( ! [SY911: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY911 @ ( c_Hilbert__Choice_OEps @ SV118 @ SY911 ) ) )
                  | ~ ! [SX2: $i] :
                        ~ ( hBOOL @ ( hAPP @ SY911 @ SX2 ) ) )
              | ~ ( ~ ~ ! [SX2: $i] :
                          ~ ( hBOOL @ ( hAPP @ SY911 @ SX2 ) )
                  | ( hBOOL @ ( hAPP @ SY911 @ ( c_Hilbert__Choice_OEps @ SV118 @ SY911 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5570]) ).

thf(5699,plain,
    ! [SV119: $i] :
      ( ( ! [SY914: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY914 )
                   != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
                  | ( SY914 = SV119 ) )
              | ~ ( ( SY914 != SV119 )
                  | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY914 )
                    = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5571]) ).

thf(5700,plain,
    ! [SV120: $i] :
      ( ( ! [SY915: $i,SY916: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY916 ) @ SY915 )
                   != ( hAPP @ ( c_List_Orev @ SY916 ) @ SV120 ) )
                  | ( SY915 = SV120 ) )
              | ~ ( ( SY915 != SV120 )
                  | ( ( hAPP @ ( c_List_Orev @ SY916 ) @ SY915 )
                    = ( hAPP @ ( c_List_Orev @ SY916 ) @ SV120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5572]) ).

thf(5701,plain,
    ! [SV121: $i] :
      ( ( ! [SY917: $i,SY918: $i,SY919: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY919 @ SY918 @ SY917 ) @ SV121 ) )
                  | ~ ! [SY920: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY917 @ SV121 ) @ SY920 ) ) )
              | ~ ( ~ ~ ! [SY921: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY917 @ SV121 ) @ SY921 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY919 @ SY918 @ SY917 ) @ SV121 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5573]) ).

thf(5702,plain,
    ! [SV122: $i] :
      ( ( ! [SY922: $i,SY923: $i,SY924: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY924 @ SY923 ) ) @ SY922 ) @ SV122 ) )
                  | ~ ! [SY925: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY924 ) @ SY922 ) @ SY925 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY923 ) @ SY925 ) @ SV122 ) ) ) )
              | ~ ( ~ ~ ! [SY926: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY924 ) @ SY922 ) @ SY926 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY923 ) @ SY926 ) @ SV122 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY924 @ SY923 ) ) @ SY922 ) @ SV122 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5574]) ).

thf(5703,plain,
    ! [SV123: $i] :
      ( ( ! [SY927: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY927 )
                   != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
                  | ( SY927 = SV123 ) )
              | ~ ( ( SY927 != SV123 )
                  | ( ( hAPP @ c_Int_ORep__Integ @ SY927 )
                    = ( hAPP @ c_Int_ORep__Integ @ SV123 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5575]) ).

thf(5704,plain,
    ! [SV124: $i] :
      ( ( ! [SY928: $i,SY929: $i,SY930: $i,SY931: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY931 @ SY930 @ SY929 ) ) @ SY928 ) @ SV124 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY931 @ SY928 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY930 ) @ SY928 ) @ SV124 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY931 @ SY928 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY929 ) @ SY928 ) @ SV124 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5576]) ).

thf(5705,plain,
    ! [SV125: $i] :
      ( ( ! [SY932: $i,SY933: $i,SY934: $i,SY935: $i,SY936: $i,SY937: $i,SY938: $i,SY939: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY939 @ SY938 @ SY937 @ SY936 ) @ SY935 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY934 @ SY938 @ SY937 @ SY933 ) @ SY932 ) )
            | ( ( hAPP @ SY936 @ ( hAPP @ SY935 @ SV125 ) )
              = ( hAPP @ SY933 @ ( hAPP @ SY932 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5577]) ).

thf(5706,plain,
    ! [SV126: $i] :
      ( ( ! [SY940: $i,SY941: $i,SY942: $i,SY943: $i,SY944: $i,SY945: $i,SY946: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY946 ) @ SY945 ) @ SY944 ) @ SY943 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY942 ) @ SY941 ) @ SY940 ) @ SV126 ) )
            | ~ ! [SY947: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY946 ) @ SY945 ) @ SY947 ) @ SY943 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY942 ) @ SY941 ) @ SY947 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5578]) ).

thf(5707,plain,
    ! [SV3: $i,SV127: $i] :
      ( ( ! [SY948: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY948 ) @ SV127 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY948 ) @ SV127 ) @ SV3 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY948 ) @ SV127 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5581]) ).

thf(5708,plain,
    ! [SV4: $i,SV128: $i] :
      ( ( ! [SY949: $i,SY950: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY950 ) @ SY949 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY950 ) @ SV128 ) @ SV4 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY950 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY950 ) @ SY949 ) @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5582]) ).

thf(5709,plain,
    ! [SV5: $i,SV129: $i] :
      ( ( ! [SY951: $i,SY952: $i,SY953: $i,SY954: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY954 @ SY953 @ SY952 @ SY951 ) @ SV129 ) @ SV5 )
            = ( hAPP @ SY951 @ ( hAPP @ SV129 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5583]) ).

thf(5710,plain,
    ! [SV6: $i,SV130: $i] :
      ( ( ! [SY955: $i,SY956: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY956 @ SY955 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
            = SV130 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5584]) ).

thf(5711,plain,
    ! [SV7: $i,SV131: $i] :
      ( ( ! [SY957: $i,SY958: $i,SY959: $i,SY960: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY960 @ SY959 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY960 @ SY959 ) @ SY958 ) @ SY957 ) @ SV131 ) ) @ SY957 ) @ SV7 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY960 @ SY959 ) @ SY958 ) @ SY957 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5585]) ).

thf(5712,plain,
    ! [SV8: $i,SV132: $i] :
      ( ( ! [SY961: $i,SY962: $i,SY963: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY963 @ SY962 ) @ SY961 ) @ SV132 ) @ SV8 ) @ SV132 )
            = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5586]) ).

thf(5713,plain,
    ! [SV9: $i,SV133: $i] :
      ( ( ! [SY964: $i,SY965: $i,SY966: $i,SY967: $i,SY968: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY968 @ SY967 @ SY966 @ SY965 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY964 @ SY968 @ SY966 @ SV133 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SY964 @ SY967 @ SY966 @ ( hAPP @ ( c_Fun_Ocomp @ SY968 @ SY967 @ SY964 @ SY965 ) @ SV133 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5587]) ).

thf(5714,plain,
    ! [SV10: $i,SV134: $i] :
      ( ( ! [SY969: $i,SY970: $i,SY971: $i,SY972: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY972 @ SY971 @ SY970 @ SY969 ) @ SV134 ) @ SV10 )
            = ( hAPP @ SY969 @ ( hAPP @ SV134 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5588]) ).

thf(5715,plain,
    ! [SV11: $i,SV135: $i] :
      ( ( ( hAPP @ ( c_Set_OCollect @ SV135 ) @ SV11 )
        = SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5589]) ).

thf(5716,plain,
    ! [SV12: $i,SV136: $i] :
      ( ( ( hAPP @ ( c_Fun_Oid @ SV136 ) @ SV12 )
        = SV12 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5590]) ).

thf(5717,plain,
    ! [SV13: $i,SV137: $i] :
      ( ( ( hAPP @ ( c_Fun_Oid @ SV137 ) @ SV13 )
        = SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5591]) ).

thf(5718,plain,
    ! [SV14: $i,SV138: $i] :
      ( ( ! [SY973: $i,SY974: $i,SY975: $i,SY976: $i,SY977: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY977 @ SY976 @ SY975 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY977 @ SY974 @ SY976 ) @ SY973 ) @ SV138 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY977 @ SY974 @ SY975 ) @ SY973 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY974 @ SY976 @ SY975 ) @ SV138 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5592]) ).

thf(5719,plain,
    ! [SV15: $i,SV139: $i] :
      ( ( ! [SY978: $i,SY979: $i,SY980: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY980 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY980 @ SY979 ) @ SY978 ) @ SV139 ) ) @ SY978 ) @ SV15 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY980 @ SY979 ) @ SY978 ) @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5593]) ).

thf(5720,plain,
    ! [SV16: $i,SV140: $i] :
      ( ( ! [SY981: $i,SY982: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY982 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY982 ) @ SY981 ) @ SV140 ) ) @ SV16 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY982 ) @ SY981 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY982 ) @ SV140 ) @ SV16 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5594]) ).

thf(5721,plain,
    ! [SV17: $i,SV141: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ SV141 ) @ ( hAPP @ ( c_List_Orev @ SV141 ) @ SV17 ) )
        = SV17 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5595]) ).

thf(5722,plain,
    ! [SV18: $i,SV142: $i] :
      ( ( ! [SY983: $i] :
            ( ( hAPP @ ( c_Relation_Oconverse @ SY983 @ SV142 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV142 @ SY983 ) @ SV18 ) )
            = SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5596]) ).

thf(5723,plain,
    ! [SV19: $i,SV143: $i] :
      ( ( ! [SY984: $i,SY985: $i] :
            ( ( hAPP @ SY985 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY984 @ SY984 ) @ SV143 ) @ SY985 ) @ SV19 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY984 @ SY984 ) @ SV143 ) @ SY985 ) @ ( hAPP @ SY985 @ SV19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5597]) ).

thf(5724,plain,
    ! [SV20: $i,SV144: $i] :
      ( ( ( hAPP @ ( c_COMBI @ SV144 ) @ SV20 )
        = SV20 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5598]) ).

thf(5725,plain,
    ! [SV21: $i,SV145: $i] :
      ( ( ! [SY986: $i,SY987: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY987 @ SY986 ) @ SV145 ) @ SV21 )
            = SV145 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5599]) ).

thf(5726,plain,
    ! [SV22: $i,SV146: $i] :
      ( ( ! [SY988: $i,SY989: $i,SY990: $i,SY991: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY991 @ SY990 @ SY989 ) @ SY988 ) @ SV146 ) @ SV22 )
            = ( hAPP @ SY988 @ ( hAPP @ SV146 @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5600]) ).

thf(5727,plain,
    ! [SV23: $i,SV147: $i] :
      ( ( ! [SY992: $i,SY993: $i,SY994: $i,SY995: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY995 @ SY994 @ SY993 ) @ SY992 ) @ SV147 ) @ SV23 )
            = ( hAPP @ ( hAPP @ SY992 @ SV23 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5601]) ).

thf(5728,plain,
    ! [SV24: $i,SV148: $i] :
      ( ( ! [SY996: $i,SY997: $i,SY998: $i,SY999: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY999 @ SY998 @ SY997 ) @ SY996 ) @ SV148 ) @ SV24 )
            = ( hAPP @ ( hAPP @ SY996 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5602]) ).

thf(5729,plain,
    ! [SV25: $i,SV149: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) )
        | ( SV149 = SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5603]) ).

thf(5730,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5605]) ).

thf(5731,plain,
    ! [SV27: $i] :
      ( ( ( ~ ~ ( hBOOL @ SV27 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5606]) ).

thf(5732,plain,
    ! [SV28: $i,SV150: $i] :
      ( ( ~ ( hBOOL @ SV150 )
        | ~ ( hBOOL @ SV28 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5607]) ).

thf(5733,plain,
    ! [SV29: $i,SV151: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) )
        | ( hBOOL @ SV151 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5608]) ).

thf(5734,plain,
    ! [SV30: $i,SV152: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) )
        | ( hBOOL @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5609]) ).

thf(5735,plain,
    ! [SV31: $i,SV153: $i] :
      ( ( ~ ( hBOOL @ SV153 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5610]) ).

thf(5736,plain,
    ! [SV32: $i,SV154: $i] :
      ( ( ~ ( hBOOL @ SV154 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5611]) ).

thf(5737,plain,
    ! [SV33: $i,SV155: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
        | ( hBOOL @ SV155 )
        | ( hBOOL @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5612]) ).

thf(5738,plain,
    ! [SV34: $i,SV156: $i] :
      ( ( ( hBOOL @ SV156 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV156 ) @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5613]) ).

thf(5739,plain,
    ! [SV35: $i,SV157: $i] :
      ( ( ~ ( hBOOL @ SV157 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5614]) ).

thf(5740,plain,
    ! [SV36: $i,SV158: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
        | ~ ( hBOOL @ SV158 )
        | ( hBOOL @ SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5615]) ).

thf(5741,plain,
    ! [SV37: $i] :
      ( ( SV37
        = ( hAPP @ c_Nat_OSuc @ SV37 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5617]) ).

thf(5742,plain,
    ! [SV38: $i,SV159: $i] :
      ( ( ! [SY1000: $i,SY1001: $i,SY1002: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1002 @ SY1001 @ SY1000 ) @ SV159 ) @ SV38 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1001 @ SV159 ) @ SV38 ) )
                      | ~ ( hBOOL @ ( hAPP @ SY1000 @ SV38 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1001 @ SV159 ) @ SV38 ) )
                        | ~ ( hBOOL @ ( hAPP @ SY1000 @ SV38 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1002 @ SY1001 @ SY1000 ) @ SV159 ) @ SV38 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5618]) ).

thf(5743,plain,
    ! [SV39: $i,SV160: $i] :
      ( ( ! [SY1003: $i,SY1004: $i,SY1005: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1005 ) @ SY1004 ) @ SY1003 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SY1003 ) @ SV39 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1005 @ SV160 ) ) @ SY1004 ) @ SV39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5619]) ).

thf(5744,plain,
    ! [SV40: $i,SV161: $i] :
      ( ( ! [SY1006: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1006 @ SV161 ) ) @ SV40 ) @ SV40 ) )
                  | ~ ( hBOOL @ ( hAPP @ SY1006 @ SV40 ) )
                  | ~ ! [SY1007: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1007 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1006 @ SV161 ) ) @ SY1007 ) @ SV40 ) ) ) )
              | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1006 @ SV40 ) )
                      | ~ ! [SY1008: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1008 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1006 @ SV161 ) ) @ SY1008 ) @ SV40 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1006 @ SV161 ) ) @ SV40 ) @ SV40 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5620]) ).

thf(5745,plain,
    ! [SV41: $i,SV162: $i] :
      ( ( ! [SY1009: $i,SY1010: $i,SY1011: $i,SY1012: $i] :
            ( ( SY1012 != SY1011 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1010 @ SY1009 @ SV162 ) @ SV41 ) @ SY1012 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1010 @ SY1009 @ SV162 ) @ SV41 ) @ SY1011 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5621]) ).

thf(5746,plain,
    ! [SV42: $i,SV163: $i] :
      ( ( ! [SY1013: $i] :
            ( ~ ~ ! [SX3: $i] :
                    ~ ( hBOOL @ ( hAPP @ SY1013 @ SX3 ) )
            | ( SV163
             != ( c_Hilbert__Choice_OEps @ SV42 @ SY1013 ) )
            | ( hBOOL @ ( hAPP @ SY1013 @ SV163 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5622]) ).

thf(5747,plain,
    ! [SV43: $i,SV164: $i] :
      ( ( ! [SY1015: $i,SY1016: $i,SY1017: $i,SY1018: $i,SY1019: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1019 ) @ SY1018 ) @ SY1017 ) @ SY1016 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1019 ) @ SY1015 ) @ SV164 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SY1018 != SY1015 )
                            | ( SY1017 != SV164 ) )
                      | ( SY1016 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1018 != SY1015 )
                              | ( SY1017 != SV164 ) )
                        | ( SY1016 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1019 ) @ SY1018 ) @ SY1017 ) @ SY1016 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1019 ) @ SY1015 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5623]) ).

thf(5748,plain,
    ! [SV44: $i,SV165: $i] :
      ( ( ! [SY1020: $i,SY1021: $i,SY1022: $i,SY1023: $i] :
            ( ~ ( ( SY1023 != SY1022 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1021 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1021 @ SY1020 ) @ SY1023 ) @ SV165 ) ) @ SY1022 ) @ SV44 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1021 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1021 @ SY1020 ) @ SY1022 ) @ SV44 ) ) @ SY1023 ) @ SV165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5624]) ).

thf(5749,plain,
    ! [SV45: $i,SV166: $i] :
      ( ( ! [SY1024: $i,SY1025: $i,SY1026: $i,SY1027: $i] :
            ~ ( ~ ( ( SY1027 != SY1026 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1025 @ SY1024 ) @ SV166 ) @ SY1026 ) @ SV45 ) @ SY1027 )
                    = SV45 ) )
              | ~ ( ~ ( ( SY1027 != SY1026 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1025 @ SY1024 ) @ SV166 ) @ SY1026 ) @ SV45 ) @ SY1027 )
                    = ( hAPP @ SV166 @ SY1027 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5625]) ).

thf(5750,plain,
    ! [SV46: $i,SV167: $i] :
      ( ( ( SV167 != SV46 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV167 ) @ SV46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5626]) ).

thf(5751,plain,
    ! [SV47: $i,SV168: $i] :
      ( ( ! [SY1028: $i,SY1029: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1029 @ SY1028 ) ) @ SV168 ) @ SV47 ) )
                  | ~ ( ( SV47 != SV168 )
                      | ~ ~ ( hBOOL @ ( hAPP @ SY1029 @ SV168 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1029 @ SV168 ) )
                      | ~ ~ ! [SY1030: $i] :
                              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1028 ) @ SV168 ) @ SY1030 ) )
                                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1029 @ SY1028 ) ) @ SY1030 ) @ SV47 ) ) ) ) )
              | ~ ( ~ ( ~ ( ( SV47 != SV168 )
                          | ~ ~ ( hBOOL @ ( hAPP @ SY1029 @ SV168 ) ) )
                      | ~ ( ~ ( hBOOL @ ( hAPP @ SY1029 @ SV168 ) )
                          | ~ ~ ! [SY1031: $i] :
                                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1028 ) @ SV168 ) @ SY1031 ) )
                                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1029 @ SY1028 ) ) @ SY1031 ) @ SV47 ) ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1029 @ SY1028 ) ) @ SV168 ) @ SV47 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5627]) ).

thf(5752,plain,
    ! [SV48: $i,SV169: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV169 )
         != ( hAPP @ c_Nat_OSuc @ SV48 ) )
        | ( SV169 = SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5628]) ).

thf(5753,plain,
    ! [SV49: $i,SV170: $i] :
      ( ( ! [SY1032: $i,SY1033: $i,SY1034: $i,SY1035: $i,SY1036: $i,SY1037: $i,SY1038: $i,SY1039: $i,SY1040: $i] :
            ( ( ( hAPP @ SY1040 @ ( hAPP @ SY1039 @ SY1038 ) )
             != ( hAPP @ SY1037 @ ( hAPP @ SY1036 @ SY1035 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1034 @ SY1033 @ SY1032 @ SY1040 ) @ SY1039 ) @ SY1038 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SY1033 @ SV49 @ SY1037 ) @ SY1036 ) @ SY1035 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5629]) ).

thf(5754,plain,
    ! [SV50: $i,SV171: $i] :
      ( ( ! [SY1041: $i,SY1042: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1042 @ SY1041 ) ) @ SV171 ) @ SV50 ) )
            | ~ ! [SY1043: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1042 ) @ SV171 ) @ SY1043 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1041 ) @ SY1043 ) @ SV50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5630]) ).

thf(5755,plain,
    ! [SV51: $i,SV172: $i] :
      ( ( ! [SY1044: $i,SY1045: $i,SY1046: $i,SY1047: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1047 @ SY1046 ) @ SY1045 ) @ SY1044 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1047 @ SY1046 ) @ SV172 ) @ SV51 ) )
                  | ~ ( ( SY1045 != SV172 )
                      | ( SY1044 != SV51 ) ) )
              | ~ ( ~ ~ ( ( SY1045 != SV172 )
                        | ( SY1044 != SV51 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1047 @ SY1046 ) @ SY1045 ) @ SY1044 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1047 @ SY1046 ) @ SV172 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5631]) ).

thf(5756,plain,
    ! [SV52: $i,SV173: $i] :
      ( ( ! [SY1048: $i,SY1049: $i,SY1050: $i,SY1051: $i,SY1052: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1052 @ SY1051 @ SY1050 @ SY1049 ) @ SY1048 )
             != SV173 )
            | ( ( hAPP @ SY1049 @ ( hAPP @ SY1048 @ SV52 ) )
              = ( hAPP @ SV173 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5632]) ).

thf(5757,plain,
    ! [SV53: $i,SV174: $i] :
      ( ( ! [SY1053: $i,SY1054: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1054 ) @ SY1053 ) @ SV174 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1054 ) @ SV53 ) @ SV174 ) )
                  | ( SY1053 = SV53 ) )
              | ~ ( ( SY1053 != SV53 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1054 ) @ SY1053 ) @ SV174 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1054 ) @ SV53 ) @ SV174 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5633]) ).

thf(5758,plain,
    ! [SV54: $i,SV175: $i] :
      ( ( ! [SY1055: $i,SY1056: $i,SY1057: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1056 ) @ SY1055 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SV175 ) @ SV54 ) )
                  | ~ ! [SY1058: $i] :
                        ~ ( ~ ( ( SY1056
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SV175 ) @ SY1058 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1058 ) @ SY1055 )
                               != SV54 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1056 ) @ SY1058 )
                               != SV175 )
                              | ( SY1055
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1058 ) @ SV54 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1059: $i] :
                          ~ ( ~ ( ( SY1056
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SV175 ) @ SY1059 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1059 ) @ SY1055 )
                                 != SV54 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1056 ) @ SY1059 )
                                 != SV175 )
                                | ( SY1055
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1059 ) @ SV54 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SY1056 ) @ SY1055 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1057 ) @ SV175 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5634]) ).

thf(5759,plain,
    ! [SV55: $i,SV176: $i] :
      ( ( ! [SY1060: $i,SY1061: $i] :
            ( ( SY1061 != SY1060 )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1061 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1060 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1061 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1060 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5635]) ).

thf(5760,plain,
    ! [SV56: $i,SV177: $i] :
      ( ( ! [SY1062: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1062 @ SV177 ) )
            | ( hBOOL @ ( hAPP @ SY1062 @ ( c_Hilbert__Choice_OEps @ SV56 @ SY1062 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5636]) ).

thf(5761,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
                | ( SV178 = SV57 ) )
            | ~ ( ( SV178 != SV57 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5637]) ).

thf(5762,plain,
    ! [SV58: $i,SV179: $i] :
      ( ( ! [SY1063: $i,SY1064: $i,SY1065: $i,SY1066: $i,SY1067: $i] :
            ( ( SY1067 != SY1066 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1065 @ SY1064 @ SY1063 @ SV179 @ SV58 ) @ SY1067 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1065 @ SY1064 @ SY1063 @ SV179 @ SV58 ) @ SY1066 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5638]) ).

thf(5763,plain,
    ! [SV59: $i,SV180: $i] :
      ( ( ! [SY1068: $i,SY1069: $i,SY1070: $i,SY1071: $i,SY1072: $i] :
            ( ~ ( ( SY1072 != SY1071 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1070 @ SY1069 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1070 @ SY1069 ) @ SY1068 ) @ SY1072 ) @ SV180 ) ) @ SY1071 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1070 @ SY1069 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1070 @ SY1069 ) @ SY1068 ) @ SY1071 ) @ SV59 ) ) @ SY1072 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5639]) ).

thf(5764,plain,
    ! [SV60: $i,SV181: $i] :
      ( ( ! [SY1073: $i,SY1074: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1074 ) @ SY1073 ) @ SV181 ) @ SV60 ) )
                  | ( SY1073 = SV60 )
                  | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
              | ~ ( ~ ( ( SY1073 = SV60 )
                      | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1074 ) @ SY1073 ) @ SV181 ) @ SV60 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5640]) ).

thf(5765,plain,
    ! [SV61: $i,SV182: $i] :
      ( ( ! [SY1075: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY1075 @ SV182 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1075 @ SV61 ) ) @ SV182 ) @ SV182 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5641]) ).

thf(5766,plain,
    ! [SV62: $i,SV183: $i] :
      ( ( ! [SY1076: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1076 ) @ SV183 ) @ SV62 )
           != SV62 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5642]) ).

thf(5767,plain,
    ! [SV63: $i,SV184: $i] :
      ( ( ! [SY1077: $i,SY1078: $i,SY1079: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1079 @ SY1078 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1077 ) @ SY1078 ) @ SV184 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1079 @ SY1077 ) ) @ SV184 ) @ SV63 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1079 @ SY1077 ) ) @ SY1078 ) @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5643]) ).

thf(5768,plain,
    ! [SV64: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ SV64 )
        = SV64 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5644]) ).

thf(5769,plain,
    ! [SV65: $i,SV185: $i] :
      ( ( ! [SY1080: $i,SY1081: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1081 @ SY1080 ) ) @ SV185 ) @ SV65 ) )
            | ~ ( ( SV65 != SV185 )
                | ( hBOOL @ ( hAPP @ SY1081 @ SV185 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY1081 @ SV185 ) )
                | ! [SY1082: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1080 ) @ SV185 ) @ SY1082 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1081 @ SY1080 ) ) @ SY1082 ) @ SV65 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5645]) ).

thf(5770,plain,
    ! [SV66: $i,SV186: $i] :
      ( ( ! [SY1083: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1083 @ SV186 ) @ SV66 ) )
                  | ! [SY1084: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1084 ) @ SV66 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1083 @ SV186 ) @ SY1084 ) ) ) )
              | ~ ( ~ ! [SY1085: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1085 ) @ SV66 ) )
                        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1083 @ SV186 ) @ SY1085 ) ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1083 @ SV186 ) @ SV66 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5646]) ).

thf(5771,plain,
    ! [SV67: $i,SV187: $i] :
      ( ( ! [SY1086: $i] :
            ( ~ ( c_Predicate_Oreflp @ SY1086 @ SV187 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SV187 @ SV67 ) @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5647]) ).

thf(5772,plain,
    ! [SV68: $i,SV188: $i] :
      ( ( ! [SY1087: $i,SY1088: $i,SY1089: $i,SY1090: $i,SY1091: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1091 @ SY1090 @ SY1089 @ SY1088 @ SY1087 @ SV188 @ SV68 )
                  | ~ ! [SY1092: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1088 @ SV188 ) @ SY1092 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1087 @ SY1092 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY1093: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1088 @ SV188 ) @ SY1093 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1087 @ SY1093 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY1091 @ SY1090 @ SY1089 @ SY1088 @ SY1087 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5648]) ).

thf(5773,plain,
    ! [SV69: $i,SV189: $i] :
      ( ( ! [SY1094: $i,SY1095: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1095 @ SY1094 ) @ SV189 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1094 @ SV69 ) @ SV189 ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1095 @ SY1094 ) @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5649]) ).

thf(5774,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
                 != ( hAPP @ c_Nat_OSuc @ SV70 ) )
                | ( SV190 = SV70 ) )
            | ~ ( ( SV190 != SV70 )
                | ( ( hAPP @ c_Nat_OSuc @ SV190 )
                  = ( hAPP @ c_Nat_OSuc @ SV70 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5650]) ).

thf(5775,plain,
    ! [SV71: $i,SV191: $i] :
      ( ( ! [SY1096: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1096 @ SV191 ) @ SV71 ) )
                  | ! [SY1097: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1097 ) @ SV71 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1096 @ SV191 ) @ SY1097 ) ) ) )
              | ~ ( ~ ! [SY1098: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1098 ) @ SV71 ) )
                        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1096 @ SV191 ) @ SY1098 ) ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1096 @ SV191 ) @ SV71 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5651]) ).

thf(5776,plain,
    ! [SV72: $i,SV192: $i] :
      ( ( ! [SY1099: $i,SY1100: $i,SY1101: $i] :
            ( ( ( hAPP @ SY1101 @ SY1100 )
             != SY1099 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SY1101 ) @ SY1100 ) @ SY1099 )
              = SY1101 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5652]) ).

thf(5777,plain,
    ! [SV73: $i,SV193: $i] :
      ( ( ! [SY1102: $i,SY1103: $i,SY1104: $i,SY1105: $i] :
            ( ~ ( ( SY1105 != SY1104 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1103 @ SY1102 ) @ SV193 ) @ SY1104 ) @ SV73 ) @ SY1105 )
              = ( hAPP @ SV193 @ SY1105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5653]) ).

thf(5778,plain,
    ! [SV74: $i,SV194: $i] :
      ( ( ! [SY1106: $i,SY1107: $i] :
            ( ( SY1107 != SY1106 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1107 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1106 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1106 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1107 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5654]) ).

thf(5779,plain,
    ! [SV75: $i,SV195: $i] :
      ( ( ! [SY1108: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1108 ) @ SV195 )
                   != SV75 )
                  | ( SV195
                    = ( hAPP @ ( c_List_Orev @ SY1108 ) @ SV75 ) ) )
              | ~ ( ( SV195
                   != ( hAPP @ ( c_List_Orev @ SY1108 ) @ SV75 ) )
                  | ( ( hAPP @ ( c_List_Orev @ SY1108 ) @ SV195 )
                    = SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5655]) ).

thf(5780,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
                | ! [SY760: $i,SY761: $i] :
                    ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                          | ( ( hAPP @ SV76 @ SY760 )
                            = ( hAPP @ SV76 @ SY761 ) ) )
                      | ~ ( ( ( hAPP @ SV76 @ SY760 )
                           != ( hAPP @ SV76 @ SY761 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
            | ~ ( ~ ! [SY762: $i,SY763: $i] :
                      ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                            | ( ( hAPP @ SV76 @ SY762 )
                              = ( hAPP @ SV76 @ SY763 ) ) )
                        | ~ ( ( ( hAPP @ SV76 @ SY762 )
                             != ( hAPP @ SV76 @ SY763 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) )
                | ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5656]) ).

thf(5781,plain,
    ! [SV77: $i,SV197: $i] :
      ( ( ! [SY1113: $i,SY1114: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1114 @ SY1113 @ SV197 ) @ SV77 ) )
                  | ~ ! [SY1115: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
              | ~ ( ~ ~ ! [SY1116: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1114 @ SY1113 @ SV197 ) @ SV77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5657]) ).

thf(5782,plain,
    ! [SV78: $i,SV198: $i] :
      ( ( ! [SY1117: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1117 ) @ SV198 )
                   != ( hAPP @ ( c_Option_Ooption_OSome @ SY1117 ) @ SV78 ) )
                  | ( SV198 = SV78 ) )
              | ~ ( ( SV198 != SV78 )
                  | ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1117 ) @ SV198 )
                    = ( hAPP @ ( c_Option_Ooption_OSome @ SY1117 ) @ SV78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5658]) ).

thf(5783,plain,
    ! [SV79: $i,SV199: $i] :
      ( ( ! [SY1118: $i,SY1119: $i,SY1120: $i,SY1121: $i,SY1122: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1122 @ SY1121 @ SY1120 @ SY1119 @ SY1118 )
            | ~ ( ~ ( ( ( hAPP @ SY1120 @ SV199 )
                     != ( hAPP @ SY1120 @ SV79 ) )
                    | ( SV199 = SV79 ) )
                | ~ ( ( SV199 != SV79 )
                    | ( ( hAPP @ SY1120 @ SV199 )
                      = ( hAPP @ SY1120 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5659]) ).

thf(5784,plain,
    ! [SV80: $i,SV200: $i] :
      ( ( ! [SY1123: $i,SY1124: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1124 @ SY1123 @ SV200 )
            | ( ( hAPP @ ( hAPP @ SY1123 @ SV80 ) @ SV80 )
              = SV80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5660]) ).

thf(5785,plain,
    ! [SV81: $i,SV201: $i] :
      ( ( ! [SY1125: $i,SY1126: $i,SY1127: $i,SY1128: $i,SY1129: $i,SY1130: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1130 @ SY1129 @ SY1128 @ SY1127 ) @ SY1126 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1125 @ SY1129 @ SY1128 @ SV201 ) @ SV81 ) )
            | ! [SY1131: $i] :
                ( ( hAPP @ SY1127 @ ( hAPP @ SY1126 @ SY1131 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1131 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5661]) ).

thf(5786,plain,
    ! [SV82: $i,SV202: $i] :
      ( ( ! [SY1132: $i,SY1133: $i,SY1134: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1134 @ SY1133 @ SY1132 ) ) @ SV202 ) @ SV82 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1134 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1133 ) @ SV202 ) @ SV82 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1134 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1132 ) @ SV202 ) @ SV82 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1134 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1133 ) @ SV202 ) @ SV82 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1134 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1132 ) @ SV202 ) @ SV82 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1134 @ SY1133 @ SY1132 ) ) @ SV202 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5662]) ).

thf(5787,plain,
    ! [SV83: $i,SV203: $i] :
      ( ( ! [SY1135: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1135 @ SV203 )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV83 ) @ SV83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5663]) ).

thf(5788,plain,
    ! [SV84: $i,SV204: $i] :
      ( ( ! [SY1136: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1136 ) @ SV204 ) @ SV84 ) )
                  | ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1136 ) @ SV204 ) @ SV84 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5664]) ).

thf(5789,plain,
    ! [SV85: $i,SV205: $i] :
      ( ( ! [SY1137: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1137 ) @ SV205 ) @ SV85 ) )
            | ~ ! [SY1138: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1137 ) @ SV205 ) @ SY1138 ) @ SV85 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5665]) ).

thf(5790,plain,
    ! [SV86: $i,SV206: $i] :
      ( ( ! [SY1139: $i,SY1140: $i,SY1141: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1141 @ SY1140 ) @ SY1139 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SY1141 ) @ SY1140 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5666]) ).

thf(5791,plain,
    ! [SV87: $i,SV207: $i] :
      ( ( ! [SY1142: $i,SY1143: $i,SY1144: $i,SY1145: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1145 @ SY1144 @ SY1143 @ SY1142 @ SV207 )
            | ( ( hAPP @ SY1142 @ ( hAPP @ SY1143 @ SV87 ) )
              = SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5667]) ).

thf(5792,plain,
    ! [SV88: $i,SV208: $i] :
      ( ( ! [SY1146: $i,SY1147: $i,SY1148: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1148 @ SY1147 @ SY1146 )
            | ( ( hAPP @ ( hAPP @ SY1146 @ SV208 ) @ ( hAPP @ ( hAPP @ SY1146 @ SV208 ) @ SV88 ) )
              = ( hAPP @ ( hAPP @ SY1146 @ SV208 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5668]) ).

thf(5793,plain,
    ! [SV89: $i,SV209: $i] :
      ( ( ! [SY1149: $i,SY1150: $i,SY1151: $i,SY1152: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1152 ) @ SY1151 ) @ SY1150 )
             != SY1149 )
            | ( SV209
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1152 ) @ SY1150 ) @ SV89 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1152 ) @ SY1151 ) @ SV209 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1152 ) @ SY1149 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5669]) ).

thf(5794,plain,
    ! [SV90: $i] :
      ( ( ( ~ ! [SY817: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY817 ) )
                | ( SV90 = SY817 ) ) )
        = $true )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5670]) ).

thf(5795,plain,
    ! [SV91: $i,SV210: $i] :
      ( ( ! [SY1153: $i,SY1154: $i,SY1155: $i,SY1156: $i,SY1157: $i,SY1158: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1158 @ SY1157 ) @ SY1156 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1155 @ SY1156 ) @ SY1154 ) )
            | ( c_Predicate_Opred__comp @ SY1153 @ SV210 @ SV91 @ SY1158 @ SY1155 @ SY1157 @ SY1154 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5671]) ).

thf(5796,plain,
    ! [SV92: $i,SV211: $i] :
      ( ( ! [SY1159: $i,SY1160: $i,SY1161: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY1161 @ SY1160 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1159 ) @ SY1160 ) @ SV211 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1161 @ SV92 @ SY1159 ) ) @ SY1160 ) @ SV211 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5672]) ).

thf(5797,plain,
    ! [SV93: $i,SV212: $i] :
      ( ( ! [SY1162: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1162 ) @ SV212 ) @ SV93 ) )
                  | ~ ! [SY1163: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1162 ) @ SV212 ) @ SY1163 ) @ SV93 ) ) )
              | ~ ( ~ ~ ! [SY1164: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1162 ) @ SV212 ) @ SY1164 ) @ SV93 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1162 ) @ SV212 ) @ SV93 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5673]) ).

thf(5798,plain,
    ! [SV94: $i,SV213: $i] :
      ( ( ! [SY1165: $i,SY1166: $i,SY1167: $i,SY1168: $i] :
            ~ ( ~ ( ( SY1168 != SY1167 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1166 @ SY1165 ) @ SV213 ) @ SY1167 ) @ SV94 ) @ SY1168 )
                    = SV94 ) )
              | ~ ( ~ ( ( SY1168 != SY1167 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1166 @ SY1165 ) @ SV213 ) @ SY1167 ) @ SV94 ) @ SY1168 )
                    = ( hAPP @ SV213 @ SY1168 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5674]) ).

thf(5799,plain,
    ! [SV95: $i,SV214: $i] :
      ( ( ! [SY1169: $i,SY1170: $i,SY1171: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1171 @ SY1170 ) @ SY1169 ) @ SV214 ) @ SV95 )
                   != SY1169 )
                  | ( ( hAPP @ SY1169 @ SV214 )
                    = SV95 ) )
              | ~ ( ( ( hAPP @ SY1169 @ SV214 )
                   != SV95 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1171 @ SY1170 ) @ SY1169 ) @ SV214 ) @ SV95 )
                    = SY1169 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5675]) ).

thf(5800,plain,
    ! [SV96: $i,SV215: $i] :
      ( ( ! [SY1172: $i,SY1173: $i] :
            ( ( SY1173 != SY1172 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1173 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1172 ) @ SV96 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1172 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1173 ) @ SV96 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5676]) ).

thf(5801,plain,
    ! [SV97: $i,SV216: $i] :
      ( ( ! [SY1174: $i,SY1175: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1175 ) @ SY1174 ) @ SV216 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1175 ) @ SY1174 ) @ SV97 ) )
                  | ( SV216 = SV97 ) )
              | ~ ( ( SV216 != SV97 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1175 ) @ SY1174 ) @ SV216 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1175 ) @ SY1174 ) @ SV97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5677]) ).

thf(5802,plain,
    ! [SV98: $i,SV217: $i] :
      ( ( ! [SY1176: $i,SY1177: $i] :
            ( ( SY1177 != SY1176 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SY1176 ) @ SV98 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SY1177 ) @ SV98 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5678]) ).

thf(5803,plain,
    ! [SV99: $i,SV218: $i] :
      ( ( ~ ! [SY1178: $i] :
              ( ( hAPP @ SV218 @ SY1178 )
              = ( hAPP @ SV99 @ SY1178 ) )
        | ( SV218 = SV99 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5679]) ).

thf(5804,plain,
    ! [SV100: $i,SV219: $i] :
      ( ( ! [SY1179: $i,SY1180: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1180 ) @ SY1179 ) @ SV219 ) @ SV100 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1180 ) @ SY1179 ) @ SV100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5680]) ).

thf(5805,plain,
    ! [SV101: $i,SV220: $i] :
      ( ( ! [SY1181: $i] :
            ~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1181 @ SX3 ) )
                  | ! [SY1183: $i,SY1184: $i] : ( hBOOL @ ( hAPP @ SY1181 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1183 ) @ SY1184 ) ) ) )
              | ~ ( ~ ! [SY1185: $i,SY1186: $i] : ( hBOOL @ ( hAPP @ SY1181 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1185 ) @ SY1186 ) ) )
                  | ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1181 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5681]) ).

thf(5806,plain,
    ! [SV102: $i,SV221: $i] :
      ( ( ! [SY1188: $i,SY1189: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1189 @ SY1188 ) @ SV221 ) )
            | ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1189 @ SY1188 ) @ SV102 ) )
            | ( SV221 = SV102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5682]) ).

thf(5807,plain,
    ! [SV103: $i,SV222: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV222 ) @ SV103 ) )
        | ( SV103 = SV222 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5683]) ).

thf(5808,plain,
    ! [SV104: $i,SV223: $i] :
      ( ( ! [SY1190: $i,SY1191: $i,SY1192: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1192 @ SY1191 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1190 ) @ SY1191 ) @ SV223 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1192 @ SY1190 @ SV104 ) ) @ SY1191 ) @ SV223 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5684]) ).

thf(5809,plain,
    ! [SV105: $i,SV224: $i] :
      ( ( ~ ~ ! [SY1193: $i] :
                ~ ( hBOOL @ ( hAPP @ SV224 @ SY1193 ) )
        | ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5685]) ).

thf(5810,plain,
    ! [SV106: $i,SV225: $i] :
      ( ( ! [SY1194: $i,SY1195: $i,SY1196: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1196 @ SY1195 @ SY1194 ) @ SV225 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SY1194 @ SV106 ) ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SY1194 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1196 @ SY1195 @ SY1194 ) @ SV225 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5686]) ).

thf(5811,plain,
    ! [SV107: $i,SV226: $i] :
      ( ( ! [SY1197: $i,SY1198: $i,SY1199: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1199 @ SY1198 @ SY1197 ) ) @ SV226 ) @ SV107 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1199 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1198 ) @ SV226 ) @ SV107 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1199 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1197 ) @ SV226 ) @ SV107 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1199 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1198 ) @ SV226 ) @ SV107 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1199 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1197 ) @ SV226 ) @ SV107 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1199 @ SY1198 @ SY1197 ) ) @ SV226 ) @ SV107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5687]) ).

thf(5812,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
                 != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
                | ( SV227 = SV108 ) )
            | ~ ( ( SV227 != SV108 )
                | ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
                  = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5688]) ).

thf(5813,plain,
    ! [SV109: $i,SV228: $i] :
      ( ( ! [SY1200: $i,SY1201: $i,SY1202: $i,SY1203: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1203 @ SY1202 ) @ SY1201 ) @ SY1200 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1203 @ SY1202 ) @ SV228 ) @ SV109 ) )
            | ~ ( ( SY1201 != SV228 )
                | ( SY1200 != SV109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5689]) ).

thf(5814,plain,
    ! [SV110: $i,SV229: $i] :
      ( ( ! [SY1204: $i,SY1205: $i,SY1206: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1206 @ SY1205 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1205 @ SY1204 ) @ SV229 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1205 @ SV229 ) @ SV110 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY1205 @ SY1204 ) @ SV110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5690]) ).

thf(5815,plain,
    ! [SV111: $i,SV230: $i] :
      ( ( ! [SY1207: $i,SY1208: $i,SY1209: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1209 @ SY1208 ) @ SY1207 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SY1209 ) @ SY1207 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5691]) ).

thf(5816,plain,
    ! [SV112: $i,SV231: $i] :
      ( ( ~ ~ ! [SY1210: $i] :
                ~ ( hBOOL @ ( hAPP @ SV231 @ SY1210 ) )
        | ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5692]) ).

thf(5817,plain,
    ! [SV113: $i,SV232: $i] :
      ( ( ! [SY1211: $i,SY1212: $i,SY1213: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1213 ) @ SY1212 ) @ SY1211 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1213 ) @ SV232 ) @ SV113 ) )
                  | ~ ( ( SY1212 != SV232 )
                      | ( SY1211 != SV113 ) ) )
              | ~ ( ~ ~ ( ( SY1212 != SV232 )
                        | ( SY1211 != SV113 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1213 ) @ SY1212 ) @ SY1211 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1213 ) @ SV232 ) @ SV113 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5693]) ).

thf(5818,plain,
    ! [SV114: $i,SV233: $i] :
      ( ( ! [SY1214: $i,SY1215: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1215 ) @ SY1214 ) @ SV233 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1215 ) @ SY1214 ) @ SV114 ) )
            | ( SV114 = SV233 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5694]) ).

thf(5819,plain,
    ! [SV115: $i,SV234: $i] :
      ( ( ! [SY1216: $i] :
            ( SY1216
           != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV234 ) @ SV115 ) @ SY1216 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5695]) ).

thf(5820,plain,
    ! [SV116: $i,SV235: $i] :
      ( ( ! [SY1217: $i,SY1218: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1218 @ SY1217 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1217 @ SV235 ) @ SV116 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY1217 @ SV116 ) @ SV235 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5696]) ).

thf(5821,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
                | ( SV236 = SV117 ) )
            | ~ ( ( SV236 != SV117 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5697]) ).

thf(5822,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
                | ~ ! [SY1219: $i] :
                      ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
            | ~ ( ~ ~ ! [SY1220: $i] :
                        ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) )
                | ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5698]) ).

thf(5823,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
                 != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
                | ( SV238 = SV119 ) )
            | ~ ( ( SV238 != SV119 )
                | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
                  = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5699]) ).

thf(5824,plain,
    ! [SV120: $i,SV239: $i] :
      ( ( ! [SY1221: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1221 ) @ SV239 )
                   != ( hAPP @ ( c_List_Orev @ SY1221 ) @ SV120 ) )
                  | ( SV239 = SV120 ) )
              | ~ ( ( SV239 != SV120 )
                  | ( ( hAPP @ ( c_List_Orev @ SY1221 ) @ SV239 )
                    = ( hAPP @ ( c_List_Orev @ SY1221 ) @ SV120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5700]) ).

thf(5825,plain,
    ! [SV121: $i,SV240: $i] :
      ( ( ! [SY1222: $i,SY1223: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1223 @ SY1222 @ SV240 ) @ SV121 ) )
                  | ~ ! [SY1224: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
              | ~ ( ~ ~ ! [SY1225: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1223 @ SY1222 @ SV240 ) @ SV121 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5701]) ).

thf(5826,plain,
    ! [SV122: $i,SV241: $i] :
      ( ( ! [SY1226: $i,SY1227: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1227 @ SY1226 ) ) @ SV241 ) @ SV122 ) )
                  | ~ ! [SY1228: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1227 ) @ SV241 ) @ SY1228 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1226 ) @ SY1228 ) @ SV122 ) ) ) )
              | ~ ( ~ ~ ! [SY1229: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1227 ) @ SV241 ) @ SY1229 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1226 ) @ SY1229 ) @ SV122 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1227 @ SY1226 ) ) @ SV241 ) @ SV122 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5702]) ).

thf(5827,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
                 != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
                | ( SV242 = SV123 ) )
            | ~ ( ( SV242 != SV123 )
                | ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
                  = ( hAPP @ c_Int_ORep__Integ @ SV123 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5703]) ).

thf(5828,plain,
    ! [SV124: $i,SV243: $i] :
      ( ( ! [SY1230: $i,SY1231: $i,SY1232: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1232 @ SY1231 @ SY1230 ) ) @ SV243 ) @ SV124 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY1232 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1231 ) @ SV243 ) @ SV124 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1232 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1230 ) @ SV243 ) @ SV124 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5704]) ).

thf(5829,plain,
    ! [SV125: $i,SV244: $i] :
      ( ( ! [SY1233: $i,SY1234: $i,SY1235: $i,SY1236: $i,SY1237: $i,SY1238: $i,SY1239: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1239 @ SY1238 @ SY1237 @ SY1236 ) @ SY1235 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1234 @ SY1238 @ SY1237 @ SY1233 ) @ SV244 ) )
            | ( ( hAPP @ SY1236 @ ( hAPP @ SY1235 @ SV125 ) )
              = ( hAPP @ SY1233 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5705]) ).

thf(5830,plain,
    ! [SV126: $i,SV245: $i] :
      ( ( ! [SY1240: $i,SY1241: $i,SY1242: $i,SY1243: $i,SY1244: $i,SY1245: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1245 ) @ SY1244 ) @ SY1243 ) @ SY1242 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1241 ) @ SY1240 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY947: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1245 ) @ SY1244 ) @ SY947 ) @ SY1242 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1241 ) @ SY1240 ) @ SY947 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5706]) ).

thf(5831,plain,
    ! [SV3: $i,SV127: $i,SV246: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ SV3 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5707]) ).

thf(5832,plain,
    ! [SV4: $i,SV128: $i,SV247: $i] :
      ( ( ! [SY1247: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1247 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1247 ) @ SV128 ) @ SV4 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1247 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1247 ) @ SV247 ) @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5708]) ).

thf(5833,plain,
    ! [SV5: $i,SV129: $i,SV248: $i] :
      ( ( ! [SY1248: $i,SY1249: $i,SY1250: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1250 @ SY1249 @ SY1248 @ SV248 ) @ SV129 ) @ SV5 )
            = ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5709]) ).

thf(5834,plain,
    ! [SV6: $i,SV130: $i,SV249: $i] :
      ( ( ! [SY1251: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1251 @ SV249 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
            = SV130 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5710]) ).

thf(5835,plain,
    ! [SV7: $i,SV131: $i,SV250: $i] :
      ( ( ! [SY1252: $i,SY1253: $i,SY1254: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1254 @ SY1253 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1254 @ SY1253 ) @ SY1252 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1254 @ SY1253 ) @ SY1252 ) @ SV250 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5711]) ).

thf(5836,plain,
    ! [SV8: $i,SV132: $i,SV251: $i] :
      ( ( ! [SY1255: $i,SY1256: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1256 @ SY1255 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
            = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5712]) ).

thf(5837,plain,
    ! [SV9: $i,SV133: $i,SV252: $i] :
      ( ( ! [SY1257: $i,SY1258: $i,SY1259: $i,SY1260: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1260 @ SY1259 @ SY1258 @ SY1257 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1260 @ SY1258 @ SV133 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1259 @ SY1258 @ ( hAPP @ ( c_Fun_Ocomp @ SY1260 @ SY1259 @ SV252 @ SY1257 ) @ SV133 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5713]) ).

thf(5838,plain,
    ! [SV10: $i,SV134: $i,SV253: $i] :
      ( ( ! [SY1261: $i,SY1262: $i,SY1263: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1263 @ SY1262 @ SY1261 @ SV253 ) @ SV134 ) @ SV10 )
            = ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5714]) ).

thf(5839,plain,
    ! [SV14: $i,SV138: $i,SV254: $i] :
      ( ( ! [SY1264: $i,SY1265: $i,SY1266: $i,SY1267: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1267 @ SY1266 @ SY1265 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1267 @ SY1264 @ SY1266 ) @ SV254 ) @ SV138 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1267 @ SY1264 @ SY1265 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1264 @ SY1266 @ SY1265 ) @ SV138 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5718]) ).

thf(5840,plain,
    ! [SV15: $i,SV139: $i,SV255: $i] :
      ( ( ! [SY1268: $i,SY1269: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1269 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1269 @ SY1268 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1269 @ SY1268 ) @ SV255 ) @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5719]) ).

thf(5841,plain,
    ! [SV16: $i,SV140: $i,SV256: $i] :
      ( ( ! [SY1270: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1270 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1270 ) @ SV256 ) @ SV140 ) ) @ SV16 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1270 ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1270 ) @ SV140 ) @ SV16 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5720]) ).

thf(5842,plain,
    ! [SV18: $i,SV142: $i,SV257: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ SV257 @ SV142 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV142 @ SV257 ) @ SV18 ) )
        = SV18 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5722]) ).

thf(5843,plain,
    ! [SV19: $i,SV143: $i,SV258: $i] :
      ( ( ! [SY1271: $i] :
            ( ( hAPP @ SY1271 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SY1271 ) @ SV19 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SY1271 ) @ ( hAPP @ SY1271 @ SV19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5723]) ).

thf(5844,plain,
    ! [SV21: $i,SV145: $i,SV259: $i] :
      ( ( ! [SY1272: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1272 @ SV259 ) @ SV145 ) @ SV21 )
            = SV145 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5725]) ).

thf(5845,plain,
    ! [SV22: $i,SV146: $i,SV260: $i] :
      ( ( ! [SY1273: $i,SY1274: $i,SY1275: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1275 @ SY1274 @ SY1273 ) @ SV260 ) @ SV146 ) @ SV22 )
            = ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5726]) ).

thf(5846,plain,
    ! [SV23: $i,SV147: $i,SV261: $i] :
      ( ( ! [SY1276: $i,SY1277: $i,SY1278: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1278 @ SY1277 @ SY1276 ) @ SV261 ) @ SV147 ) @ SV23 )
            = ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5727]) ).

thf(5847,plain,
    ! [SV24: $i,SV148: $i,SV262: $i] :
      ( ( ! [SY1279: $i,SY1280: $i,SY1281: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1281 @ SY1280 @ SY1279 ) @ SV262 ) @ SV148 ) @ SV24 )
            = ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5728]) ).

thf(5848,plain,
    ! [SV25: $i,SV149: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) ) )
        = $true )
      | ( ( SV149 = SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5729]) ).

thf(5849,plain,
    ! [SV26: $i] :
      ( ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
        = $false )
      | ( ( ~ ( hBOOL @ SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5730]) ).

thf(5850,plain,
    ! [SV27: $i] :
      ( ( ( ~ ( hBOOL @ SV27 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5731]) ).

thf(5851,plain,
    ! [SV28: $i,SV150: $i] :
      ( ( ( ~ ( hBOOL @ SV150 )
          | ~ ( hBOOL @ SV28 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5732]) ).

thf(5852,plain,
    ! [SV29: $i,SV151: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) ) )
        = $true )
      | ( ( hBOOL @ SV151 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5733]) ).

thf(5853,plain,
    ! [SV30: $i,SV152: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) ) )
        = $true )
      | ( ( hBOOL @ SV30 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5734]) ).

thf(5854,plain,
    ! [SV31: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5735]) ).

thf(5855,plain,
    ! [SV32: $i,SV154: $i] :
      ( ( ( ~ ( hBOOL @ SV154 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5736]) ).

thf(5856,plain,
    ! [SV33: $i,SV155: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
          | ( hBOOL @ SV155 ) )
        = $true )
      | ( ( hBOOL @ SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5737]) ).

thf(5857,plain,
    ! [SV34: $i,SV156: $i] :
      ( ( ( hBOOL @ SV156 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV156 ) @ SV34 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5738]) ).

thf(5858,plain,
    ! [SV35: $i,SV157: $i] :
      ( ( ( ~ ( hBOOL @ SV157 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5739]) ).

thf(5859,plain,
    ! [SV36: $i,SV158: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
          | ~ ( hBOOL @ SV158 ) )
        = $true )
      | ( ( hBOOL @ SV36 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5740]) ).

thf(5860,plain,
    ! [SV38: $i,SV159: $i,SV263: $i] :
      ( ( ! [SY1282: $i,SY1283: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1283 @ SY1282 @ SV263 ) @ SV159 ) @ SV38 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1282 @ SV159 ) @ SV38 ) )
                      | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1282 @ SV159 ) @ SV38 ) )
                        | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1283 @ SY1282 @ SV263 ) @ SV159 ) @ SV38 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5742]) ).

thf(5861,plain,
    ! [SV39: $i,SV160: $i,SV264: $i] :
      ( ( ! [SY1284: $i,SY1285: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1285 ) @ SY1284 ) @ SV264 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1285 @ SV160 ) ) @ SY1284 ) @ SV39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5743]) ).

thf(5862,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
                | ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
                | ~ ! [SY1286: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
                    | ~ ! [SY1287: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5744]) ).

thf(5863,plain,
    ! [SV41: $i,SV162: $i,SV266: $i] :
      ( ( ! [SY1288: $i,SY1289: $i,SY1290: $i] :
            ( ( SY1290 != SY1289 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1288 @ SV266 @ SV162 ) @ SV41 ) @ SY1290 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1288 @ SV266 @ SV162 ) @ SV41 ) @ SY1289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5745]) ).

thf(5864,plain,
    ! [SV42: $i,SV163: $i,SV267: $i] :
      ( ( ~ ~ ! [SY1291: $i] :
                ~ ( hBOOL @ ( hAPP @ SV267 @ SY1291 ) )
        | ( SV163
         != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
        | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5746]) ).

thf(5865,plain,
    ! [SV43: $i,SV164: $i,SV268: $i] :
      ( ( ! [SY1292: $i,SY1293: $i,SY1294: $i,SY1295: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1295 ) @ SY1294 ) @ SY1293 ) @ SY1292 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1295 ) @ SV268 ) @ SV164 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SY1294 != SV268 )
                            | ( SY1293 != SV164 ) )
                      | ( SY1292 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1294 != SV268 )
                              | ( SY1293 != SV164 ) )
                        | ( SY1292 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1295 ) @ SY1294 ) @ SY1293 ) @ SY1292 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1295 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5747]) ).

thf(5866,plain,
    ! [SV44: $i,SV165: $i,SV269: $i] :
      ( ( ! [SY1296: $i,SY1297: $i,SY1298: $i] :
            ( ~ ( ( SY1298 != SY1297 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1296 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1296 @ SV269 ) @ SY1298 ) @ SV165 ) ) @ SY1297 ) @ SV44 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1296 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1296 @ SV269 ) @ SY1297 ) @ SV44 ) ) @ SY1298 ) @ SV165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5748]) ).

thf(5867,plain,
    ! [SV45: $i,SV166: $i,SV270: $i] :
      ( ( ! [SY1299: $i,SY1300: $i,SY1301: $i] :
            ~ ( ~ ( ( SY1301 != SY1300 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1299 @ SV270 ) @ SV166 ) @ SY1300 ) @ SV45 ) @ SY1301 )
                    = SV45 ) )
              | ~ ( ~ ( ( SY1301 != SY1300 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1299 @ SV270 ) @ SV166 ) @ SY1300 ) @ SV45 ) @ SY1301 )
                    = ( hAPP @ SV166 @ SY1301 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5749]) ).

thf(5868,plain,
    ! [SV46: $i,SV167: $i] :
      ( ( ( SV167 != SV46 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV167 ) @ SV46 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5750]) ).

thf(5869,plain,
    ! [SV47: $i,SV168: $i,SV271: $i] :
      ( ( ! [SY1302: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1302 @ SV271 ) ) @ SV168 ) @ SV47 ) )
                  | ~ ( ( SV47 != SV168 )
                      | ~ ~ ( hBOOL @ ( hAPP @ SY1302 @ SV168 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1302 @ SV168 ) )
                      | ~ ~ ! [SY1303: $i] :
                              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1303 ) )
                                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1302 @ SV271 ) ) @ SY1303 ) @ SV47 ) ) ) ) )
              | ~ ( ~ ( ~ ( ( SV47 != SV168 )
                          | ~ ~ ( hBOOL @ ( hAPP @ SY1302 @ SV168 ) ) )
                      | ~ ( ~ ( hBOOL @ ( hAPP @ SY1302 @ SV168 ) )
                          | ~ ~ ! [SY1304: $i] :
                                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1304 ) )
                                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1302 @ SV271 ) ) @ SY1304 ) @ SV47 ) ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1302 @ SV271 ) ) @ SV168 ) @ SV47 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5751]) ).

thf(5870,plain,
    ! [SV48: $i,SV169: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV169 )
         != ( hAPP @ c_Nat_OSuc @ SV48 ) )
        = $true )
      | ( ( SV169 = SV48 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5752]) ).

thf(5871,plain,
    ! [SV49: $i,SV170: $i,SV272: $i] :
      ( ( ! [SY1305: $i,SY1306: $i,SY1307: $i,SY1308: $i,SY1309: $i,SY1310: $i,SY1311: $i,SY1312: $i] :
            ( ( ( hAPP @ SY1312 @ ( hAPP @ SY1311 @ SY1310 ) )
             != ( hAPP @ SY1309 @ ( hAPP @ SY1308 @ SY1307 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1306 @ SY1305 @ SV272 @ SY1312 ) @ SY1311 ) @ SY1310 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SY1305 @ SV49 @ SY1309 ) @ SY1308 ) @ SY1307 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5753]) ).

thf(5872,plain,
    ! [SV50: $i,SV171: $i,SV273: $i] :
      ( ( ! [SY1313: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1313 @ SV273 ) ) @ SV171 ) @ SV50 ) )
            | ~ ! [SY1314: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1313 ) @ SV171 ) @ SY1314 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SY1314 ) @ SV50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5754]) ).

thf(5873,plain,
    ! [SV51: $i,SV172: $i,SV274: $i] :
      ( ( ! [SY1315: $i,SY1316: $i,SY1317: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1317 @ SY1316 ) @ SY1315 ) @ SV274 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1317 @ SY1316 ) @ SV172 ) @ SV51 ) )
                  | ~ ( ( SY1315 != SV172 )
                      | ( SV274 != SV51 ) ) )
              | ~ ( ~ ~ ( ( SY1315 != SV172 )
                        | ( SV274 != SV51 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1317 @ SY1316 ) @ SY1315 ) @ SV274 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1317 @ SY1316 ) @ SV172 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5755]) ).

thf(5874,plain,
    ! [SV52: $i,SV173: $i,SV275: $i] :
      ( ( ! [SY1318: $i,SY1319: $i,SY1320: $i,SY1321: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1321 @ SY1320 @ SY1319 @ SY1318 ) @ SV275 )
             != SV173 )
            | ( ( hAPP @ SY1318 @ ( hAPP @ SV275 @ SV52 ) )
              = ( hAPP @ SV173 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5756]) ).

thf(5875,plain,
    ! [SV53: $i,SV174: $i,SV276: $i] :
      ( ( ! [SY1322: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1322 ) @ SV276 ) @ SV174 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1322 ) @ SV53 ) @ SV174 ) )
                  | ( SV276 = SV53 ) )
              | ~ ( ( SV276 != SV53 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1322 ) @ SV276 ) @ SV174 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1322 ) @ SV53 ) @ SV174 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5757]) ).

thf(5876,plain,
    ! [SV54: $i,SV175: $i,SV277: $i] :
      ( ( ! [SY1323: $i,SY1324: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1323 ) @ SV277 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SV175 ) @ SV54 ) )
                  | ~ ! [SY1325: $i] :
                        ~ ( ~ ( ( SY1323
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SV175 ) @ SY1325 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1325 ) @ SV277 )
                               != SV54 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1323 ) @ SY1325 )
                               != SV175 )
                              | ( SV277
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1325 ) @ SV54 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1326: $i] :
                          ~ ( ~ ( ( SY1323
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SV175 ) @ SY1326 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1326 ) @ SV277 )
                                 != SV54 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1323 ) @ SY1326 )
                                 != SV175 )
                                | ( SV277
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1326 ) @ SV54 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SY1323 ) @ SV277 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1324 ) @ SV175 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5758]) ).

thf(5877,plain,
    ! [SV55: $i,SV176: $i,SV278: $i] :
      ( ( ! [SY1327: $i] :
            ( ( SY1327 != SV278 )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1327 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SY1327 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5759]) ).

thf(5878,plain,
    ! [SV56: $i,SV177: $i,SV279: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV279 @ SV177 ) )
        | ( hBOOL @ ( hAPP @ SV279 @ ( c_Hilbert__Choice_OEps @ SV56 @ SV279 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5760]) ).

thf(5879,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
            | ( SV178 = SV57 ) )
        | ~ ( ( SV178 != SV57 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5761]) ).

thf(5880,plain,
    ! [SV58: $i,SV179: $i,SV280: $i] :
      ( ( ! [SY1328: $i,SY1329: $i,SY1330: $i,SY1331: $i] :
            ( ( SY1331 != SY1330 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1329 @ SY1328 @ SV280 @ SV179 @ SV58 ) @ SY1331 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1329 @ SY1328 @ SV280 @ SV179 @ SV58 ) @ SY1330 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5762]) ).

thf(5881,plain,
    ! [SV59: $i,SV180: $i,SV281: $i] :
      ( ( ! [SY1332: $i,SY1333: $i,SY1334: $i,SY1335: $i] :
            ( ~ ( ( SY1335 != SY1334 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ SV281 ) @ SY1335 ) @ SV180 ) ) @ SY1334 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ SV281 ) @ SY1334 ) @ SV59 ) ) @ SY1335 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5763]) ).

thf(5882,plain,
    ! [SV60: $i,SV181: $i,SV282: $i] :
      ( ( ! [SY1336: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1336 ) @ SV282 ) @ SV181 ) @ SV60 ) )
                  | ( SV282 = SV60 )
                  | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
              | ~ ( ~ ( ( SV282 = SV60 )
                      | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1336 ) @ SV282 ) @ SV181 ) @ SV60 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5764]) ).

thf(5883,plain,
    ! [SV61: $i,SV182: $i,SV283: $i] :
      ( ( ~ ~ ( hBOOL @ ( hAPP @ SV283 @ SV182 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV283 @ SV61 ) ) @ SV182 ) @ SV182 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5765]) ).

thf(5884,plain,
    ! [SV62: $i,SV183: $i,SV284: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV284 ) @ SV183 ) @ SV62 )
       != SV62 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5766]) ).

thf(5885,plain,
    ! [SV63: $i,SV184: $i,SV285: $i] :
      ( ( ! [SY1337: $i,SY1338: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1338 @ SY1337 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SY1337 ) @ SV184 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1338 @ SV285 ) ) @ SV184 ) @ SV63 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1338 @ SV285 ) ) @ SY1337 ) @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5767]) ).

thf(5886,plain,
    ! [SV65: $i,SV185: $i,SV286: $i] :
      ( ( ! [SY1339: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1339 @ SV286 ) ) @ SV185 ) @ SV65 ) )
            | ~ ( ( SV65 != SV185 )
                | ( hBOOL @ ( hAPP @ SY1339 @ SV185 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY1339 @ SV185 ) )
                | ! [SY1340: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1340 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1339 @ SV286 ) ) @ SY1340 ) @ SV65 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5769]) ).

thf(5887,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
                | ! [SY1341: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
                    | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) )
            | ~ ( ~ ! [SY1342: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5770]) ).

thf(5888,plain,
    ! [SV67: $i,SV187: $i,SV288: $i] :
      ( ( ~ ( c_Predicate_Oreflp @ SV288 @ SV187 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ SV187 @ SV67 ) @ SV67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5771]) ).

thf(5889,plain,
    ! [SV68: $i,SV188: $i,SV289: $i] :
      ( ( ! [SY1343: $i,SY1344: $i,SY1345: $i,SY1346: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1346 @ SY1345 @ SY1344 @ SY1343 @ SV289 @ SV188 @ SV68 )
                  | ~ ! [SY1347: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1343 @ SV188 ) @ SY1347 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1347 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY1348: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1343 @ SV188 ) @ SY1348 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1348 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY1346 @ SY1345 @ SY1344 @ SY1343 @ SV289 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5772]) ).

thf(5890,plain,
    ! [SV69: $i,SV189: $i,SV290: $i] :
      ( ( ! [SY1349: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV290 ) @ SV189 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV290 ) @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5773]) ).

thf(5891,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
             != ( hAPP @ c_Nat_OSuc @ SV70 ) )
            | ( SV190 = SV70 ) )
        | ~ ( ( SV190 != SV70 )
            | ( ( hAPP @ c_Nat_OSuc @ SV190 )
              = ( hAPP @ c_Nat_OSuc @ SV70 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5774]) ).

thf(5892,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
                | ! [SY1350: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
                    | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) )
            | ~ ( ~ ! [SY1351: $i] :
                      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
                      | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5775]) ).

thf(5893,plain,
    ! [SV72: $i,SV192: $i,SV292: $i] :
      ( ( ! [SY1352: $i,SY1353: $i] :
            ( ( ( hAPP @ SY1353 @ SY1352 )
             != SV292 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SY1353 ) @ SY1352 ) @ SV292 )
              = SY1353 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5776]) ).

thf(5894,plain,
    ! [SV73: $i,SV193: $i,SV293: $i] :
      ( ( ! [SY1354: $i,SY1355: $i,SY1356: $i] :
            ( ~ ( ( SY1356 != SY1355 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1354 @ SV293 ) @ SV193 ) @ SY1355 ) @ SV73 ) @ SY1356 )
              = ( hAPP @ SV193 @ SY1356 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5777]) ).

thf(5895,plain,
    ! [SV74: $i,SV194: $i,SV294: $i] :
      ( ( ! [SY1357: $i] :
            ( ( SY1357 != SV294 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1357 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SY1357 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5778]) ).

thf(5896,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
                 != SV75 )
                | ( SV195
                  = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) ) )
            | ~ ( ( SV195
                 != ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
                | ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
                  = SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5779]) ).

thf(5897,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
            | ! [SY760: $i,SY761: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                      | ( ( hAPP @ SV76 @ SY760 )
                        = ( hAPP @ SV76 @ SY761 ) ) )
                  | ~ ( ( ( hAPP @ SV76 @ SY760 )
                       != ( hAPP @ SV76 @ SY761 ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
        | ~ ( ~ ! [SY762: $i,SY763: $i] :
                  ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                        | ( ( hAPP @ SV76 @ SY762 )
                          = ( hAPP @ SV76 @ SY763 ) ) )
                    | ~ ( ( ( hAPP @ SV76 @ SY762 )
                         != ( hAPP @ SV76 @ SY763 ) )
                        | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) )
            | ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5780]) ).

thf(5898,plain,
    ! [SV77: $i,SV197: $i,SV296: $i] :
      ( ( ! [SY1358: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1358 @ SV296 @ SV197 ) @ SV77 ) )
                  | ~ ! [SY1115: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
              | ~ ( ~ ~ ! [SY1116: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1358 @ SV296 @ SV197 ) @ SV77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5781]) ).

thf(5899,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
                 != ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
                | ( SV198 = SV78 ) )
            | ~ ( ( SV198 != SV78 )
                | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
                  = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5782]) ).

thf(5900,plain,
    ! [SV79: $i,SV199: $i,SV298: $i] :
      ( ( ! [SY1361: $i,SY1362: $i,SY1363: $i,SY1364: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1364 @ SY1363 @ SY1362 @ SY1361 @ SV298 )
            | ~ ( ~ ( ( ( hAPP @ SY1362 @ SV199 )
                     != ( hAPP @ SY1362 @ SV79 ) )
                    | ( SV199 = SV79 ) )
                | ~ ( ( SV199 != SV79 )
                    | ( ( hAPP @ SY1362 @ SV199 )
                      = ( hAPP @ SY1362 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5783]) ).

thf(5901,plain,
    ! [SV80: $i,SV200: $i,SV299: $i] :
      ( ( ! [SY1365: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1365 @ SV299 @ SV200 )
            | ( ( hAPP @ ( hAPP @ SV299 @ SV80 ) @ SV80 )
              = SV80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5784]) ).

thf(5902,plain,
    ! [SV81: $i,SV201: $i,SV300: $i] :
      ( ( ! [SY1366: $i,SY1367: $i,SY1368: $i,SY1369: $i,SY1370: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1370 @ SY1369 @ SY1368 @ SY1367 ) @ SY1366 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SY1369 @ SY1368 @ SV201 ) @ SV81 ) )
            | ! [SY1131: $i] :
                ( ( hAPP @ SY1367 @ ( hAPP @ SY1366 @ SY1131 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1131 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5785]) ).

thf(5903,plain,
    ! [SV82: $i,SV202: $i,SV301: $i] :
      ( ( ! [SY1372: $i,SY1373: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1373 @ SY1372 @ SV301 ) ) @ SV202 ) @ SV82 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1373 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1372 ) @ SV202 ) @ SV82 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1373 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1373 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1372 ) @ SV202 ) @ SV82 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1373 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1373 @ SY1372 @ SV301 ) ) @ SV202 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5786]) ).

thf(5904,plain,
    ! [SV83: $i,SV203: $i,SV302: $i] :
      ( ( ~ ( c_Equiv__Relations_Oequivp @ SV302 @ SV203 )
        | ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV83 ) @ SV83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5787]) ).

thf(5905,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
                | ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5788]) ).

thf(5906,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) )
        | ~ ! [SY1374: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ SY1374 ) @ SV85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5789]) ).

thf(5907,plain,
    ! [SV86: $i,SV206: $i,SV305: $i] :
      ( ( ! [SY1375: $i,SY1376: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1376 @ SY1375 ) @ SV305 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SY1376 ) @ SY1375 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5790]) ).

thf(5908,plain,
    ! [SV87: $i,SV207: $i,SV306: $i] :
      ( ( ! [SY1377: $i,SY1378: $i,SY1379: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1379 @ SY1378 @ SY1377 @ SV306 @ SV207 )
            | ( ( hAPP @ SV306 @ ( hAPP @ SY1377 @ SV87 ) )
              = SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5791]) ).

thf(5909,plain,
    ! [SV88: $i,SV208: $i,SV307: $i] :
      ( ( ! [SY1380: $i,SY1381: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1381 @ SY1380 @ SV307 )
            | ( ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
              = ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5792]) ).

thf(5910,plain,
    ! [SV89: $i,SV209: $i,SV308: $i] :
      ( ( ! [SY1382: $i,SY1383: $i,SY1384: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1384 ) @ SY1383 ) @ SY1382 )
             != SV308 )
            | ( SV209
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1384 ) @ SY1382 ) @ SV89 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1384 ) @ SY1383 ) @ SV209 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1384 ) @ SV308 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5793]) ).

thf(5911,plain,
    ! [SV90: $i] :
      ( ( ( ! [SY817: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY817 ) )
              | ( SV90 = SY817 ) ) )
        = $false )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5794]) ).

thf(5912,plain,
    ! [SV91: $i,SV210: $i,SV309: $i] :
      ( ( ! [SY1385: $i,SY1386: $i,SY1387: $i,SY1388: $i,SY1389: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1389 @ SY1388 ) @ SY1387 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1386 @ SY1387 ) @ SY1385 ) )
            | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SY1389 @ SY1386 @ SY1388 @ SY1385 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5795]) ).

thf(5913,plain,
    ! [SV92: $i,SV211: $i,SV310: $i] :
      ( ( ! [SY1390: $i,SY1391: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY1391 @ SY1390 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SY1390 ) @ SV211 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1391 @ SV92 @ SV310 ) ) @ SY1390 ) @ SV211 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5796]) ).

thf(5914,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
                | ~ ! [SY1392: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
            | ~ ( ~ ~ ! [SY1393: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5797]) ).

thf(5915,plain,
    ! [SV94: $i,SV213: $i,SV312: $i] :
      ( ( ! [SY1394: $i,SY1395: $i,SY1396: $i] :
            ~ ( ~ ( ( SY1396 != SY1395 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1394 @ SV312 ) @ SV213 ) @ SY1395 ) @ SV94 ) @ SY1396 )
                    = SV94 ) )
              | ~ ( ~ ( ( SY1396 != SY1395 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1394 @ SV312 ) @ SV213 ) @ SY1395 ) @ SV94 ) @ SY1396 )
                    = ( hAPP @ SV213 @ SY1396 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5798]) ).

thf(5916,plain,
    ! [SV95: $i,SV214: $i,SV313: $i] :
      ( ( ! [SY1397: $i,SY1398: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1398 @ SY1397 ) @ SV313 ) @ SV214 ) @ SV95 )
                   != SV313 )
                  | ( ( hAPP @ SV313 @ SV214 )
                    = SV95 ) )
              | ~ ( ( ( hAPP @ SV313 @ SV214 )
                   != SV95 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1398 @ SY1397 ) @ SV313 ) @ SV214 ) @ SV95 )
                    = SV313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5799]) ).

thf(5917,plain,
    ! [SV96: $i,SV215: $i,SV314: $i] :
      ( ( ! [SY1399: $i] :
            ( ( SY1399 != SV314 )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1399 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SY1399 ) @ SV96 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5800]) ).

thf(5918,plain,
    ! [SV97: $i,SV216: $i,SV315: $i] :
      ( ( ! [SY1400: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1400 ) @ SV315 ) @ SV216 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1400 ) @ SV315 ) @ SV97 ) )
                  | ( SV216 = SV97 ) )
              | ~ ( ( SV216 != SV97 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1400 ) @ SV315 ) @ SV216 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1400 ) @ SV315 ) @ SV97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5801]) ).

thf(5919,plain,
    ! [SV98: $i,SV217: $i,SV316: $i] :
      ( ( ! [SY1401: $i] :
            ( ( SY1401 != SV316 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SY1401 ) @ SV98 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5802]) ).

thf(5920,plain,
    ! [SV99: $i,SV218: $i] :
      ( ( ( ~ ! [SY1178: $i] :
                ( ( hAPP @ SV218 @ SY1178 )
                = ( hAPP @ SV99 @ SY1178 ) ) )
        = $true )
      | ( ( SV218 = SV99 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5803]) ).

thf(5921,plain,
    ! [SV100: $i,SV219: $i,SV317: $i] :
      ( ( ! [SY1402: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1402 ) @ SV317 ) @ SV219 ) @ SV100 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1402 ) @ SV317 ) @ SV100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5804]) ).

thf(5922,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ( ~ ( ~ ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) )
                | ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
            | ~ ( ~ ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) )
                | ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5805]) ).

thf(5923,plain,
    ! [SV102: $i,SV221: $i,SV319: $i] :
      ( ( ! [SY1409: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1409 @ SV319 ) @ SV221 ) )
            | ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1409 @ SV319 ) @ SV102 ) )
            | ( SV221 = SV102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5806]) ).

thf(5924,plain,
    ! [SV103: $i,SV222: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV222 ) @ SV103 ) ) )
        = $true )
      | ( ( SV103 = SV222 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5807]) ).

thf(5925,plain,
    ! [SV104: $i,SV223: $i,SV320: $i] :
      ( ( ! [SY1410: $i,SY1411: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1411 @ SY1410 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SY1410 ) @ SV223 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1411 @ SV320 @ SV104 ) ) @ SY1410 ) @ SV223 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5808]) ).

thf(5926,plain,
    ! [SV105: $i,SV224: $i] :
      ( ( ( ~ ~ ! [SY1193: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV224 @ SY1193 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5809]) ).

thf(5927,plain,
    ! [SV106: $i,SV225: $i,SV321: $i] :
      ( ( ! [SY1412: $i,SY1413: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1413 @ SY1412 @ SV321 ) @ SV225 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1413 @ SY1412 @ SV321 ) @ SV225 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5810]) ).

thf(5928,plain,
    ! [SV107: $i,SV226: $i,SV322: $i] :
      ( ( ! [SY1414: $i,SY1415: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1415 @ SY1414 @ SV322 ) ) @ SV226 ) @ SV107 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1415 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1414 ) @ SV226 ) @ SV107 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1415 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1415 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1414 ) @ SV226 ) @ SV107 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1415 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1415 @ SY1414 @ SV322 ) ) @ SV226 ) @ SV107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5811]) ).

thf(5929,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
             != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
            | ( SV227 = SV108 ) )
        | ~ ( ( SV227 != SV108 )
            | ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
              = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5812]) ).

thf(5930,plain,
    ! [SV109: $i,SV228: $i,SV323: $i] :
      ( ( ! [SY1416: $i,SY1417: $i,SY1418: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1418 @ SY1417 ) @ SY1416 ) @ SV323 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1418 @ SY1417 ) @ SV228 ) @ SV109 ) )
            | ~ ( ( SY1416 != SV228 )
                | ( SV323 != SV109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5813]) ).

thf(5931,plain,
    ! [SV110: $i,SV229: $i,SV324: $i] :
      ( ( ! [SY1419: $i,SY1420: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1420 @ SY1419 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1419 @ SV324 ) @ SV229 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1419 @ SV229 ) @ SV110 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SY1419 @ SV324 ) @ SV110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5814]) ).

thf(5932,plain,
    ! [SV111: $i,SV230: $i,SV325: $i] :
      ( ( ! [SY1421: $i,SY1422: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1422 @ SY1421 ) @ SV325 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SY1422 ) @ SV325 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5815]) ).

thf(5933,plain,
    ! [SV112: $i,SV231: $i] :
      ( ( ( ~ ~ ! [SY1210: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV231 @ SY1210 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5816]) ).

thf(5934,plain,
    ! [SV113: $i,SV232: $i,SV326: $i] :
      ( ( ! [SY1423: $i,SY1424: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1424 ) @ SY1423 ) @ SV326 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1424 ) @ SV232 ) @ SV113 ) )
                  | ~ ( ( SY1423 != SV232 )
                      | ( SV326 != SV113 ) ) )
              | ~ ( ~ ~ ( ( SY1423 != SV232 )
                        | ( SV326 != SV113 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1424 ) @ SY1423 ) @ SV326 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1424 ) @ SV232 ) @ SV113 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5817]) ).

thf(5935,plain,
    ! [SV114: $i,SV233: $i,SV327: $i] :
      ( ( ! [SY1425: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1425 ) @ SV327 ) @ SV233 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1425 ) @ SV327 ) @ SV114 ) )
            | ( SV114 = SV233 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5818]) ).

thf(5936,plain,
    ! [SV115: $i,SV234: $i,SV328: $i] :
      ( ( SV328
       != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV234 ) @ SV115 ) @ SV328 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5819]) ).

thf(5937,plain,
    ! [SV116: $i,SV235: $i,SV329: $i] :
      ( ( ! [SY1426: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1426 @ SV329 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5820]) ).

thf(5938,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
            | ( SV236 = SV117 ) )
        | ~ ( ( SV236 != SV117 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5821]) ).

thf(5939,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
            | ~ ! [SY1219: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
        | ~ ( ~ ~ ! [SY1220: $i] :
                    ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) )
            | ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5822]) ).

thf(5940,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
             != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
            | ( SV238 = SV119 ) )
        | ~ ( ( SV238 != SV119 )
            | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
              = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5823]) ).

thf(5941,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
                 != ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
                | ( SV239 = SV120 ) )
            | ~ ( ( SV239 != SV120 )
                | ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
                  = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5824]) ).

thf(5942,plain,
    ! [SV121: $i,SV240: $i,SV331: $i] :
      ( ( ! [SY1427: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1427 @ SV331 @ SV240 ) @ SV121 ) )
                  | ~ ! [SY1224: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
              | ~ ( ~ ~ ! [SY1225: $i] :
                          ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1427 @ SV331 @ SV240 ) @ SV121 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5825]) ).

thf(5943,plain,
    ! [SV122: $i,SV241: $i,SV332: $i] :
      ( ( ! [SY1430: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1430 @ SV332 ) ) @ SV241 ) @ SV122 ) )
                  | ~ ! [SY1431: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1430 ) @ SV241 ) @ SY1431 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1431 ) @ SV122 ) ) ) )
              | ~ ( ~ ~ ! [SY1432: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1430 ) @ SV241 ) @ SY1432 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1432 ) @ SV122 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1430 @ SV332 ) ) @ SV241 ) @ SV122 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5826]) ).

thf(5944,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
             != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
            | ( SV242 = SV123 ) )
        | ~ ( ( SV242 != SV123 )
            | ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
              = ( hAPP @ c_Int_ORep__Integ @ SV123 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5827]) ).

thf(5945,plain,
    ! [SV124: $i,SV243: $i,SV333: $i] :
      ( ( ! [SY1433: $i,SY1434: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1434 @ SY1433 @ SV333 ) ) @ SV243 ) @ SV124 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY1434 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1433 ) @ SV243 ) @ SV124 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1434 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5828]) ).

thf(5946,plain,
    ! [SV125: $i,SV244: $i,SV334: $i] :
      ( ( ! [SY1435: $i,SY1436: $i,SY1437: $i,SY1438: $i,SY1439: $i,SY1440: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1440 @ SY1439 @ SY1438 @ SY1437 ) @ SY1436 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1435 @ SY1439 @ SY1438 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SY1437 @ ( hAPP @ SY1436 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5829]) ).

thf(5947,plain,
    ! [SV126: $i,SV245: $i,SV335: $i] :
      ( ( ! [SY1441: $i,SY1442: $i,SY1443: $i,SY1444: $i,SY1445: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1445 ) @ SY1444 ) @ SY1443 ) @ SY1442 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1441 ) @ SV335 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY1446: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1445 ) @ SY1444 ) @ SY1446 ) @ SY1442 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1441 ) @ SV335 ) @ SY1446 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5830]) ).

thf(5948,plain,
    ! [SV4: $i,SV128: $i,SV247: $i,SV336: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV128 ) @ SV4 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV247 ) @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5832]) ).

thf(5949,plain,
    ! [SV5: $i,SV129: $i,SV248: $i,SV337: $i] :
      ( ( ! [SY1447: $i,SY1448: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1448 @ SY1447 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
            = ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5833]) ).

thf(5950,plain,
    ! [SV6: $i,SV130: $i,SV249: $i,SV338: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV338 @ SV249 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
        = SV130 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5834]) ).

thf(5951,plain,
    ! [SV7: $i,SV131: $i,SV250: $i,SV339: $i] :
      ( ( ! [SY1449: $i,SY1450: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1450 @ SY1449 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1450 @ SY1449 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1450 @ SY1449 ) @ SV339 ) @ SV250 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5835]) ).

thf(5952,plain,
    ! [SV8: $i,SV132: $i,SV251: $i,SV340: $i] :
      ( ( ! [SY1451: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1451 @ SV340 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
            = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5836]) ).

thf(5953,plain,
    ! [SV9: $i,SV133: $i,SV252: $i,SV341: $i] :
      ( ( ! [SY1452: $i,SY1453: $i,SY1454: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1454 @ SY1453 @ SY1452 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1454 @ SY1452 @ SV133 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1453 @ SY1452 @ ( hAPP @ ( c_Fun_Ocomp @ SY1454 @ SY1453 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5837]) ).

thf(5954,plain,
    ! [SV10: $i,SV134: $i,SV253: $i,SV342: $i] :
      ( ( ! [SY1455: $i,SY1456: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1456 @ SY1455 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
            = ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5838]) ).

thf(5955,plain,
    ! [SV14: $i,SV138: $i,SV254: $i,SV343: $i] :
      ( ( ! [SY1457: $i,SY1458: $i,SY1459: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1459 @ SY1458 @ SY1457 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1459 @ SV343 @ SY1458 ) @ SV254 ) @ SV138 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1459 @ SV343 @ SY1457 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SY1458 @ SY1457 ) @ SV138 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5839]) ).

thf(5956,plain,
    ! [SV15: $i,SV139: $i,SV255: $i,SV344: $i] :
      ( ( ! [SY1460: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1460 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1460 @ SV344 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1460 @ SV344 ) @ SV255 ) @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5840]) ).

thf(5957,plain,
    ! [SV16: $i,SV140: $i,SV256: $i,SV345: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV256 ) @ SV140 ) ) @ SV16 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV140 ) @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5841]) ).

thf(5958,plain,
    ! [SV19: $i,SV143: $i,SV258: $i,SV346: $i] :
      ( ( ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SV346 ) @ SV19 ) )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SV346 ) @ ( hAPP @ SV346 @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5843]) ).

thf(5959,plain,
    ! [SV21: $i,SV145: $i,SV259: $i,SV347: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV347 @ SV259 ) @ SV145 ) @ SV21 )
        = SV145 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5844]) ).

thf(5960,plain,
    ! [SV22: $i,SV146: $i,SV260: $i,SV348: $i] :
      ( ( ! [SY1461: $i,SY1462: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1462 @ SY1461 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
            = ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5845]) ).

thf(5961,plain,
    ! [SV23: $i,SV147: $i,SV261: $i,SV349: $i] :
      ( ( ! [SY1463: $i,SY1464: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1464 @ SY1463 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
            = ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5846]) ).

thf(5962,plain,
    ! [SV24: $i,SV148: $i,SV262: $i,SV350: $i] :
      ( ( ! [SY1465: $i,SY1466: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1466 @ SY1465 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
            = ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5847]) ).

thf(5963,plain,
    ! [SV25: $i,SV149: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) )
        = $false )
      | ( ( SV149 = SV25 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5848]) ).

thf(5964,plain,
    ! [SV26: $i] :
      ( ( ( hBOOL @ SV26 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5849]) ).

thf(5965,plain,
    ! [SV27: $i] :
      ( ( ( hBOOL @ SV27 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5850]) ).

thf(5966,plain,
    ! [SV28: $i,SV150: $i] :
      ( ( ( ~ ( hBOOL @ SV150 ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV28 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5851]) ).

thf(5967,plain,
    ! [SV29: $i,SV151: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) )
        = $false )
      | ( ( hBOOL @ SV151 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5852]) ).

thf(5968,plain,
    ! [SV30: $i,SV152: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) )
        = $false )
      | ( ( hBOOL @ SV30 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5853]) ).

thf(5969,plain,
    ! [SV31: $i,SV153: $i] :
      ( ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5854]) ).

thf(5970,plain,
    ! [SV32: $i,SV154: $i] :
      ( ( ( hBOOL @ SV154 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5855]) ).

thf(5971,plain,
    ! [SV33: $i,SV155: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) ) )
        = $true )
      | ( ( hBOOL @ SV155 )
        = $true )
      | ( ( hBOOL @ SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5856]) ).

thf(5972,plain,
    ! [SV35: $i,SV157: $i] :
      ( ( ( hBOOL @ SV157 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5858]) ).

thf(5973,plain,
    ! [SV36: $i,SV158: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV158 ) )
        = $true )
      | ( ( hBOOL @ SV36 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5859]) ).

thf(5974,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i] :
      ( ( ! [SY1467: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1467 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                      | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                        | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1467 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5860]) ).

thf(5975,plain,
    ! [SV39: $i,SV160: $i,SV264: $i,SV352: $i] :
      ( ( ! [SY1468: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1468 ) @ SV352 ) @ SV264 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1468 @ SV160 ) ) @ SV352 ) @ SV39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5861]) ).

thf(5976,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
            | ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
            | ~ ! [SY1286: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
                | ~ ! [SY1287: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5862]) ).

thf(5977,plain,
    ! [SV41: $i,SV162: $i,SV266: $i,SV353: $i] :
      ( ( ! [SY1469: $i,SY1470: $i] :
            ( ( SY1470 != SY1469 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SY1470 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SY1469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5863]) ).

thf(5978,plain,
    ! [SV42: $i,SV163: $i,SV267: $i] :
      ( ( ( ~ ~ ! [SY1291: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV267 @ SY1291 ) ) )
        = $true )
      | ( ( ( SV163
           != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
          | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5864]) ).

thf(5979,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i] :
      ( ( ! [SY1471: $i,SY1472: $i,SY1473: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1473 ) @ SY1472 ) @ SY1471 ) @ SV354 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1473 ) @ SV268 ) @ SV164 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SY1472 != SV268 )
                            | ( SY1471 != SV164 ) )
                      | ( SV354 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1472 != SV268 )
                              | ( SY1471 != SV164 ) )
                        | ( SV354 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1473 ) @ SY1472 ) @ SY1471 ) @ SV354 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1473 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5865]) ).

thf(5980,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i] :
      ( ( ! [SY1474: $i,SY1475: $i] :
            ( ~ ( ( SY1475 != SY1474 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SY1475 ) @ SV165 ) ) @ SY1474 ) @ SV44 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SY1474 ) @ SV44 ) ) @ SY1475 ) @ SV165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5866]) ).

thf(5981,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i] :
      ( ( ! [SY1476: $i,SY1477: $i] :
            ~ ( ~ ( ( SY1477 != SY1476 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SY1476 ) @ SV45 ) @ SY1477 )
                    = SV45 ) )
              | ~ ( ~ ( ( SY1477 != SY1476 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SY1476 ) @ SV45 ) @ SY1477 )
                    = ( hAPP @ SV166 @ SY1477 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5867]) ).

thf(5982,plain,
    ! [SV46: $i,SV167: $i] :
      ( ( ( SV167 = SV46 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV167 ) @ SV46 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5868]) ).

thf(5983,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
                | ~ ( ( SV47 != SV168 )
                    | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                    | ~ ~ ! [SY1478: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
            | ~ ( ~ ( ~ ( ( SV47 != SV168 )
                        | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
                    | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                        | ~ ~ ! [SY1479: $i] :
                                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5869]) ).

thf(5984,plain,
    ! [SV48: $i,SV169: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV169 )
          = ( hAPP @ c_Nat_OSuc @ SV48 ) )
        = $false )
      | ( ( SV169 = SV48 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5870]) ).

thf(5985,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i] :
      ( ( ! [SY1480: $i,SY1481: $i,SY1482: $i,SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i] :
            ( ( ( hAPP @ SY1486 @ ( hAPP @ SY1485 @ SY1484 ) )
             != ( hAPP @ SY1483 @ ( hAPP @ SY1482 @ SY1481 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1480 @ SV358 @ SV272 @ SY1486 ) @ SY1485 ) @ SY1484 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SY1483 ) @ SY1482 ) @ SY1481 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5871]) ).

thf(5986,plain,
    ! [SV50: $i,SV171: $i,SV273: $i,SV359: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        | ~ ! [SY1487: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ SY1487 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SY1487 ) @ SV50 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5872]) ).

thf(5987,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i] :
      ( ( ! [SY1488: $i,SY1489: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SV360 ) @ SV274 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SV172 ) @ SV51 ) )
                  | ~ ( ( SV360 != SV172 )
                      | ( SV274 != SV51 ) ) )
              | ~ ( ~ ~ ( ( SV360 != SV172 )
                        | ( SV274 != SV51 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SV360 ) @ SV274 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SV172 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5873]) ).

thf(5988,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i] :
      ( ( ! [SY1490: $i,SY1491: $i,SY1492: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1492 @ SY1491 @ SY1490 @ SV361 ) @ SV275 )
             != SV173 )
            | ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
              = ( hAPP @ SV173 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5874]) ).

thf(5989,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
                | ( SV276 = SV53 ) )
            | ~ ( ( SV276 != SV53 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5875]) ).

thf(5990,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i] :
      ( ( ! [SY1493: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV363 ) @ SV277 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV175 ) @ SV54 ) )
                  | ~ ! [SY1494: $i] :
                        ~ ( ~ ( ( SV363
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV175 ) @ SY1494 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SY1494 ) @ SV277 )
                               != SV54 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV363 ) @ SY1494 )
                               != SV175 )
                              | ( SV277
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SY1494 ) @ SV54 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1495: $i] :
                          ~ ( ~ ( ( SV363
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV175 ) @ SY1495 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SY1495 ) @ SV277 )
                                 != SV54 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV363 ) @ SY1495 )
                                 != SV175 )
                                | ( SV277
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SY1495 ) @ SV54 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV363 ) @ SV277 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1493 ) @ SV175 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5876]) ).

thf(5991,plain,
    ! [SV55: $i,SV176: $i,SV278: $i,SV364: $i] :
      ( ( ( SV364 != SV278 )
        | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
        | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5877]) ).

thf(5992,plain,
    ! [SV56: $i,SV177: $i,SV279: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV279 @ SV177 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV279 @ ( c_Hilbert__Choice_OEps @ SV56 @ SV279 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5878]) ).

thf(5993,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
            | ( SV178 = SV57 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5879]) ).

thf(5994,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ~ ( ( SV178 != SV57 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5879]) ).

thf(5995,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i] :
      ( ( ! [SY1496: $i,SY1497: $i,SY1498: $i] :
            ( ( SY1498 != SY1497 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1496 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SY1498 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1496 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SY1497 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5880]) ).

thf(5996,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i] :
      ( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
            ( ~ ( ( SY1501 != SY1500 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1499 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1499 @ SV366 ) @ SV281 ) @ SY1501 ) @ SV180 ) ) @ SY1500 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1499 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1499 @ SV366 ) @ SV281 ) @ SY1500 ) @ SV59 ) ) @ SY1501 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5881]) ).

thf(5997,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
                | ( SV282 = SV60 )
                | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
            | ~ ( ~ ( ( SV282 = SV60 )
                    | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5882]) ).

thf(5998,plain,
    ! [SV61: $i,SV182: $i,SV283: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV283 @ SV182 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV283 @ SV61 ) ) @ SV182 ) @ SV182 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5883]) ).

thf(5999,plain,
    ! [SV62: $i,SV183: $i,SV284: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV284 ) @ SV183 ) @ SV62 )
        = SV62 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5884]) ).

thf(6000,plain,
    ! [SV63: $i,SV184: $i,SV285: $i,SV368: $i] :
      ( ( ! [SY1502: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1502 @ SV368 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1502 @ SV285 ) ) @ SV184 ) @ SV63 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1502 @ SV285 ) ) @ SV368 ) @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5885]) ).

thf(6001,plain,
    ! [SV65: $i,SV185: $i,SV286: $i,SV369: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        | ~ ( ( SV65 != SV185 )
            | ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
            | ! [SY1503: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5886]) ).

thf(6002,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
            | ! [SY1341: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) )
        | ~ ( ~ ! [SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5887]) ).

thf(6003,plain,
    ! [SV67: $i,SV187: $i,SV288: $i] :
      ( ( ( ~ ( c_Predicate_Oreflp @ SV288 @ SV187 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV187 @ SV67 ) @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5888]) ).

thf(6004,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i] :
      ( ( ! [SY1504: $i,SY1505: $i,SY1506: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1506 @ SY1505 @ SY1504 @ SV370 @ SV289 @ SV188 @ SV68 )
                  | ~ ! [SY1507: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY1508: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY1506 @ SY1505 @ SY1504 @ SV370 @ SV289 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5889]) ).

thf(6005,plain,
    ! [SV69: $i,SV189: $i,SV290: $i,SV371: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV189 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) )
        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5890]) ).

thf(6006,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
             != ( hAPP @ c_Nat_OSuc @ SV70 ) )
            | ( SV190 = SV70 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5891]) ).

thf(6007,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ~ ( ( SV190 != SV70 )
            | ( ( hAPP @ c_Nat_OSuc @ SV190 )
              = ( hAPP @ c_Nat_OSuc @ SV70 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5891]) ).

thf(6008,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
            | ! [SY1350: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) )
        | ~ ( ~ ! [SY1351: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5892]) ).

thf(6009,plain,
    ! [SV72: $i,SV192: $i,SV292: $i,SV372: $i] :
      ( ( ! [SY1509: $i] :
            ( ( ( hAPP @ SY1509 @ SV372 )
             != SV292 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SY1509 ) @ SV372 ) @ SV292 )
              = SY1509 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5893]) ).

thf(6010,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i] :
      ( ( ! [SY1510: $i,SY1511: $i] :
            ( ~ ( ( SY1511 != SY1510 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SY1510 ) @ SV73 ) @ SY1511 )
              = ( hAPP @ SV193 @ SY1511 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5894]) ).

thf(6011,plain,
    ! [SV74: $i,SV194: $i,SV294: $i,SV374: $i] :
      ( ( ( SV374 != SV294 )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5895]) ).

thf(6012,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
             != SV75 )
            | ( SV195
              = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) ) )
        | ~ ( ( SV195
             != ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
            | ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
              = SV75 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5896]) ).

thf(6013,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
            | ! [SY760: $i,SY761: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                      | ( ( hAPP @ SV76 @ SY760 )
                        = ( hAPP @ SV76 @ SY761 ) ) )
                  | ~ ( ( ( hAPP @ SV76 @ SY760 )
                       != ( hAPP @ SV76 @ SY761 ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5897]) ).

thf(6014,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ~ ( ~ ! [SY762: $i,SY763: $i] :
                  ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                        | ( ( hAPP @ SV76 @ SY762 )
                          = ( hAPP @ SV76 @ SY763 ) ) )
                    | ~ ( ( ( hAPP @ SV76 @ SY762 )
                         != ( hAPP @ SV76 @ SY763 ) )
                        | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) )
            | ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5897]) ).

thf(6015,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
                | ~ ! [SY1115: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
            | ~ ( ~ ~ ! [SY1116: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
                | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5898]) ).

thf(6016,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
             != ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
            | ( SV198 = SV78 ) )
        | ~ ( ( SV198 != SV78 )
            | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
              = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5899]) ).

thf(6017,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i] :
      ( ( ! [SY1514: $i,SY1515: $i,SY1516: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1516 @ SY1515 @ SY1514 @ SV376 @ SV298 )
            | ~ ( ~ ( ( ( hAPP @ SY1514 @ SV199 )
                     != ( hAPP @ SY1514 @ SV79 ) )
                    | ( SV199 = SV79 ) )
                | ~ ( ( SV199 != SV79 )
                    | ( ( hAPP @ SY1514 @ SV199 )
                      = ( hAPP @ SY1514 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5900]) ).

thf(6018,plain,
    ! [SV80: $i,SV200: $i,SV299: $i,SV377: $i] :
      ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV377 @ SV299 @ SV200 )
        | ( ( hAPP @ ( hAPP @ SV299 @ SV80 ) @ SV80 )
          = SV80 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5901]) ).

thf(6019,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i] :
      ( ( ! [SY1517: $i,SY1518: $i,SY1519: $i,SY1520: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1520 @ SY1519 @ SY1518 @ SY1517 ) @ SV378 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SY1519 @ SY1518 @ SV201 ) @ SV81 ) )
            | ! [SY1521: $i] :
                ( ( hAPP @ SY1517 @ ( hAPP @ SV378 @ SY1521 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1521 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5902]) ).

thf(6020,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i] :
      ( ( ! [SY1522: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1522 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1522 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1522 @ SV202 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1522 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1522 @ SV202 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1522 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5903]) ).

thf(6021,plain,
    ! [SV83: $i,SV203: $i,SV302: $i] :
      ( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV302 @ SV203 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV83 ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5904]) ).

thf(6022,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
            | ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5905]) ).

thf(6023,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) ) )
        = $true )
      | ( ( ~ ! [SY1374: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ SY1374 ) @ SV85 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5906]) ).

thf(6024,plain,
    ! [SV86: $i,SV206: $i,SV305: $i,SV380: $i] :
      ( ( ! [SY1523: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1523 @ SV380 ) @ SV305 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SY1523 ) @ SV380 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5907]) ).

thf(6025,plain,
    ! [SV87: $i,SV207: $i,SV306: $i,SV381: $i] :
      ( ( ! [SY1524: $i,SY1525: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1525 @ SY1524 @ SV381 @ SV306 @ SV207 )
            | ( ( hAPP @ SV306 @ ( hAPP @ SV381 @ SV87 ) )
              = SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5908]) ).

thf(6026,plain,
    ! [SV88: $i,SV208: $i,SV307: $i,SV382: $i] :
      ( ( ! [SY1526: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1526 @ SV382 @ SV307 )
            | ( ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
              = ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5909]) ).

thf(6027,plain,
    ! [SV89: $i,SV209: $i,SV308: $i,SV383: $i] :
      ( ( ! [SY1527: $i,SY1528: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1528 ) @ SY1527 ) @ SV383 )
             != SV308 )
            | ( SV209
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1528 ) @ SV383 ) @ SV89 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1528 ) @ SY1527 ) @ SV209 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1528 ) @ SV308 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5910]) ).

thf(6028,plain,
    ! [SV90: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK1_SY817 @ SV90 ) ) )
          | ( SV90
            = ( sK1_SY817 @ SV90 ) ) )
        = $false )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[5911]) ).

thf(6029,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i] :
      ( ( ! [SY1529: $i,SY1530: $i,SY1531: $i,SY1532: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1532 @ SY1531 ) @ SY1530 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1529 @ SY1530 ) @ SV384 ) )
            | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SY1532 @ SY1529 @ SY1531 @ SV384 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5912]) ).

thf(6030,plain,
    ! [SV92: $i,SV211: $i,SV310: $i,SV385: $i] :
      ( ( ! [SY1533: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP @ SY1533 @ SV385 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1533 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5913]) ).

thf(6031,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
            | ~ ! [SY1392: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
        | ~ ( ~ ~ ! [SY1393: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5914]) ).

thf(6032,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i] :
      ( ( ! [SY1534: $i,SY1535: $i] :
            ~ ( ~ ( ( SY1535 != SY1534 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SY1534 ) @ SV94 ) @ SY1535 )
                    = SV94 ) )
              | ~ ( ~ ( ( SY1535 != SY1534 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SY1534 ) @ SV94 ) @ SY1535 )
                    = ( hAPP @ SV213 @ SY1535 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5915]) ).

thf(6033,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i] :
      ( ( ! [SY1536: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1536 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
                   != SV313 )
                  | ( ( hAPP @ SV313 @ SV214 )
                    = SV95 ) )
              | ~ ( ( ( hAPP @ SV313 @ SV214 )
                   != SV95 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1536 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
                    = SV313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5916]) ).

thf(6034,plain,
    ! [SV96: $i,SV215: $i,SV314: $i,SV388: $i] :
      ( ( ( SV388 != SV314 )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5917]) ).

thf(6035,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
                | ( SV216 = SV97 ) )
            | ~ ( ( SV216 != SV97 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5918]) ).

thf(6036,plain,
    ! [SV98: $i,SV217: $i,SV316: $i,SV390: $i] :
      ( ( ( SV390 != SV316 )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV390 ) @ SV98 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5919]) ).

thf(6037,plain,
    ! [SV99: $i,SV218: $i] :
      ( ( ( ! [SY1178: $i] :
              ( ( hAPP @ SV218 @ SY1178 )
              = ( hAPP @ SV99 @ SY1178 ) ) )
        = $false )
      | ( ( SV218 = SV99 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5920]) ).

thf(6038,plain,
    ! [SV100: $i,SV219: $i,SV317: $i,SV391: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV391 ) @ SV317 ) @ SV219 ) @ SV100 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV391 ) @ SV317 ) @ SV100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5921]) ).

thf(6039,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ( ~ ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) )
            | ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
        | ~ ( ~ ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) )
            | ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5922]) ).

thf(6040,plain,
    ! [SV102: $i,SV221: $i,SV319: $i,SV392: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV221 ) )
        | ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV102 ) )
        | ( SV221 = SV102 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5923]) ).

thf(6041,plain,
    ! [SV103: $i,SV222: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV222 ) @ SV103 ) )
        = $false )
      | ( ( SV103 = SV222 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5924]) ).

thf(6042,plain,
    ! [SV104: $i,SV223: $i,SV320: $i,SV393: $i] :
      ( ( ! [SY1537: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SY1537 @ SV393 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1537 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5925]) ).

thf(6043,plain,
    ! [SV105: $i,SV224: $i] :
      ( ( ( ~ ! [SY1193: $i] :
                ~ ( hBOOL @ ( hAPP @ SV224 @ SY1193 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5926]) ).

thf(6044,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i] :
      ( ( ! [SY1538: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1538 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1538 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5927]) ).

thf(6045,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i] :
      ( ( ! [SY1539: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1539 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP @ SY1539 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                  | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1539 @ SV226 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
              | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1539 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                      | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1539 @ SV226 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1539 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5928]) ).

thf(6046,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
             != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
            | ( SV227 = SV108 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5929]) ).

thf(6047,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ~ ( ( SV227 != SV108 )
            | ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
              = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5929]) ).

thf(6048,plain,
    ! [SV109: $i,SV228: $i,SV323: $i,SV396: $i] :
      ( ( ! [SY1540: $i,SY1541: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1541 @ SY1540 ) @ SV396 ) @ SV323 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1541 @ SY1540 ) @ SV228 ) @ SV109 ) )
            | ~ ( ( SV396 != SV228 )
                | ( SV323 != SV109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5930]) ).

thf(6049,plain,
    ! [SV110: $i,SV229: $i,SV324: $i,SV397: $i] :
      ( ( ! [SY1542: $i] :
            ( ~ ( c_Equiv__Relations_Oequivp @ SY1542 @ SV397 )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5931]) ).

thf(6050,plain,
    ! [SV111: $i,SV230: $i,SV325: $i,SV398: $i] :
      ( ( ! [SY1543: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1543 @ SV398 ) @ SV325 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SY1543 ) @ SV325 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5932]) ).

thf(6051,plain,
    ! [SV112: $i,SV231: $i] :
      ( ( ( ~ ! [SY1210: $i] :
                ~ ( hBOOL @ ( hAPP @ SV231 @ SY1210 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5933]) ).

thf(6052,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i] :
      ( ( ! [SY1544: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1544 ) @ SV399 ) @ SV326 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1544 ) @ SV232 ) @ SV113 ) )
                  | ~ ( ( SV399 != SV232 )
                      | ( SV326 != SV113 ) ) )
              | ~ ( ~ ~ ( ( SV399 != SV232 )
                        | ( SV326 != SV113 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1544 ) @ SV399 ) @ SV326 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1544 ) @ SV232 ) @ SV113 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5934]) ).

thf(6053,plain,
    ! [SV114: $i,SV233: $i,SV327: $i,SV400: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV233 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV114 ) )
        | ( SV114 = SV233 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5935]) ).

thf(6054,plain,
    ! [SV115: $i,SV234: $i,SV328: $i] :
      ( ( SV328
        = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV234 ) @ SV115 ) @ SV328 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5936]) ).

thf(6055,plain,
    ! [SV116: $i,SV235: $i,SV329: $i,SV401: $i] :
      ( ( ~ ( c_Equiv__Relations_Oequivp @ SV401 @ SV329 )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5937]) ).

thf(6056,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
            | ( SV236 = SV117 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5938]) ).

thf(6057,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ~ ( ( SV236 != SV117 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5938]) ).

thf(6058,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
            | ~ ! [SY1219: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5939]) ).

thf(6059,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ( ~ ~ ! [SY1220: $i] :
                    ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) )
            | ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5939]) ).

thf(6060,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
             != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
            | ( SV238 = SV119 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5940]) ).

thf(6061,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ~ ( ( SV238 != SV119 )
            | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
              = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5940]) ).

thf(6062,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
             != ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
            | ( SV239 = SV120 ) )
        | ~ ( ( SV239 != SV120 )
            | ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
              = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5941]) ).

thf(6063,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
                | ~ ! [SY1224: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
            | ~ ( ~ ~ ! [SY1225: $i] :
                        ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
                | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5942]) ).

thf(6064,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
                | ~ ! [SY1547: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
            | ~ ( ~ ~ ! [SY1548: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5943]) ).

thf(6065,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
             != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
            | ( SV242 = SV123 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5944]) ).

thf(6066,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ~ ( ( SV242 != SV123 )
            | ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
              = ( hAPP @ c_Int_ORep__Integ @ SV123 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5944]) ).

thf(6067,plain,
    ! [SV124: $i,SV243: $i,SV333: $i,SV404: $i] :
      ( ( ! [SY1549: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1549 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SY1549 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1549 @ SV243 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5945]) ).

thf(6068,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i] :
      ( ( ! [SY1550: $i,SY1551: $i,SY1552: $i,SY1553: $i,SY1554: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1554 @ SY1553 @ SY1552 @ SY1551 ) @ SY1550 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SY1553 @ SY1552 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SY1551 @ ( hAPP @ SY1550 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5946]) ).

thf(6069,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i] :
      ( ( ! [SY1555: $i,SY1556: $i,SY1557: $i,SY1558: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1558 ) @ SY1557 ) @ SY1556 ) @ SY1555 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY1559: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1558 ) @ SY1557 ) @ SY1559 ) @ SY1555 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1559 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5947]) ).

thf(6070,plain,
    ! [SV5: $i,SV129: $i,SV248: $i,SV337: $i,SV407: $i] :
      ( ( ! [SY1560: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1560 @ SV407 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
            = ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5949]) ).

thf(6071,plain,
    ! [SV7: $i,SV131: $i,SV250: $i,SV339: $i,SV408: $i] :
      ( ( ! [SY1561: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1561 @ SV408 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1561 @ SV408 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1561 @ SV408 ) @ SV339 ) @ SV250 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5951]) ).

thf(6072,plain,
    ! [SV8: $i,SV132: $i,SV251: $i,SV340: $i,SV409: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV409 @ SV340 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
        = SV8 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5952]) ).

thf(6073,plain,
    ! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i] :
      ( ( ! [SY1562: $i,SY1563: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1563 @ SY1562 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1563 @ SV410 @ SV133 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1562 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SY1563 @ SY1562 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5953]) ).

thf(6074,plain,
    ! [SV10: $i,SV134: $i,SV253: $i,SV342: $i,SV411: $i] :
      ( ( ! [SY1564: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1564 @ SV411 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
            = ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5954]) ).

thf(6075,plain,
    ! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i] :
      ( ( ! [SY1565: $i,SY1566: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1566 @ SY1565 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1566 @ SV343 @ SY1565 ) @ SV254 ) @ SV138 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1566 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SY1565 @ SV412 ) @ SV138 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5955]) ).

thf(6076,plain,
    ! [SV15: $i,SV139: $i,SV255: $i,SV344: $i,SV413: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ SV344 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
        = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ SV344 ) @ SV255 ) @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5956]) ).

thf(6077,plain,
    ! [SV22: $i,SV146: $i,SV260: $i,SV348: $i,SV414: $i] :
      ( ( ! [SY1567: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1567 @ SV414 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
            = ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5960]) ).

thf(6078,plain,
    ! [SV23: $i,SV147: $i,SV261: $i,SV349: $i,SV415: $i] :
      ( ( ! [SY1568: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1568 @ SV415 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
            = ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5961]) ).

thf(6079,plain,
    ! [SV24: $i,SV148: $i,SV262: $i,SV350: $i,SV416: $i] :
      ( ( ! [SY1569: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1569 @ SV416 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
            = ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5962]) ).

thf(6080,plain,
    ! [SV28: $i,SV150: $i] :
      ( ( ( hBOOL @ SV150 )
        = $false )
      | ( ( ~ ( hBOOL @ SV28 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5966]) ).

thf(6081,plain,
    ! [SV33: $i,SV155: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
        = $false )
      | ( ( hBOOL @ SV155 )
        = $true )
      | ( ( hBOOL @ SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5971]) ).

thf(6082,plain,
    ! [SV36: $i,SV158: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
        = $false )
      | ( ( ~ ( hBOOL @ SV158 ) )
        = $true )
      | ( ( hBOOL @ SV36 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5973]) ).

thf(6083,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                    | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                      | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5974]) ).

thf(6084,plain,
    ! [SV39: $i,SV160: $i,SV264: $i,SV352: $i,SV418: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV418 ) @ SV352 ) @ SV264 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV418 @ SV160 ) ) @ SV352 ) @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5975]) ).

thf(6085,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
            | ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
            | ~ ! [SY1286: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5976]) ).

thf(6086,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
                | ~ ! [SY1287: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[5976]) ).

thf(6087,plain,
    ! [SV41: $i,SV162: $i,SV266: $i,SV353: $i,SV419: $i] :
      ( ( ! [SY1570: $i] :
            ( ( SY1570 != SV419 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SY1570 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV419 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5977]) ).

thf(6088,plain,
    ! [SV42: $i,SV163: $i,SV267: $i] :
      ( ( ( ~ ! [SY1291: $i] :
                ~ ( hBOOL @ ( hAPP @ SV267 @ SY1291 ) ) )
        = $false )
      | ( ( ( SV163
           != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
          | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5978]) ).

thf(6089,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i] :
      ( ( ! [SY1571: $i,SY1572: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1572 ) @ SY1571 ) @ SV420 ) @ SV354 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1572 ) @ SV268 ) @ SV164 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SY1571 != SV268 )
                            | ( SV420 != SV164 ) )
                      | ( SV354 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1571 != SV268 )
                              | ( SV420 != SV164 ) )
                        | ( SV354 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1572 ) @ SY1571 ) @ SV420 ) @ SV354 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1572 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5979]) ).

thf(6090,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i,SV421: $i] :
      ( ( ! [SY1573: $i] :
            ( ~ ( ( SY1573 != SV421 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SY1573 ) @ SV165 ) ) @ SV421 ) @ SV44 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV421 ) @ SV44 ) ) @ SY1573 ) @ SV165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5980]) ).

thf(6091,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i] :
      ( ( ! [SY1574: $i] :
            ~ ( ~ ( ( SY1574 != SV422 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SY1574 )
                    = SV45 ) )
              | ~ ( ~ ( ( SY1574 != SV422 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SY1574 )
                    = ( hAPP @ SV166 @ SY1574 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5981]) ).

thf(6092,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
            | ~ ( ( SV47 != SV168 )
                | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                | ~ ~ ! [SY1478: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        | ~ ( ~ ( ~ ( ( SV47 != SV168 )
                    | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                    | ~ ~ ! [SY1479: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5983]) ).

thf(6093,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i] :
      ( ( ! [SY1575: $i,SY1576: $i,SY1577: $i,SY1578: $i,SY1579: $i,SY1580: $i] :
            ( ( ( hAPP @ SY1580 @ ( hAPP @ SY1579 @ SY1578 ) )
             != ( hAPP @ SY1577 @ ( hAPP @ SY1576 @ SY1575 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1580 ) @ SY1579 ) @ SY1578 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SY1577 ) @ SY1576 ) @ SY1575 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5985]) ).

thf(6094,plain,
    ! [SV50: $i,SV171: $i,SV273: $i,SV359: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) ) )
        = $true )
      | ( ( ~ ! [SY1487: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ SY1487 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SY1487 ) @ SV50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5986]) ).

thf(6095,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i] :
      ( ( ! [SY1581: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1581 @ SV424 ) @ SV360 ) @ SV274 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1581 @ SV424 ) @ SV172 ) @ SV51 ) )
                  | ~ ( ( SV360 != SV172 )
                      | ( SV274 != SV51 ) ) )
              | ~ ( ~ ~ ( ( SV360 != SV172 )
                        | ( SV274 != SV51 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1581 @ SV424 ) @ SV360 ) @ SV274 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1581 @ SV424 ) @ SV172 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5987]) ).

thf(6096,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i,SV425: $i] :
      ( ( ! [SY1582: $i,SY1583: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1583 @ SY1582 @ SV425 @ SV361 ) @ SV275 )
             != SV173 )
            | ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
              = ( hAPP @ SV173 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5988]) ).

thf(6097,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
            | ( SV276 = SV53 ) )
        | ~ ( ( SV276 != SV53 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5989]) ).

thf(6098,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
                | ~ ! [SY1584: $i] :
                      ~ ( ~ ( ( SV363
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                             != SV54 ) )
                        | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                             != SV175 )
                            | ( SV277
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
            | ~ ( ~ ~ ! [SY1585: $i] :
                        ~ ( ~ ( ( SV363
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                               != SV54 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                               != SV175 )
                              | ( SV277
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5990]) ).

thf(6099,plain,
    ! [SV55: $i,SV176: $i,SV278: $i,SV364: $i] :
      ( ( ( SV364 != SV278 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5991]) ).

thf(6100,plain,
    ! [SV56: $i,SV177: $i,SV279: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV279 @ SV177 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV279 @ ( c_Hilbert__Choice_OEps @ SV56 @ SV279 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5992]) ).

thf(6101,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
        | ( SV178 = SV57 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[5993]) ).

thf(6102,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( SV178 != SV57 )
        | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[5994]) ).

thf(6103,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i,SV427: $i] :
      ( ( ! [SY1586: $i,SY1587: $i] :
            ( ( SY1587 != SY1586 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SY1587 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SY1586 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5995]) ).

thf(6104,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i] :
      ( ( ! [SY1588: $i,SY1589: $i] :
            ( ~ ( ( SY1589 != SY1588 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SY1589 ) @ SV180 ) ) @ SY1588 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SY1588 ) @ SV59 ) ) @ SY1589 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5996]) ).

thf(6105,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
            | ( SV282 = SV60 )
            | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
        | ~ ( ~ ( ( SV282 = SV60 )
                | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5997]) ).

thf(6106,plain,
    ! [SV61: $i,SV182: $i,SV283: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV283 @ SV182 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV283 @ SV61 ) ) @ SV182 ) @ SV182 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5998]) ).

thf(6107,plain,
    ! [SV63: $i,SV184: $i,SV285: $i,SV368: $i,SV429: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6000]) ).

thf(6108,plain,
    ! [SV65: $i,SV185: $i,SV286: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) ) )
        = $true )
      | ( ( ~ ( ( SV65 != SV185 )
              | ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6001]) ).

thf(6109,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
            | ! [SY1341: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6002]) ).

thf(6110,plain,
    ! [SV287: $i,SV66: $i,SV186: $i] :
      ( ( ~ ( ~ ! [SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6002]) ).

thf(6111,plain,
    ! [SV67: $i,SV187: $i,SV288: $i] :
      ( ( ( c_Predicate_Oreflp @ SV288 @ SV187 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV187 @ SV67 ) @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6003]) ).

thf(6112,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i] :
      ( ( ! [SY1590: $i,SY1591: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1591 @ SY1590 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
                  | ~ ! [SY1507: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY1508: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY1591 @ SY1590 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6004]) ).

thf(6113,plain,
    ! [SV69: $i,SV189: $i,SV290: $i,SV371: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV189 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV69 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6005]) ).

thf(6114,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
         != ( hAPP @ c_Nat_OSuc @ SV70 ) )
        | ( SV190 = SV70 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6006]) ).

thf(6115,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( SV190 != SV70 )
        | ( ( hAPP @ c_Nat_OSuc @ SV190 )
          = ( hAPP @ c_Nat_OSuc @ SV70 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6007]) ).

thf(6116,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
            | ! [SY1350: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6008]) ).

thf(6117,plain,
    ! [SV291: $i,SV71: $i,SV191: $i] :
      ( ( ~ ( ~ ! [SY1351: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
                  | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6008]) ).

thf(6118,plain,
    ! [SV72: $i,SV192: $i,SV292: $i,SV372: $i,SV431: $i] :
      ( ( ( ( hAPP @ SV431 @ SV372 )
         != SV292 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SV431 ) @ SV372 ) @ SV292 )
          = SV431 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6009]) ).

thf(6119,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i,SV432: $i] :
      ( ( ! [SY1594: $i] :
            ( ~ ( ( SY1594 != SV432 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SV432 ) @ SV73 ) @ SY1594 )
              = ( hAPP @ SV193 @ SY1594 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6010]) ).

thf(6120,plain,
    ! [SV74: $i,SV194: $i,SV294: $i,SV374: $i] :
      ( ( ( SV374 != SV294 )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6011]) ).

thf(6121,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
             != SV75 )
            | ( SV195
              = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6012]) ).

thf(6122,plain,
    ! [SV75: $i,SV295: $i,SV195: $i] :
      ( ( ~ ( ( SV195
             != ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
            | ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
              = SV75 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6012]) ).

thf(6123,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ~ ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        | ! [SY760: $i,SY761: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                  | ( ( hAPP @ SV76 @ SY760 )
                    = ( hAPP @ SV76 @ SY761 ) ) )
              | ~ ( ( ( hAPP @ SV76 @ SY760 )
                   != ( hAPP @ SV76 @ SY761 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6013]) ).

thf(6124,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ~ ! [SY762: $i,SY763: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                    | ( ( hAPP @ SV76 @ SY762 )
                      = ( hAPP @ SV76 @ SY763 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ SY762 )
                     != ( hAPP @ SV76 @ SY763 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) )
        | ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6014]) ).

thf(6125,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
            | ~ ! [SY1115: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
        | ~ ( ~ ~ ! [SY1116: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6015]) ).

thf(6126,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
             != ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
            | ( SV198 = SV78 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6016]) ).

thf(6127,plain,
    ! [SV297: $i,SV78: $i,SV198: $i] :
      ( ( ~ ( ( SV198 != SV78 )
            | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
              = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6016]) ).

thf(6128,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i,SV433: $i] :
      ( ( ! [SY1595: $i,SY1596: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1596 @ SY1595 @ SV433 @ SV376 @ SV298 )
            | ~ ( ~ ( ( ( hAPP @ SV433 @ SV199 )
                     != ( hAPP @ SV433 @ SV79 ) )
                    | ( SV199 = SV79 ) )
                | ~ ( ( SV199 != SV79 )
                    | ( ( hAPP @ SV433 @ SV199 )
                      = ( hAPP @ SV433 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6017]) ).

thf(6129,plain,
    ! [SV80: $i,SV200: $i,SV299: $i,SV377: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV377 @ SV299 @ SV200 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV299 @ SV80 ) @ SV80 )
          = SV80 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6018]) ).

thf(6130,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i] :
      ( ( ! [SY1597: $i,SY1598: $i,SY1599: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1599 @ SY1598 @ SY1597 @ SV434 ) @ SV378 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SY1598 @ SY1597 @ SV201 ) @ SV81 ) )
            | ! [SY1600: $i] :
                ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6019]) ).

thf(6131,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
            | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                    | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6020]) ).

thf(6132,plain,
    ! [SV83: $i,SV203: $i,SV302: $i] :
      ( ( ( c_Equiv__Relations_Oequivp @ SV302 @ SV203 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV83 ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6021]) ).

thf(6133,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
            | ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6022]) ).

thf(6134,plain,
    ! [SV303: $i,SV204: $i,SV84: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6022]) ).

thf(6135,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) )
        = $false )
      | ( ( ~ ! [SY1374: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ SY1374 ) @ SV85 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6023]) ).

thf(6136,plain,
    ! [SV86: $i,SV206: $i,SV305: $i,SV380: $i,SV436: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV380 ) @ SV305 ) )
        | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SV436 ) @ SV380 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6024]) ).

thf(6137,plain,
    ! [SV87: $i,SV207: $i,SV306: $i,SV381: $i,SV437: $i] :
      ( ( ! [SY1601: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1601 @ SV437 @ SV381 @ SV306 @ SV207 )
            | ( ( hAPP @ SV306 @ ( hAPP @ SV381 @ SV87 ) )
              = SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6025]) ).

thf(6138,plain,
    ! [SV88: $i,SV208: $i,SV307: $i,SV382: $i,SV438: $i] :
      ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV438 @ SV382 @ SV307 )
        | ( ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
          = ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6026]) ).

thf(6139,plain,
    ! [SV89: $i,SV209: $i,SV308: $i,SV383: $i,SV439: $i] :
      ( ( ! [SY1602: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1602 ) @ SV439 ) @ SV383 )
             != SV308 )
            | ( SV209
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1602 ) @ SV383 ) @ SV89 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1602 ) @ SV439 ) @ SV209 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1602 ) @ SV308 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6027]) ).

thf(6140,plain,
    ! [SV90: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK1_SY817 @ SV90 ) ) ) )
        = $false )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6028]) ).

thf(6141,plain,
    ! [SV90: $i] :
      ( ( ( SV90
          = ( sK1_SY817 @ SV90 ) )
        = $false )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6028]) ).

thf(6142,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i] :
      ( ( ! [SY1603: $i,SY1604: $i,SY1605: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1605 @ SY1604 ) @ SY1603 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SY1603 ) @ SV384 ) )
            | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SY1605 @ SV440 @ SY1604 @ SV384 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6029]) ).

thf(6143,plain,
    ! [SV92: $i,SV211: $i,SV310: $i,SV385: $i,SV441: $i] :
      ( ( ~ ~ ( hBOOL @ ( hAPP @ SV441 @ SV385 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6030]) ).

thf(6144,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
            | ~ ! [SY1392: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6031]) ).

thf(6145,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ( ~ ~ ! [SY1393: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6031]) ).

thf(6146,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i] :
      ( ( ! [SY1606: $i] :
            ~ ( ~ ( ( SY1606 != SV442 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SY1606 )
                    = SV94 ) )
              | ~ ( ~ ( ( SY1606 != SV442 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SY1606 )
                    = ( hAPP @ SV213 @ SY1606 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6032]) ).

thf(6147,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
                 != SV313 )
                | ( ( hAPP @ SV313 @ SV214 )
                  = SV95 ) )
            | ~ ( ( ( hAPP @ SV313 @ SV214 )
                 != SV95 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
                  = SV313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6033]) ).

thf(6148,plain,
    ! [SV96: $i,SV215: $i,SV314: $i,SV388: $i] :
      ( ( ( SV388 != SV314 )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6034]) ).

thf(6149,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
            | ( SV216 = SV97 ) )
        | ~ ( ( SV216 != SV97 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6035]) ).

thf(6150,plain,
    ! [SV98: $i,SV217: $i,SV316: $i,SV390: $i] :
      ( ( ( SV390 != SV316 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV390 ) @ SV98 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6036]) ).

thf(6151,plain,
    ! [SV99: $i,SV218: $i] :
      ( ( ( ( hAPP @ SV218 @ ( sK2_SY1178 @ SV99 @ SV218 ) )
          = ( hAPP @ SV99 @ ( sK2_SY1178 @ SV99 @ SV218 ) ) )
        = $false )
      | ( ( SV218 = SV99 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6037]) ).

thf(6152,plain,
    ! [SV100: $i,SV219: $i,SV317: $i,SV391: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV391 ) @ SV317 ) @ SV219 ) @ SV100 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV391 ) @ SV317 ) @ SV100 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6038]) ).

thf(6153,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ( ~ ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) )
            | ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6039]) ).

thf(6154,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ( ~ ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) )
            | ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6039]) ).

thf(6155,plain,
    ! [SV102: $i,SV221: $i,SV319: $i,SV392: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV221 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV102 ) )
          | ( SV221 = SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6040]) ).

thf(6156,plain,
    ! [SV104: $i,SV223: $i,SV320: $i,SV393: $i,SV444: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV444 @ SV393 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV444 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6042]) ).

thf(6157,plain,
    ! [SV105: $i,SV224: $i] :
      ( ( ( ! [SY1193: $i] :
              ~ ( hBOOL @ ( hAPP @ SV224 @ SY1193 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6043]) ).

thf(6158,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
                | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6044]) ).

thf(6159,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
            | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                    | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6045]) ).

thf(6160,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
         != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
        | ( SV227 = SV108 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6046]) ).

thf(6161,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( SV227 != SV108 )
        | ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
          = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6047]) ).

thf(6162,plain,
    ! [SV109: $i,SV228: $i,SV323: $i,SV396: $i,SV447: $i] :
      ( ( ! [SY1607: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1607 @ SV447 ) @ SV396 ) @ SV323 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1607 @ SV447 ) @ SV228 ) @ SV109 ) )
            | ~ ( ( SV396 != SV228 )
                | ( SV323 != SV109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6048]) ).

thf(6163,plain,
    ! [SV110: $i,SV229: $i,SV324: $i,SV397: $i,SV448: $i] :
      ( ( ~ ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6049]) ).

thf(6164,plain,
    ! [SV111: $i,SV230: $i,SV325: $i,SV398: $i,SV449: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV449 @ SV398 ) @ SV325 ) )
        | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SV449 ) @ SV325 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6050]) ).

thf(6165,plain,
    ! [SV112: $i,SV231: $i] :
      ( ( ( ! [SY1210: $i] :
              ~ ( hBOOL @ ( hAPP @ SV231 @ SY1210 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6051]) ).

thf(6166,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
                 != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
                | ~ ( ( SV399 != SV232 )
                    | ( SV326 != SV113 ) ) )
            | ~ ( ~ ~ ( ( SV399 != SV232 )
                      | ( SV326 != SV113 ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
                  = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6052]) ).

thf(6167,plain,
    ! [SV114: $i,SV233: $i,SV327: $i,SV400: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV233 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV114 ) )
          | ( SV114 = SV233 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6053]) ).

thf(6168,plain,
    ! [SV116: $i,SV235: $i,SV329: $i,SV401: $i] :
      ( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV401 @ SV329 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6055]) ).

thf(6169,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
        | ( SV236 = SV117 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6056]) ).

thf(6170,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( SV236 != SV117 )
        | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6057]) ).

thf(6171,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        | ~ ! [SY1219: $i] :
              ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6058]) ).

thf(6172,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ~ ~ ! [SY1220: $i] :
                ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) )
        | ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6059]) ).

thf(6173,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
         != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
        | ( SV238 = SV119 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6060]) ).

thf(6174,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( SV238 != SV119 )
        | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6061]) ).

thf(6175,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
             != ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
            | ( SV239 = SV120 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6062]) ).

thf(6176,plain,
    ! [SV330: $i,SV120: $i,SV239: $i] :
      ( ( ~ ( ( SV239 != SV120 )
            | ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
              = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6062]) ).

thf(6177,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
            | ~ ! [SY1224: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
        | ~ ( ~ ~ ! [SY1225: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6063]) ).

thf(6178,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
            | ~ ! [SY1547: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
        | ~ ( ~ ~ ! [SY1548: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6064]) ).

thf(6179,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
         != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
        | ( SV242 = SV123 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6065]) ).

thf(6180,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( SV242 != SV123 )
        | ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
          = ( hAPP @ c_Int_ORep__Integ @ SV123 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6066]) ).

thf(6181,plain,
    ! [SV124: $i,SV243: $i,SV333: $i,SV404: $i,SV451: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
        | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6067]) ).

thf(6182,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i] :
      ( ( ! [SY1608: $i,SY1609: $i,SY1610: $i,SY1611: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1611 @ SY1610 @ SY1609 @ SY1608 ) @ SV452 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SY1610 @ SY1609 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SY1608 @ ( hAPP @ SV452 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6068]) ).

thf(6183,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i] :
      ( ( ! [SY1612: $i,SY1613: $i,SY1614: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1614 ) @ SY1613 ) @ SY1612 ) @ SV453 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY1615: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1614 ) @ SY1613 ) @ SY1615 ) @ SV453 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1615 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6069]) ).

thf(6184,plain,
    ! [SV5: $i,SV129: $i,SV248: $i,SV337: $i,SV407: $i,SV454: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV454 @ SV407 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
        = ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6070]) ).

thf(6185,plain,
    ! [SV7: $i,SV131: $i,SV250: $i,SV339: $i,SV408: $i,SV455: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ SV339 ) @ SV250 ) @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6071]) ).

thf(6186,plain,
    ! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i,SV456: $i] :
      ( ( ! [SY1616: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1616 @ SV456 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1616 @ SV410 @ SV133 ) @ SV9 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV456 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SY1616 @ SV456 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6073]) ).

thf(6187,plain,
    ! [SV10: $i,SV134: $i,SV253: $i,SV342: $i,SV411: $i,SV457: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV457 @ SV411 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
        = ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6074]) ).

thf(6188,plain,
    ! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i,SV458: $i] :
      ( ( ! [SY1617: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1617 @ SV458 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1617 @ SV343 @ SV458 ) @ SV254 ) @ SV138 ) ) @ SV14 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1617 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SV458 @ SV412 ) @ SV138 ) @ SV14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6075]) ).

thf(6189,plain,
    ! [SV22: $i,SV146: $i,SV260: $i,SV348: $i,SV414: $i,SV459: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV459 @ SV414 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
        = ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6077]) ).

thf(6190,plain,
    ! [SV23: $i,SV147: $i,SV261: $i,SV349: $i,SV415: $i,SV460: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV460 @ SV415 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
        = ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6078]) ).

thf(6191,plain,
    ! [SV24: $i,SV148: $i,SV262: $i,SV350: $i,SV416: $i,SV461: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV461 @ SV416 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
        = ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6079]) ).

thf(6192,plain,
    ! [SV150: $i,SV28: $i] :
      ( ( ( hBOOL @ SV28 )
        = $false )
      | ( ( hBOOL @ SV150 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6080]) ).

thf(6193,plain,
    ! [SV36: $i,SV158: $i] :
      ( ( ( hBOOL @ SV158 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
        = $false )
      | ( ( hBOOL @ SV36 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6082]) ).

thf(6194,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                  | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6083]) ).

thf(6195,plain,
    ! [SV39: $i,SV160: $i,SV264: $i,SV352: $i,SV418: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV418 ) @ SV352 ) @ SV264 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV418 @ SV160 ) ) @ SV352 ) @ SV39 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6084]) ).

thf(6196,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        | ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        | ~ ! [SY1286: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6085]) ).

thf(6197,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
            | ~ ! [SY1287: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6086]) ).

thf(6198,plain,
    ! [SV41: $i,SV162: $i,SV266: $i,SV353: $i,SV419: $i,SV462: $i] :
      ( ( ( SV462 != SV419 )
        | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV462 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV419 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6087]) ).

thf(6199,plain,
    ! [SV42: $i,SV163: $i,SV267: $i] :
      ( ( ( ! [SY1291: $i] :
              ~ ( hBOOL @ ( hAPP @ SV267 @ SY1291 ) ) )
        = $true )
      | ( ( ( SV163
           != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
          | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6088]) ).

thf(6200,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i] :
      ( ( ! [SY1618: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1618 ) @ SV463 ) @ SV420 ) @ SV354 )
                   != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1618 ) @ SV268 ) @ SV164 ) @ SV43 ) )
                  | ~ ( ~ ~ ( ( SV463 != SV268 )
                            | ( SV420 != SV164 ) )
                      | ( SV354 != SV43 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                              | ( SV420 != SV164 ) )
                        | ( SV354 != SV43 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1618 ) @ SV463 ) @ SV420 ) @ SV354 )
                    = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1618 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6089]) ).

thf(6201,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i,SV421: $i,SV464: $i] :
      ( ( ~ ( ( SV464 != SV421 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV464 ) @ SV165 ) ) @ SV421 ) @ SV44 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV421 ) @ SV44 ) ) @ SV464 ) @ SV165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6090]) ).

thf(6202,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ~ ( ~ ( ( SV465 != SV422 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
                  = SV45 ) )
            | ~ ( ~ ( ( SV465 != SV422 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
                  = ( hAPP @ SV166 @ SV465 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6091]) ).

thf(6203,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
            | ~ ( ( SV47 != SV168 )
                | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                | ~ ~ ! [SY1478: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6092]) ).

thf(6204,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ~ ( ~ ( ~ ( ( SV47 != SV168 )
                    | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                    | ~ ~ ! [SY1479: $i] :
                            ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6092]) ).

thf(6205,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i] :
      ( ( ! [SY1619: $i,SY1620: $i,SY1621: $i,SY1622: $i,SY1623: $i] :
            ( ( ( hAPP @ SY1623 @ ( hAPP @ SY1622 @ SY1621 ) )
             != ( hAPP @ SY1620 @ ( hAPP @ SY1619 @ SV466 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1623 ) @ SY1622 ) @ SY1621 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SY1620 ) @ SY1619 ) @ SV466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6093]) ).

thf(6206,plain,
    ! [SV50: $i,SV171: $i,SV273: $i,SV359: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false )
      | ( ( ~ ! [SY1487: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ SY1487 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SY1487 ) @ SV50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6094]) ).

thf(6207,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
                 != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
                | ~ ( ( SV360 != SV172 )
                    | ( SV274 != SV51 ) ) )
            | ~ ( ~ ~ ( ( SV360 != SV172 )
                      | ( SV274 != SV51 ) )
                | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
                  = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6095]) ).

thf(6208,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i,SV425: $i,SV468: $i] :
      ( ( ! [SY1624: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1624 @ SV468 @ SV425 @ SV361 ) @ SV275 )
             != SV173 )
            | ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
              = ( hAPP @ SV173 @ SV52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6096]) ).

thf(6209,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
            | ( SV276 = SV53 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6097]) ).

thf(6210,plain,
    ! [SV174: $i,SV362: $i,SV53: $i,SV276: $i] :
      ( ( ~ ( ( SV276 != SV53 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6097]) ).

thf(6211,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
            | ~ ! [SY1584: $i] :
                  ~ ( ~ ( ( SV363
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                         != SV54 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                         != SV175 )
                        | ( SV277
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
        | ~ ( ~ ~ ! [SY1585: $i] :
                    ~ ( ~ ( ( SV363
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                           != SV54 ) )
                      | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                           != SV175 )
                          | ( SV277
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6098]) ).

thf(6212,plain,
    ! [SV55: $i,SV176: $i,SV278: $i,SV364: $i] :
      ( ( ( SV364 = SV278 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6099]) ).

thf(6213,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
        = $true )
      | ( ( SV178 = SV57 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6101]) ).

thf(6214,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( SV178 != SV57 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6102]) ).

thf(6215,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i,SV427: $i,SV469: $i] :
      ( ( ! [SY1625: $i] :
            ( ( SY1625 != SV469 )
            | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SY1625 )
              = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6103]) ).

thf(6216,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i,SV470: $i] :
      ( ( ! [SY1626: $i] :
            ( ~ ( ( SY1626 != SV470 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SY1626 ) @ SV180 ) ) @ SV470 ) @ SV59 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV470 ) @ SV59 ) ) @ SY1626 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6104]) ).

thf(6217,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
            | ( SV282 = SV60 )
            | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6105]) ).

thf(6218,plain,
    ! [SV367: $i,SV181: $i,SV60: $i,SV282: $i] :
      ( ( ~ ( ~ ( ( SV282 = SV60 )
                | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6105]) ).

thf(6219,plain,
    ! [SV61: $i,SV182: $i,SV283: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV283 @ SV182 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV283 @ SV61 ) ) @ SV182 ) @ SV182 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6106]) ).

thf(6220,plain,
    ! [SV63: $i,SV184: $i,SV285: $i,SV368: $i,SV429: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV429 @ SV368 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6107]) ).

thf(6221,plain,
    ! [SV65: $i,SV185: $i,SV286: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false )
      | ( ( ~ ( ( SV65 != SV185 )
              | ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6108]) ).

thf(6222,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        | ! [SY1341: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6109]) ).

thf(6223,plain,
    ! [SV287: $i,SV66: $i,SV186: $i] :
      ( ( ~ ! [SY1342: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) )
        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6110]) ).

thf(6224,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i] :
      ( ( ! [SY1627: $i] :
            ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1627 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
                  | ~ ! [SY1507: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
              | ~ ( ~ ~ ! [SY1508: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
                  | ( c_Predicate_Opred__comp @ SY1627 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6112]) ).

thf(6225,plain,
    ! [SV69: $i,SV189: $i,SV290: $i,SV371: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV189 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV69 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6113]) ).

thf(6226,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
         != ( hAPP @ c_Nat_OSuc @ SV70 ) )
        = $true )
      | ( ( SV190 = SV70 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6114]) ).

thf(6227,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( SV190 != SV70 )
        = $true )
      | ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
          = ( hAPP @ c_Nat_OSuc @ SV70 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6115]) ).

thf(6228,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        | ! [SY1350: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
            | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6116]) ).

thf(6229,plain,
    ! [SV291: $i,SV71: $i,SV191: $i] :
      ( ( ~ ! [SY1351: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) )
        | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6117]) ).

thf(6230,plain,
    ! [SV72: $i,SV192: $i,SV292: $i,SV372: $i,SV431: $i] :
      ( ( ( ( hAPP @ SV431 @ SV372 )
         != SV292 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SV431 ) @ SV372 ) @ SV292 )
          = SV431 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6118]) ).

thf(6231,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i,SV432: $i,SV472: $i] :
      ( ( ~ ( ( SV472 != SV432 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SV432 ) @ SV73 ) @ SV472 )
          = ( hAPP @ SV193 @ SV472 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6119]) ).

thf(6232,plain,
    ! [SV74: $i,SV194: $i,SV294: $i,SV374: $i] :
      ( ( ( SV374 = SV294 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6120]) ).

thf(6233,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
         != SV75 )
        | ( SV195
          = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6121]) ).

thf(6234,plain,
    ! [SV75: $i,SV295: $i,SV195: $i] :
      ( ( ( SV195
         != ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
        | ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
          = SV75 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6122]) ).

thf(6235,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 ) )
        = $true )
      | ( ( ! [SY760: $i,SY761: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                    | ( ( hAPP @ SV76 @ SY760 )
                      = ( hAPP @ SV76 @ SY761 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ SY760 )
                     != ( hAPP @ SV76 @ SY761 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6123]) ).

thf(6236,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ! [SY762: $i,SY763: $i] :
                ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                      | ( ( hAPP @ SV76 @ SY762 )
                        = ( hAPP @ SV76 @ SY763 ) ) )
                  | ~ ( ( ( hAPP @ SV76 @ SY762 )
                       != ( hAPP @ SV76 @ SY763 ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6124]) ).

thf(6237,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
            | ~ ! [SY1115: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6125]) ).

thf(6238,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ~ ( ~ ~ ! [SY1116: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6125]) ).

thf(6239,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
         != ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
        | ( SV198 = SV78 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6126]) ).

thf(6240,plain,
    ! [SV297: $i,SV78: $i,SV198: $i] :
      ( ( ( SV198 != SV78 )
        | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6127]) ).

thf(6241,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i,SV433: $i,SV473: $i] :
      ( ( ! [SY1630: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1630 @ SV473 @ SV433 @ SV376 @ SV298 )
            | ~ ( ~ ( ( ( hAPP @ SV433 @ SV199 )
                     != ( hAPP @ SV433 @ SV79 ) )
                    | ( SV199 = SV79 ) )
                | ~ ( ( SV199 != SV79 )
                    | ( ( hAPP @ SV433 @ SV199 )
                      = ( hAPP @ SV433 @ SV79 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6128]) ).

thf(6242,plain,
    ! [SV80: $i,SV200: $i,SV299: $i,SV377: $i] :
      ( ( ( c_Finite__Set_Ofolding__one__idem @ SV377 @ SV299 @ SV200 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV299 @ SV80 ) @ SV80 )
          = SV80 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6129]) ).

thf(6243,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i,SV474: $i] :
      ( ( ! [SY1631: $i,SY1632: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1632 @ SY1631 @ SV474 @ SV434 ) @ SV378 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SY1631 @ SV474 @ SV201 ) @ SV81 ) )
            | ! [SY1600: $i] :
                ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6130]) ).

thf(6244,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6131]) ).

thf(6245,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
        | ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6133]) ).

thf(6246,plain,
    ! [SV303: $i,SV204: $i,SV84: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6134]) ).

thf(6247,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ( ! [SY1374: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ SY1374 ) @ SV85 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6135]) ).

thf(6248,plain,
    ! [SV86: $i,SV206: $i,SV305: $i,SV380: $i,SV436: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV380 ) @ SV305 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SV436 ) @ SV380 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6136]) ).

thf(6249,plain,
    ! [SV87: $i,SV207: $i,SV306: $i,SV381: $i,SV437: $i,SV475: $i] :
      ( ( ~ ( c_Typedef_Otype__definition @ SV475 @ SV437 @ SV381 @ SV306 @ SV207 )
        | ( ( hAPP @ SV306 @ ( hAPP @ SV381 @ SV87 ) )
          = SV87 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6137]) ).

thf(6250,plain,
    ! [SV88: $i,SV208: $i,SV307: $i,SV382: $i,SV438: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV438 @ SV382 @ SV307 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
          = ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6138]) ).

thf(6251,plain,
    ! [SV89: $i,SV209: $i,SV308: $i,SV383: $i,SV439: $i,SV476: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV383 )
         != SV308 )
        | ( SV209
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV383 ) @ SV89 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV209 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV308 ) @ SV89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6139]) ).

thf(6252,plain,
    ! [SV90: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK1_SY817 @ SV90 ) ) )
        = $true )
      | ( ( SV90 = v_s_H )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6140]) ).

thf(6253,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i,SV477: $i] :
      ( ( ! [SY1634: $i,SY1635: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1635 @ SY1634 ) @ SV477 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
            | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SY1635 @ SV440 @ SY1634 @ SV384 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6142]) ).

thf(6254,plain,
    ! [SV92: $i,SV211: $i,SV310: $i,SV385: $i,SV441: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV441 @ SV385 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6143]) ).

thf(6255,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        | ~ ! [SY1392: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6144]) ).

thf(6256,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ~ ~ ! [SY1393: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6145]) ).

thf(6257,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ~ ( ~ ( ( SV478 != SV442 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
                  = SV94 ) )
            | ~ ( ~ ( ( SV478 != SV442 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
                  = ( hAPP @ SV213 @ SV478 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6146]) ).

thf(6258,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
             != SV313 )
            | ( ( hAPP @ SV313 @ SV214 )
              = SV95 ) )
        | ~ ( ( ( hAPP @ SV313 @ SV214 )
             != SV95 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
              = SV313 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6147]) ).

thf(6259,plain,
    ! [SV96: $i,SV215: $i,SV314: $i,SV388: $i] :
      ( ( ( SV388 = SV314 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6148]) ).

thf(6260,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
            | ( SV216 = SV97 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6149]) ).

thf(6261,plain,
    ! [SV315: $i,SV389: $i,SV97: $i,SV216: $i] :
      ( ( ~ ( ( SV216 != SV97 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6149]) ).

thf(6262,plain,
    ! [SV98: $i,SV217: $i,SV316: $i,SV390: $i] :
      ( ( ( SV390 = SV316 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV390 ) @ SV98 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6150]) ).

thf(6263,plain,
    ! [SV100: $i,SV219: $i,SV317: $i,SV391: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV391 ) @ SV317 ) @ SV219 ) @ SV100 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV391 ) @ SV317 ) @ SV100 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6152]) ).

thf(6264,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) )
        | ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6153]) ).

thf(6265,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ~ ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) )
        | ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6154]) ).

thf(6266,plain,
    ! [SV102: $i,SV221: $i,SV319: $i,SV392: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV221 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV102 ) )
          | ( SV221 = SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6155]) ).

thf(6267,plain,
    ! [SV104: $i,SV223: $i,SV320: $i,SV393: $i,SV444: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV444 @ SV393 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV444 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6156]) ).

thf(6268,plain,
    ! [SV105: $i,SV479: $i,SV224: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV224 @ SV479 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6157]) ).

thf(6269,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
            | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6158]) ).

thf(6270,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        | ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6159]) ).

thf(6271,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
         != ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
        = $true )
      | ( ( SV227 = SV108 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6160]) ).

thf(6272,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( SV227 != SV108 )
        = $true )
      | ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
          = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6161]) ).

thf(6273,plain,
    ! [SV109: $i,SV228: $i,SV323: $i,SV396: $i,SV447: $i,SV480: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        | ~ ( ( SV396 != SV228 )
            | ( SV323 != SV109 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6162]) ).

thf(6274,plain,
    ! [SV110: $i,SV229: $i,SV324: $i,SV397: $i,SV448: $i] :
      ( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6163]) ).

thf(6275,plain,
    ! [SV111: $i,SV230: $i,SV325: $i,SV398: $i,SV449: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV449 @ SV398 ) @ SV325 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SV449 ) @ SV325 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6164]) ).

thf(6276,plain,
    ! [SV112: $i,SV481: $i,SV231: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV231 @ SV481 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6165]) ).

thf(6277,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
             != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
            | ~ ( ( SV399 != SV232 )
                | ( SV326 != SV113 ) ) )
        | ~ ( ~ ~ ( ( SV399 != SV232 )
                  | ( SV326 != SV113 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6166]) ).

thf(6278,plain,
    ! [SV114: $i,SV233: $i,SV327: $i,SV400: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV233 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV114 ) )
          | ( SV114 = SV233 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6167]) ).

thf(6279,plain,
    ! [SV116: $i,SV235: $i,SV329: $i,SV401: $i] :
      ( ( ( c_Equiv__Relations_Oequivp @ SV401 @ SV329 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6168]) ).

thf(6280,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
        = $true )
      | ( ( SV236 = SV117 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6169]) ).

thf(6281,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( SV236 != SV117 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6170]) ).

thf(6282,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1219: $i] :
                ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6171]) ).

thf(6283,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ~ ~ ! [SY1220: $i] :
                  ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6172]) ).

thf(6284,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
         != ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
        = $true )
      | ( ( SV238 = SV119 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6173]) ).

thf(6285,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( SV238 != SV119 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6174]) ).

thf(6286,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
         != ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
        | ( SV239 = SV120 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6175]) ).

thf(6287,plain,
    ! [SV330: $i,SV120: $i,SV239: $i] :
      ( ( ( SV239 != SV120 )
        | ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
          = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6176]) ).

thf(6288,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
            | ~ ! [SY1224: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6177]) ).

thf(6289,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ~ ( ~ ~ ! [SY1225: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
            | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6177]) ).

thf(6290,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
            | ~ ! [SY1547: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6178]) ).

thf(6291,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ~ ( ~ ~ ! [SY1548: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6178]) ).

thf(6292,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
         != ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
        = $true )
      | ( ( SV242 = SV123 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6179]) ).

thf(6293,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( SV242 != SV123 )
        = $true )
      | ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
          = ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6180]) ).

thf(6294,plain,
    ! [SV124: $i,SV243: $i,SV333: $i,SV404: $i,SV451: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6181]) ).

thf(6295,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i] :
      ( ( ! [SY1636: $i,SY1637: $i,SY1638: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1638 @ SY1637 @ SY1636 @ SV482 ) @ SV452 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SY1637 @ SY1636 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6182]) ).

thf(6296,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i,SV483: $i] :
      ( ( ! [SY1639: $i,SY1640: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1640 ) @ SY1639 ) @ SV483 ) @ SV453 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY1615: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1640 ) @ SY1639 ) @ SY1615 ) @ SV453 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1615 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6183]) ).

thf(6297,plain,
    ! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i,SV456: $i,SV484: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ SV484 @ SV456 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV484 @ SV410 @ SV133 ) @ SV9 ) )
        = ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV456 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SV484 @ SV456 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6186]) ).

thf(6298,plain,
    ! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i,SV458: $i,SV485: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV458 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV343 @ SV458 ) @ SV254 ) @ SV138 ) ) @ SV14 )
        = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SV458 @ SV412 ) @ SV138 ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6188]) ).

thf(6299,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6194]) ).

thf(6300,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                  | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6194]) ).

thf(6301,plain,
    ! [SV39: $i,SV160: $i,SV264: $i,SV352: $i,SV418: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV418 ) @ SV352 ) @ SV264 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV418 @ SV160 ) ) @ SV352 ) @ SV39 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6195]) ).

thf(6302,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
          | ~ ! [SY1286: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6196]) ).

thf(6303,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
              | ~ ! [SY1287: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6197]) ).

thf(6304,plain,
    ! [SV41: $i,SV162: $i,SV266: $i,SV353: $i,SV419: $i,SV462: $i] :
      ( ( ( SV462 != SV419 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV462 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV419 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6198]) ).

thf(6305,plain,
    ! [SV42: $i,SV163: $i,SV486: $i,SV267: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV267 @ SV486 ) ) )
        = $true )
      | ( ( ( SV163
           != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
          | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6199]) ).

thf(6306,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
                 != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
                | ~ ( ~ ~ ( ( SV463 != SV268 )
                          | ( SV420 != SV164 ) )
                    | ( SV354 != SV43 ) ) )
            | ~ ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                            | ( SV420 != SV164 ) )
                      | ( SV354 != SV43 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
                  = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6200]) ).

thf(6307,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i,SV421: $i,SV464: $i] :
      ( ( ( ~ ( ( SV464 != SV421 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV464 ) @ SV165 ) ) @ SV421 ) @ SV44 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV421 ) @ SV44 ) ) @ SV464 ) @ SV165 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6201]) ).

thf(6308,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ~ ( ( SV465 != SV422 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
              = SV45 ) )
        | ~ ( ~ ( ( SV465 != SV422 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
              = ( hAPP @ SV166 @ SV465 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6202]) ).

thf(6309,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        | ~ ( ( SV47 != SV168 )
            | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
            | ~ ~ ! [SY1478: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6203]) ).

thf(6310,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ~ ( ~ ( ( SV47 != SV168 )
                | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                | ~ ~ ! [SY1479: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6204]) ).

thf(6311,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i] :
      ( ( ! [SY1642: $i,SY1643: $i,SY1644: $i,SY1645: $i] :
            ( ( ( hAPP @ SY1645 @ ( hAPP @ SY1644 @ SY1643 ) )
             != ( hAPP @ SY1642 @ ( hAPP @ SV488 @ SV466 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1645 ) @ SY1644 ) @ SY1643 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SY1642 ) @ SV488 ) @ SV466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6205]) ).

thf(6312,plain,
    ! [SV50: $i,SV273: $i,SV171: $i,SV359: $i] :
      ( ( ( ! [SY1487: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ SY1487 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SY1487 ) @ SV50 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6206]) ).

thf(6313,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
            | ~ ( ( SV360 != SV172 )
                | ( SV274 != SV51 ) ) )
        | ~ ( ~ ~ ( ( SV360 != SV172 )
                  | ( SV274 != SV51 ) )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6207]) ).

thf(6314,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i,SV425: $i,SV468: $i,SV489: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV468 @ SV425 @ SV361 ) @ SV275 )
         != SV173 )
        | ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
          = ( hAPP @ SV173 @ SV52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6208]) ).

thf(6315,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
        | ( SV276 = SV53 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6209]) ).

thf(6316,plain,
    ! [SV174: $i,SV362: $i,SV53: $i,SV276: $i] :
      ( ( ( SV276 != SV53 )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6210]) ).

thf(6317,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
            | ~ ! [SY1584: $i] :
                  ~ ( ~ ( ( SV363
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                         != SV54 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                         != SV175 )
                        | ( SV277
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6211]) ).

thf(6318,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ~ ( ~ ~ ! [SY1585: $i] :
                    ~ ( ~ ( ( SV363
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                           != SV54 ) )
                      | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                           != SV175 )
                          | ( SV277
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6211]) ).

thf(6319,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6212]) ).

thf(6320,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
        = $false )
      | ( ( SV178 = SV57 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6213]) ).

thf(6321,plain,
    ! [SV57: $i,SV178: $i] :
      ( ( ( SV178 = SV57 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV178 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV57 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6214]) ).

thf(6322,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i,SV427: $i,SV469: $i,SV490: $i] :
      ( ( ( SV490 != SV469 )
        | ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV490 )
          = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV469 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6215]) ).

thf(6323,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i,SV470: $i,SV491: $i] :
      ( ( ~ ( ( SV491 != SV470 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV491 ) @ SV180 ) ) @ SV470 ) @ SV59 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV470 ) @ SV59 ) ) @ SV491 ) @ SV180 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6216]) ).

thf(6324,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        | ( SV282 = SV60 )
        | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6217]) ).

thf(6325,plain,
    ! [SV367: $i,SV181: $i,SV60: $i,SV282: $i] :
      ( ( ~ ( ( SV282 = SV60 )
            | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6218]) ).

thf(6326,plain,
    ! [SV63: $i,SV184: $i,SV285: $i,SV368: $i,SV429: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6220]) ).

thf(6327,plain,
    ! [SV286: $i,SV369: $i,SV185: $i,SV65: $i] :
      ( ( ( ~ ( ( SV65 != SV185 )
              | ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6221]) ).

thf(6328,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) ) )
        = $true )
      | ( ( ! [SY1341: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6222]) ).

thf(6329,plain,
    ! [SV287: $i,SV66: $i,SV186: $i] :
      ( ( ( ~ ! [SY1342: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6223]) ).

thf(6330,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
                | ~ ! [SY1507: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
            | ~ ( ~ ~ ! [SY1508: $i] :
                        ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
                | ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6224]) ).

thf(6331,plain,
    ! [SV371: $i,SV189: $i,SV69: $i,SV290: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV69 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6225]) ).

thf(6332,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
          = ( hAPP @ c_Nat_OSuc @ SV70 ) )
        = $false )
      | ( ( SV190 = SV70 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6226]) ).

thf(6333,plain,
    ! [SV70: $i,SV190: $i] :
      ( ( ( SV190 = SV70 )
        = $false )
      | ( ( ( hAPP @ c_Nat_OSuc @ SV190 )
          = ( hAPP @ c_Nat_OSuc @ SV70 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6227]) ).

thf(6334,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) ) )
        = $true )
      | ( ( ! [SY1350: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6228]) ).

thf(6335,plain,
    ! [SV291: $i,SV71: $i,SV191: $i] :
      ( ( ( ~ ! [SY1351: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
                | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6229]) ).

thf(6336,plain,
    ! [SV72: $i,SV192: $i,SV292: $i,SV372: $i,SV431: $i] :
      ( ( ( ( hAPP @ SV431 @ SV372 )
          = SV292 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV192 @ SV72 ) @ SV431 ) @ SV372 ) @ SV292 )
          = SV431 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6230]) ).

thf(6337,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i,SV432: $i,SV472: $i] :
      ( ( ( ~ ( ( SV472 != SV432 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SV432 ) @ SV73 ) @ SV472 )
          = ( hAPP @ SV193 @ SV472 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6231]) ).

thf(6338,plain,
    ! [SV294: $i,SV374: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) ) )
        = $false )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6232]) ).

thf(6339,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
         != SV75 )
        = $true )
      | ( ( SV195
          = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6233]) ).

thf(6340,plain,
    ! [SV75: $i,SV295: $i,SV195: $i] :
      ( ( ( SV195
         != ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
        = $true )
      | ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
          = SV75 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6234]) ).

thf(6341,plain,
    ! [SV76: $i,SV196: $i] :
      ( ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false )
      | ( ( ! [SY760: $i,SY761: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) )
                    | ( ( hAPP @ SV76 @ SY760 )
                      = ( hAPP @ SV76 @ SY761 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ SY760 )
                     != ( hAPP @ SV76 @ SY761 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY760 ) @ SY761 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6235]) ).

thf(6342,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ! [SY762: $i,SY763: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) )
                    | ( ( hAPP @ SV76 @ SY762 )
                      = ( hAPP @ SV76 @ SY763 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ SY762 )
                     != ( hAPP @ SV76 @ SY763 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY762 ) @ SY763 ) ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6236]) ).

thf(6343,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        | ~ ! [SY1115: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6237]) ).

thf(6344,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ~ ~ ! [SY1116: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) )
        | ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6238]) ).

thf(6345,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
         != ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
        = $true )
      | ( ( SV198 = SV78 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6239]) ).

thf(6346,plain,
    ! [SV297: $i,SV78: $i,SV198: $i] :
      ( ( ( SV198 != SV78 )
        = $true )
      | ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6240]) ).

thf(6347,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i,SV433: $i,SV473: $i,SV493: $i] :
      ( ( ~ ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        | ~ ( ~ ( ( ( hAPP @ SV433 @ SV199 )
                 != ( hAPP @ SV433 @ SV79 ) )
                | ( SV199 = SV79 ) )
            | ~ ( ( SV199 != SV79 )
                | ( ( hAPP @ SV433 @ SV199 )
                  = ( hAPP @ SV433 @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6241]) ).

thf(6348,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i,SV474: $i,SV494: $i] :
      ( ( ! [SY1648: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1648 @ SV494 @ SV474 @ SV434 ) @ SV378 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SV494 @ SV474 @ SV201 ) @ SV81 ) )
            | ! [SY1600: $i] :
                ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
                = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6243]) ).

thf(6349,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6244]) ).

thf(6350,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6244]) ).

thf(6351,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6245]) ).

thf(6352,plain,
    ! [SV303: $i,SV204: $i,SV84: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV84 @ SV204 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6246]) ).

thf(6353,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ ( sK3_SY1374 @ SV85 @ SV205 @ SV304 ) ) @ SV85 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6247]) ).

thf(6354,plain,
    ! [SV86: $i,SV206: $i,SV305: $i,SV380: $i,SV436: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV380 ) @ SV305 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV206 @ SV86 @ SV436 ) @ SV380 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6248]) ).

thf(6355,plain,
    ! [SV87: $i,SV207: $i,SV306: $i,SV381: $i,SV437: $i,SV475: $i] :
      ( ( ( ~ ( c_Typedef_Otype__definition @ SV475 @ SV437 @ SV381 @ SV306 @ SV207 ) )
        = $true )
      | ( ( ( hAPP @ SV306 @ ( hAPP @ SV381 @ SV87 ) )
          = SV87 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6249]) ).

thf(6356,plain,
    ! [SV88: $i,SV208: $i,SV307: $i,SV382: $i,SV438: $i] :
      ( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV438 @ SV382 @ SV307 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
          = ( hAPP @ ( hAPP @ SV307 @ SV208 ) @ SV88 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6250]) ).

thf(6357,plain,
    ! [SV89: $i,SV209: $i,SV308: $i,SV383: $i,SV439: $i,SV476: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV383 )
         != SV308 )
        = $true )
      | ( ( ( SV209
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV383 ) @ SV89 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV209 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV308 ) @ SV89 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6251]) ).

thf(6358,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i,SV477: $i,SV495: $i] :
      ( ( ! [SY1650: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1650 @ SV495 ) @ SV477 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
            | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SY1650 @ SV440 @ SV495 @ SV384 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6253]) ).

thf(6359,plain,
    ! [SV92: $i,SV211: $i,SV310: $i,SV385: $i,SV441: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV441 @ SV385 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6254]) ).

thf(6360,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) ) )
        = $true )
      | ( ( ~ ! [SY1392: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6255]) ).

thf(6361,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ~ ~ ! [SY1393: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6256]) ).

thf(6362,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ~ ( ( SV478 != SV442 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
              = SV94 ) )
        | ~ ( ~ ( ( SV478 != SV442 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
              = ( hAPP @ SV213 @ SV478 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6257]) ).

thf(6363,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
             != SV313 )
            | ( ( hAPP @ SV313 @ SV214 )
              = SV95 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6258]) ).

thf(6364,plain,
    ! [SV387: $i,SV443: $i,SV95: $i,SV214: $i,SV313: $i] :
      ( ( ~ ( ( ( hAPP @ SV313 @ SV214 )
             != SV95 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
              = SV313 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6258]) ).

thf(6365,plain,
    ! [SV314: $i,SV96: $i,SV388: $i,SV215: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) ) )
        = $false )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6259]) ).

thf(6366,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
        | ( SV216 = SV97 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6260]) ).

thf(6367,plain,
    ! [SV315: $i,SV389: $i,SV97: $i,SV216: $i] :
      ( ( ( SV216 != SV97 )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6261]) ).

thf(6368,plain,
    ! [SV390: $i,SV98: $i,SV316: $i,SV217: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV390 ) @ SV98 ) )
        = $true )
      | ( ( SV390 = SV316 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6262]) ).

thf(6369,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ~ ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) ) )
        = $true )
      | ( ( ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6264]) ).

thf(6370,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ~ ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) ) )
        = $true )
      | ( ( ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6265]) ).

thf(6371,plain,
    ! [SV221: $i,SV102: $i,SV319: $i,SV392: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV102 ) ) )
        = $true )
      | ( ( SV221 = SV102 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV221 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6266]) ).

thf(6372,plain,
    ! [SV104: $i,SV223: $i,SV320: $i,SV393: $i,SV444: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV444 @ SV393 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV444 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6267]) ).

thf(6373,plain,
    ! [SV105: $i,SV479: $i,SV224: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV224 @ SV479 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV224 @ ( c_Hilbert__Choice_OEps @ SV105 @ SV224 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6268]) ).

thf(6374,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
            | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6269]) ).

thf(6375,plain,
    ! [SV394: $i,SV445: $i,SV106: $i,SV321: $i,SV225: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6269]) ).

thf(6376,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6270]) ).

thf(6377,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
                | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6270]) ).

thf(6378,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
          = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
        = $false )
      | ( ( SV227 = SV108 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6271]) ).

thf(6379,plain,
    ! [SV108: $i,SV227: $i] :
      ( ( ( SV227 = SV108 )
        = $false )
      | ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV227 )
          = ( hAPP @ c_Com_Ocom_OBODY @ SV108 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6272]) ).

thf(6380,plain,
    ! [SV109: $i,SV228: $i,SV323: $i,SV396: $i,SV447: $i,SV480: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $true )
      | ( ( ~ ( ( SV396 != SV228 )
              | ( SV323 != SV109 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6273]) ).

thf(6381,plain,
    ! [SV110: $i,SV229: $i,SV324: $i,SV397: $i,SV448: $i] :
      ( ( ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6274]) ).

thf(6382,plain,
    ! [SV111: $i,SV230: $i,SV325: $i,SV398: $i,SV449: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV449 @ SV398 ) @ SV325 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV230 @ SV111 @ SV449 ) @ SV325 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6275]) ).

thf(6383,plain,
    ! [SV112: $i,SV481: $i,SV231: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV231 @ SV481 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV231 @ ( c_Hilbert__Choice_OEps @ SV112 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6276]) ).

thf(6384,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
             != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
            | ~ ( ( SV399 != SV232 )
                | ( SV326 != SV113 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6277]) ).

thf(6385,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ~ ( ~ ~ ( ( SV399 != SV232 )
                  | ( SV326 != SV113 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6277]) ).

thf(6386,plain,
    ! [SV233: $i,SV114: $i,SV327: $i,SV400: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV114 ) ) )
        = $true )
      | ( ( SV114 = SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV233 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6278]) ).

thf(6387,plain,
    ! [SV401: $i,SV116: $i,SV235: $i,SV329: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV401 @ SV329 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6279]) ).

thf(6388,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
        = $false )
      | ( ( SV236 = SV117 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6280]) ).

thf(6389,plain,
    ! [SV117: $i,SV236: $i] :
      ( ( ( SV236 = SV117 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV236 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV117 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6281]) ).

thf(6390,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $false )
      | ( ( ~ ! [SY1219: $i] :
                ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6282]) ).

thf(6391,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ~ ! [SY1220: $i] :
                ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6283]) ).

thf(6392,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
        = $false )
      | ( ( SV238 = SV119 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6284]) ).

thf(6393,plain,
    ! [SV119: $i,SV238: $i] :
      ( ( ( SV238 = SV119 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV238 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV119 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6285]) ).

thf(6394,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
         != ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
        = $true )
      | ( ( SV239 = SV120 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6286]) ).

thf(6395,plain,
    ! [SV330: $i,SV120: $i,SV239: $i] :
      ( ( ( SV239 != SV120 )
        = $true )
      | ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
          = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6287]) ).

thf(6396,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        | ~ ! [SY1224: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6288]) ).

thf(6397,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ~ ~ ! [SY1225: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) )
        | ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6289]) ).

thf(6398,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        | ~ ! [SY1547: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6290]) ).

thf(6399,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ~ ~ ! [SY1548: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6291]) ).

thf(6400,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
          = ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
        = $false )
      | ( ( SV242 = SV123 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6292]) ).

thf(6401,plain,
    ! [SV123: $i,SV242: $i] :
      ( ( ( SV242 = SV123 )
        = $false )
      | ( ( ( hAPP @ c_Int_ORep__Integ @ SV242 )
          = ( hAPP @ c_Int_ORep__Integ @ SV123 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6293]) ).

thf(6402,plain,
    ! [SV124: $i,SV243: $i,SV333: $i,SV404: $i,SV451: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6294]) ).

thf(6403,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i,SV496: $i] :
      ( ( ! [SY1651: $i,SY1652: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1652 @ SY1651 @ SV496 @ SV482 ) @ SV452 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SY1651 @ SV496 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6295]) ).

thf(6404,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i,SV483: $i,SV497: $i] :
      ( ( ! [SY1653: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1653 ) @ SV497 ) @ SV483 ) @ SV453 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
            | ~ ! [SY1654: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1653 ) @ SV497 ) @ SY1654 ) @ SV453 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1654 ) @ SV126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6296]) ).

thf(6405,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
            | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6299]) ).

thf(6406,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
              | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6300]) ).

thf(6407,plain,
    ! [SV352: $i,SV418: $i,SV39: $i,SV264: $i,SV160: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV418 @ SV160 ) ) @ SV352 ) @ SV39 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV418 ) @ SV352 ) @ SV264 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6301]) ).

thf(6408,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
          | ~ ! [SY1286: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6302]) ).

thf(6409,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
          | ~ ! [SY1287: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6303]) ).

thf(6410,plain,
    ! [SV41: $i,SV162: $i,SV266: $i,SV353: $i,SV419: $i,SV462: $i] :
      ( ( ( SV462 = SV419 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV462 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV353 @ SV266 @ SV162 ) @ SV41 ) @ SV419 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6304]) ).

thf(6411,plain,
    ! [SV42: $i,SV163: $i,SV486: $i,SV267: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV267 @ SV486 ) )
        = $false )
      | ( ( ( SV163
           != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
          | ( hBOOL @ ( hAPP @ SV267 @ SV163 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6305]) ).

thf(6412,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
             != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
            | ~ ( ~ ~ ( ( SV463 != SV268 )
                      | ( SV420 != SV164 ) )
                | ( SV354 != SV43 ) ) )
        | ~ ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                        | ( SV420 != SV164 ) )
                  | ( SV354 != SV43 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6306]) ).

thf(6413,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i,SV421: $i,SV464: $i] :
      ( ( ( SV464 != SV421 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV464 ) @ SV165 ) ) @ SV421 ) @ SV44 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV421 ) @ SV44 ) ) @ SV464 ) @ SV165 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6307]) ).

thf(6414,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ~ ( ( SV465 != SV422 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
              = SV45 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6308]) ).

thf(6415,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ~ ( ~ ( ( SV465 != SV422 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
              = ( hAPP @ SV166 @ SV465 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6308]) ).

thf(6416,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) ) )
        = $true )
      | ( ( ~ ( ( SV47 != SV168 )
              | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6309]) ).

thf(6417,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ~ ( ~ ( ( SV47 != SV168 )
                  | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
                  | ~ ~ ! [SY1479: $i] :
                          ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6310]) ).

thf(6418,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i] :
      ( ( ! [SY1655: $i,SY1656: $i,SY1657: $i] :
            ( ( ( hAPP @ SY1657 @ ( hAPP @ SY1656 @ SY1655 ) )
             != ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1657 ) @ SY1656 ) @ SY1655 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6311]) ).

thf(6419,plain,
    ! [SV273: $i,SV50: $i,SV171: $i,SV359: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) @ SV50 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6312]) ).

thf(6420,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
            | ~ ( ( SV360 != SV172 )
                | ( SV274 != SV51 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6313]) ).

thf(6421,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ~ ( ~ ~ ( ( SV360 != SV172 )
                  | ( SV274 != SV51 ) )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6313]) ).

thf(6422,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i,SV425: $i,SV468: $i,SV489: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV468 @ SV425 @ SV361 ) @ SV275 )
         != SV173 )
        = $true )
      | ( ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
          = ( hAPP @ SV173 @ SV52 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6314]) ).

thf(6423,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
        = $true )
      | ( ( SV276 = SV53 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6315]) ).

thf(6424,plain,
    ! [SV174: $i,SV362: $i,SV53: $i,SV276: $i] :
      ( ( ( SV276 != SV53 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6316]) ).

thf(6425,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        | ~ ! [SY1584: $i] :
              ~ ( ~ ( ( SV363
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                     != SV54 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                     != SV175 )
                    | ( SV277
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6317]) ).

thf(6426,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ~ ~ ! [SY1585: $i] :
                ~ ( ~ ( ( SV363
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                       != SV54 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                       != SV175 )
                      | ( SV277
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6318]) ).

thf(6427,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6319]) ).

thf(6428,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i,SV427: $i,SV469: $i,SV490: $i] :
      ( ( ( SV490 != SV469 )
        = $true )
      | ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV490 )
          = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV469 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6322]) ).

thf(6429,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i,SV470: $i,SV491: $i] :
      ( ( ( ~ ( ( SV491 != SV470 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV491 ) @ SV180 ) ) @ SV470 ) @ SV59 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV470 ) @ SV59 ) ) @ SV491 ) @ SV180 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6323]) ).

thf(6430,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) ) )
        = $true )
      | ( ( ( SV282 = SV60 )
          | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6324]) ).

thf(6431,plain,
    ! [SV367: $i,SV181: $i,SV60: $i,SV282: $i] :
      ( ( ( ~ ( ( SV282 = SV60 )
              | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6325]) ).

thf(6432,plain,
    ! [SV63: $i,SV429: $i,SV184: $i,SV368: $i,SV285: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6326]) ).

thf(6433,plain,
    ! [SV286: $i,SV369: $i,SV185: $i,SV65: $i] :
      ( ( ( ( SV65 != SV185 )
          | ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6327]) ).

thf(6434,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $false )
      | ( ( ! [SY1341: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1341 ) @ SV66 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1341 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6328]) ).

thf(6435,plain,
    ! [SV287: $i,SV66: $i,SV186: $i] :
      ( ( ( ! [SY1342: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SY1342 ) @ SV66 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SY1342 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6329]) ).

thf(6436,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ~ ( ~ ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
            | ~ ! [SY1507: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
        | ~ ( ~ ~ ! [SY1508: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
            | ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6330]) ).

thf(6437,plain,
    ! [SV371: $i,SV189: $i,SV69: $i,SV290: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV290 @ SV69 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV69 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV371 @ SV290 ) @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6331]) ).

thf(6438,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $false )
      | ( ( ! [SY1350: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1350 ) @ SV71 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1350 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6334]) ).

thf(6439,plain,
    ! [SV291: $i,SV71: $i,SV191: $i] :
      ( ( ( ! [SY1351: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SY1351 ) @ SV71 ) )
              | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SY1351 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6335]) ).

thf(6440,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i,SV432: $i,SV472: $i] :
      ( ( ( SV472 != SV432 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SV432 ) @ SV73 ) @ SV472 )
          = ( hAPP @ SV193 @ SV472 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6337]) ).

thf(6441,plain,
    ! [SV294: $i,SV374: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) ) )
        = $false )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6338]) ).

thf(6442,plain,
    ! [SV374: $i,SV294: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) ) )
        = $false )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6338]) ).

thf(6443,plain,
    ! [SV75: $i,SV195: $i,SV295: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
          = SV75 )
        = $false )
      | ( ( SV195
          = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6339]) ).

thf(6444,plain,
    ! [SV75: $i,SV295: $i,SV195: $i] :
      ( ( ( SV195
          = ( hAPP @ ( c_List_Orev @ SV295 ) @ SV75 ) )
        = $false )
      | ( ( ( hAPP @ ( c_List_Orev @ SV295 ) @ SV195 )
          = SV75 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6340]) ).

thf(6445,plain,
    ! [SV196: $i,SV499: $i,SV76: $i] :
      ( ( ( ! [SY1658: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SY1658 ) )
                    | ( ( hAPP @ SV76 @ SV499 )
                      = ( hAPP @ SV76 @ SY1658 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ SV499 )
                     != ( hAPP @ SV76 @ SY1658 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SY1658 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6341]) ).

thf(6446,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ! [SY1659: $i] :
              ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ SY1659 ) )
                    | ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                      = ( hAPP @ SV76 @ SY1659 ) ) )
                | ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                     != ( hAPP @ SV76 @ SY1659 ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ SY1659 ) ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6342]) ).

thf(6447,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) ) )
        = $true )
      | ( ( ~ ! [SY1115: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6343]) ).

thf(6448,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ( ~ ~ ! [SY1116: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6344]) ).

thf(6449,plain,
    ! [SV78: $i,SV198: $i,SV297: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
        = $false )
      | ( ( SV198 = SV78 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6345]) ).

thf(6450,plain,
    ! [SV297: $i,SV78: $i,SV198: $i] :
      ( ( ( SV198 = SV78 )
        = $false )
      | ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV198 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV297 ) @ SV78 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6346]) ).

thf(6451,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i,SV433: $i,SV473: $i,SV493: $i] :
      ( ( ( ~ ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( hAPP @ SV433 @ SV199 )
                   != ( hAPP @ SV433 @ SV79 ) )
                  | ( SV199 = SV79 ) )
              | ~ ( ( SV199 != SV79 )
                  | ( ( hAPP @ SV433 @ SV199 )
                    = ( hAPP @ SV433 @ SV79 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6347]) ).

thf(6452,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i,SV474: $i,SV494: $i,SV500: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV500 @ SV494 @ SV474 @ SV434 ) @ SV378 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SV494 @ SV474 @ SV201 ) @ SV81 ) )
        | ! [SY1600: $i] :
            ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
            = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6348]) ).

thf(6453,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6349]) ).

thf(6454,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6350]) ).

thf(6455,plain,
    ! [SV84: $i,SV204: $i,SV303: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6351]) ).

thf(6456,plain,
    ! [SV303: $i,SV204: $i,SV84: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV84 @ SV204 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV303 ) @ SV204 ) @ SV84 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6352]) ).

thf(6457,plain,
    ! [SV85: $i,SV205: $i,SV304: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV304 ) @ SV205 ) @ ( sK3_SY1374 @ SV85 @ SV205 @ SV304 ) ) @ SV85 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV304 ) @ SV205 ) @ SV85 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6353]) ).

thf(6458,plain,
    ! [SV87: $i,SV207: $i,SV306: $i,SV381: $i,SV437: $i,SV475: $i] :
      ( ( ( c_Typedef_Otype__definition @ SV475 @ SV437 @ SV381 @ SV306 @ SV207 )
        = $false )
      | ( ( ( hAPP @ SV306 @ ( hAPP @ SV381 @ SV87 ) )
          = SV87 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6355]) ).

thf(6459,plain,
    ! [SV89: $i,SV209: $i,SV308: $i,SV383: $i,SV439: $i,SV476: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV383 )
          = SV308 )
        = $false )
      | ( ( ( SV209
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV383 ) @ SV89 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV209 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV308 ) @ SV89 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6357]) ).

thf(6460,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i,SV477: $i,SV495: $i,SV501: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV501 @ SV495 ) @ SV477 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
        | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SV501 @ SV440 @ SV495 @ SV384 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6358]) ).

thf(6461,plain,
    ! [SV92: $i,SV211: $i,SV310: $i,SV385: $i,SV441: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV441 @ SV385 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6359]) ).

thf(6462,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $false )
      | ( ( ~ ! [SY1392: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6360]) ).

thf(6463,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ~ ! [SY1393: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6361]) ).

thf(6464,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ~ ( ( SV478 != SV442 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
              = SV94 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6362]) ).

thf(6465,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ~ ( ~ ( ( SV478 != SV442 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
              = ( hAPP @ SV213 @ SV478 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6362]) ).

thf(6466,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
         != SV313 )
        | ( ( hAPP @ SV313 @ SV214 )
          = SV95 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6363]) ).

thf(6467,plain,
    ! [SV387: $i,SV443: $i,SV95: $i,SV214: $i,SV313: $i] :
      ( ( ( ( hAPP @ SV313 @ SV214 )
         != SV95 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
          = SV313 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6364]) ).

thf(6468,plain,
    ! [SV314: $i,SV96: $i,SV388: $i,SV215: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) ) )
        = $false )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6365]) ).

thf(6469,plain,
    ! [SV388: $i,SV96: $i,SV314: $i,SV215: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) ) )
        = $false )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6365]) ).

thf(6470,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
        = $true )
      | ( ( SV216 = SV97 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6366]) ).

thf(6471,plain,
    ! [SV315: $i,SV389: $i,SV97: $i,SV216: $i] :
      ( ( ( SV216 != SV97 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6367]) ).

thf(6472,plain,
    ! [SV390: $i,SV98: $i,SV316: $i,SV217: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV316 ) @ SV98 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV217 ) @ SV390 ) @ SV98 ) )
        = $true )
      | ( ( SV390 = SV316 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6368]) ).

thf(6473,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ! [SY1403: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1403 ) ) )
        = $false )
      | ( ( ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6369]) ).

thf(6474,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ! [SY1406: $i,SY1407: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1406 ) @ SY1407 ) ) ) )
        = $false )
      | ( ( ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6370]) ).

thf(6475,plain,
    ! [SV221: $i,SV102: $i,SV319: $i,SV392: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV102 ) )
        = $false )
      | ( ( SV221 = SV102 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV392 @ SV319 ) @ SV221 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6371]) ).

thf(6476,plain,
    ! [SV104: $i,SV444: $i,SV223: $i,SV393: $i,SV320: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV444 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV444 @ SV393 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6372]) ).

thf(6477,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
        | ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6374]) ).

thf(6478,plain,
    ! [SV394: $i,SV445: $i,SV106: $i,SV321: $i,SV225: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6375]) ).

thf(6479,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
            | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6376]) ).

thf(6480,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
            | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6377]) ).

thf(6481,plain,
    ! [SV109: $i,SV228: $i,SV323: $i,SV396: $i,SV447: $i,SV480: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false )
      | ( ( ~ ( ( SV396 != SV228 )
              | ( SV323 != SV109 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6380]) ).

thf(6482,plain,
    ! [SV448: $i,SV110: $i,SV229: $i,SV324: $i,SV397: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6381]) ).

thf(6483,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        | ~ ( ( SV399 != SV232 )
            | ( SV326 != SV113 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6384]) ).

thf(6484,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ~ ~ ( ( SV399 != SV232 )
              | ( SV326 != SV113 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6385]) ).

thf(6485,plain,
    ! [SV233: $i,SV114: $i,SV327: $i,SV400: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV114 ) )
        = $false )
      | ( ( SV114 = SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV400 ) @ SV327 ) @ SV233 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6386]) ).

thf(6486,plain,
    ! [SV401: $i,SV116: $i,SV235: $i,SV329: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV235 ) @ SV116 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV329 @ SV116 ) @ SV235 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV401 @ SV329 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6387]) ).

thf(6487,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ! [SY1219: $i] :
              ~ ( hBOOL @ ( hAPP @ SV237 @ SY1219 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6390]) ).

thf(6488,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ! [SY1220: $i] :
              ~ ( hBOOL @ ( hAPP @ SV237 @ SY1220 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6391]) ).

thf(6489,plain,
    ! [SV120: $i,SV239: $i,SV330: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
          = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
        = $false )
      | ( ( SV239 = SV120 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6394]) ).

thf(6490,plain,
    ! [SV330: $i,SV120: $i,SV239: $i] :
      ( ( ( SV239 = SV120 )
        = $false )
      | ( ( ( hAPP @ ( c_List_Orev @ SV330 ) @ SV239 )
          = ( hAPP @ ( c_List_Orev @ SV330 ) @ SV120 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6395]) ).

thf(6491,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) ) )
        = $true )
      | ( ( ~ ! [SY1224: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6396]) ).

thf(6492,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ( ~ ~ ! [SY1225: $i] :
                  ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6397]) ).

thf(6493,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) ) )
        = $true )
      | ( ( ~ ! [SY1547: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6398]) ).

thf(6494,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ~ ! [SY1548: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6399]) ).

thf(6495,plain,
    ! [SV333: $i,SV124: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6402]) ).

thf(6496,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i,SV496: $i,SV502: $i] :
      ( ( ! [SY1661: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1661 @ SV502 @ SV496 @ SV482 ) @ SV452 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SV502 @ SV496 @ SV334 ) @ SV244 ) )
            | ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
              = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6403]) ).

thf(6497,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        | ~ ! [SY1662: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6404]) ).

thf(6498,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
              | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6405]) ).

thf(6499,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
                | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6406]) ).

thf(6500,plain,
    ! [SV352: $i,SV418: $i,SV39: $i,SV264: $i,SV160: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV160 ) @ SV264 ) @ SV39 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV418 @ SV160 ) ) @ SV352 ) @ SV39 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV418 ) @ SV352 ) @ SV264 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6407]) ).

thf(6501,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) ) )
        = $true )
      | ( ( ~ ! [SY1286: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6408]) ).

thf(6502,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV265 @ SV40 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6409]) ).

thf(6503,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ! [SY1287: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6409]) ).

thf(6504,plain,
    ! [SV486: $i,SV267: $i,SV42: $i,SV163: $i] :
      ( ( ( SV163
         != ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV267 @ SV163 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV267 @ SV486 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6411]) ).

thf(6505,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
             != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
            | ~ ( ~ ~ ( ( SV463 != SV268 )
                      | ( SV420 != SV164 ) )
                | ( SV354 != SV43 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6412]) ).

thf(6506,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ~ ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                        | ( SV420 != SV164 ) )
                  | ( SV354 != SV43 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6412]) ).

thf(6507,plain,
    ! [SV44: $i,SV165: $i,SV269: $i,SV355: $i,SV421: $i,SV464: $i] :
      ( ( ( SV464 = SV421 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV464 ) @ SV165 ) ) @ SV421 ) @ SV44 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV355 @ SV269 ) @ SV421 ) @ SV44 ) ) @ SV464 ) @ SV165 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6413]) ).

thf(6508,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( SV465 != SV422 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = SV45 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6414]) ).

thf(6509,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ~ ( ( SV465 != SV422 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = ( hAPP @ SV166 @ SV465 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6415]) ).

thf(6510,plain,
    ! [SV47: $i,SV168: $i,SV271: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false )
      | ( ( ~ ( ( SV47 != SV168 )
              | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6416]) ).

thf(6511,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ~ ( ( SV47 != SV168 )
              | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1479: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6417]) ).

thf(6512,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i,SV504: $i] :
      ( ( ! [SY1663: $i,SY1664: $i] :
            ( ( ( hAPP @ SY1664 @ ( hAPP @ SY1663 @ SV504 ) )
             != ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1664 ) @ SY1663 ) @ SV504 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6418]) ).

thf(6513,plain,
    ! [SV273: $i,SV50: $i,SV171: $i,SV359: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6419]) ).

thf(6514,plain,
    ! [SV359: $i,SV171: $i,SV50: $i,SV273: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) @ SV50 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6419]) ).

thf(6515,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        | ~ ( ( SV360 != SV172 )
            | ( SV274 != SV51 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6420]) ).

thf(6516,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ~ ~ ( ( SV360 != SV172 )
              | ( SV274 != SV51 ) )
        | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6421]) ).

thf(6517,plain,
    ! [SV52: $i,SV173: $i,SV275: $i,SV361: $i,SV425: $i,SV468: $i,SV489: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV468 @ SV425 @ SV361 ) @ SV275 )
          = SV173 )
        = $false )
      | ( ( ( hAPP @ SV361 @ ( hAPP @ SV275 @ SV52 ) )
          = ( hAPP @ SV173 @ SV52 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6422]) ).

thf(6518,plain,
    ! [SV53: $i,SV174: $i,SV276: $i,SV362: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
        = $false )
      | ( ( SV276 = SV53 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6423]) ).

thf(6519,plain,
    ! [SV174: $i,SV362: $i,SV53: $i,SV276: $i] :
      ( ( ( SV276 = SV53 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV276 ) @ SV174 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV362 ) @ SV53 ) @ SV174 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6424]) ).

thf(6520,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true )
      | ( ( ~ ! [SY1584: $i] :
                ~ ( ~ ( ( SV363
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                       != SV54 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                       != SV175 )
                      | ( SV277
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6425]) ).

thf(6521,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ~ ! [SY1585: $i] :
                  ~ ( ~ ( ( SV363
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                         != SV54 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                         != SV175 )
                        | ( SV277
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6426]) ).

thf(6522,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6427]) ).

thf(6523,plain,
    ! [SV364: $i,SV278: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6427]) ).

thf(6524,plain,
    ! [SV58: $i,SV179: $i,SV280: $i,SV365: $i,SV427: $i,SV469: $i,SV490: $i] :
      ( ( ( SV490 = SV469 )
        = $false )
      | ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV490 )
          = ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV427 @ SV365 @ SV280 @ SV179 @ SV58 ) @ SV469 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6428]) ).

thf(6525,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i,SV470: $i,SV491: $i] :
      ( ( ( SV491 != SV470 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV491 ) @ SV180 ) ) @ SV470 ) @ SV59 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV470 ) @ SV59 ) ) @ SV491 ) @ SV180 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6429]) ).

thf(6526,plain,
    ! [SV60: $i,SV181: $i,SV282: $i,SV367: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $false )
      | ( ( ( SV282 = SV60 )
          | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6430]) ).

thf(6527,plain,
    ! [SV367: $i,SV181: $i,SV60: $i,SV282: $i] :
      ( ( ( ( SV282 = SV60 )
          | ( hBOOL @ ( hAPP @ SV181 @ SV60 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6431]) ).

thf(6528,plain,
    ! [SV63: $i,SV429: $i,SV184: $i,SV368: $i,SV285: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6432]) ).

thf(6529,plain,
    ! [SV286: $i,SV369: $i,SV185: $i,SV65: $i] :
      ( ( ( SV65 != SV185 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6433]) ).

thf(6530,plain,
    ! [SV65: $i,SV286: $i,SV185: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6433]) ).

thf(6531,plain,
    ! [SV287: $i,SV66: $i,SV505: $i,SV186: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SV505 ) @ SV66 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV505 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6434]) ).

thf(6532,plain,
    ! [SV66: $i,SV287: $i,SV186: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ ( sK6_SY1342 @ SV287 @ SV66 @ SV186 ) ) @ SV66 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ ( sK6_SY1342 @ SV287 @ SV66 @ SV186 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6435]) ).

thf(6533,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ~ ( ~ ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
            | ~ ! [SY1507: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6436]) ).

thf(6534,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ~ ( ~ ~ ! [SY1508: $i] :
                    ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                        | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
            | ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6436]) ).

thf(6535,plain,
    ! [SV291: $i,SV71: $i,SV506: $i,SV191: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SV506 ) @ SV71 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV506 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6438]) ).

thf(6536,plain,
    ! [SV71: $i,SV291: $i,SV191: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ ( sK7_SY1351 @ SV291 @ SV71 @ SV191 ) ) @ SV71 ) )
          | ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ ( sK7_SY1351 @ SV291 @ SV71 @ SV191 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6439]) ).

thf(6537,plain,
    ! [SV73: $i,SV193: $i,SV293: $i,SV373: $i,SV432: $i,SV472: $i] :
      ( ( ( SV472 = SV432 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV373 @ SV293 ) @ SV193 ) @ SV432 ) @ SV73 ) @ SV472 )
          = ( hAPP @ SV193 @ SV472 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6440]) ).

thf(6538,plain,
    ! [SV294: $i,SV374: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6441]) ).

thf(6539,plain,
    ! [SV374: $i,SV294: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6442]) ).

thf(6540,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
                  | ( ( hAPP @ SV76 @ SV499 )
                    = ( hAPP @ SV76 @ SV507 ) ) )
              | ~ ( ( ( hAPP @ SV76 @ SV499 )
                   != ( hAPP @ SV76 @ SV507 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6445]) ).

thf(6541,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
                  | ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                    = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
              | ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                   != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6446]) ).

thf(6542,plain,
    ! [SV77: $i,SV197: $i,SV296: $i,SV375: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $false )
      | ( ( ~ ! [SY1115: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6447]) ).

thf(6543,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ( ~ ! [SY1116: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6448]) ).

thf(6544,plain,
    ! [SV79: $i,SV199: $i,SV298: $i,SV376: $i,SV433: $i,SV473: $i,SV493: $i] :
      ( ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false )
      | ( ( ~ ( ~ ( ( ( hAPP @ SV433 @ SV199 )
                   != ( hAPP @ SV433 @ SV79 ) )
                  | ( SV199 = SV79 ) )
              | ~ ( ( SV199 != SV79 )
                  | ( ( hAPP @ SV433 @ SV199 )
                    = ( hAPP @ SV433 @ SV79 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6451]) ).

thf(6545,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i,SV474: $i,SV494: $i,SV500: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV500 @ SV494 @ SV474 @ SV434 ) @ SV378 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SV494 @ SV474 @ SV201 ) @ SV81 ) )
        = $true )
      | ( ( ! [SY1600: $i] :
              ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
              = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6452]) ).

thf(6546,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6453]) ).

thf(6547,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
              | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6454]) ).

thf(6548,plain,
    ! [SV308: $i,SV439: $i,SV89: $i,SV383: $i,SV476: $i,SV209: $i] :
      ( ( ( SV209
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV383 ) @ SV89 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV209 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV308 ) @ SV89 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV383 )
          = SV308 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6459]) ).

thf(6549,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i,SV477: $i,SV495: $i,SV501: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV501 @ SV495 ) @ SV477 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
          | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SV501 @ SV440 @ SV495 @ SV384 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6460]) ).

thf(6550,plain,
    ! [SV92: $i,SV441: $i,SV211: $i,SV385: $i,SV310: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV441 @ SV385 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6461]) ).

thf(6551,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ! [SY1392: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1392 ) @ SV93 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6462]) ).

thf(6552,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ! [SY1393: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SY1393 ) @ SV93 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6463]) ).

thf(6553,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( SV478 != SV442 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = SV94 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6464]) ).

thf(6554,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ~ ( ( SV478 != SV442 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = ( hAPP @ SV213 @ SV478 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6465]) ).

thf(6555,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
         != SV313 )
        = $true )
      | ( ( ( hAPP @ SV313 @ SV214 )
          = SV95 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6466]) ).

thf(6556,plain,
    ! [SV387: $i,SV443: $i,SV95: $i,SV214: $i,SV313: $i] :
      ( ( ( ( hAPP @ SV313 @ SV214 )
         != SV95 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
          = SV313 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6467]) ).

thf(6557,plain,
    ! [SV314: $i,SV96: $i,SV388: $i,SV215: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6468]) ).

thf(6558,plain,
    ! [SV388: $i,SV96: $i,SV314: $i,SV215: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6469]) ).

thf(6559,plain,
    ! [SV97: $i,SV216: $i,SV315: $i,SV389: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
        = $false )
      | ( ( SV216 = SV97 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6470]) ).

thf(6560,plain,
    ! [SV315: $i,SV389: $i,SV97: $i,SV216: $i] :
      ( ( ( SV216 = SV97 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV216 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV389 ) @ SV315 ) @ SV97 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6471]) ).

thf(6561,plain,
    ! [SV220: $i,SV101: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV318 @ ( sK9_SY1403 @ SV101 @ SV220 @ SV318 ) ) )
        = $false )
      | ( ( ! [SY1404: $i,SY1405: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SY1404 ) @ SY1405 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6473]) ).

thf(6562,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ! [SY1665: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ ( sK10_SY1406 @ SV101 @ SV220 @ SV318 ) ) @ SY1665 ) ) ) )
        = $false )
      | ( ( ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6474]) ).

thf(6563,plain,
    ! [SV104: $i,SV444: $i,SV223: $i,SV393: $i,SV320: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV320 ) @ SV393 ) @ SV223 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV444 @ SV320 @ SV104 ) ) @ SV393 ) @ SV223 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV444 @ SV393 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6476]) ).

thf(6564,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6477]) ).

thf(6565,plain,
    ! [SV394: $i,SV445: $i,SV106: $i,SV321: $i,SV225: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6478]) ).

thf(6566,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6479]) ).

thf(6567,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
              | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6480]) ).

thf(6568,plain,
    ! [SV447: $i,SV480: $i,SV109: $i,SV323: $i,SV228: $i,SV396: $i] :
      ( ( ( ( SV396 != SV228 )
          | ( SV323 != SV109 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6481]) ).

thf(6569,plain,
    ! [SV448: $i,SV110: $i,SV229: $i,SV324: $i,SV397: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6482]) ).

thf(6570,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true )
      | ( ( ~ ( ( SV399 != SV232 )
              | ( SV326 != SV113 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6483]) ).

thf(6571,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( ~ ~ ( ( SV399 != SV232 )
                | ( SV326 != SV113 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6484]) ).

thf(6572,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV237 @ ( sK11_SY1219 @ SV118 @ SV237 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6487]) ).

thf(6573,plain,
    ! [SV118: $i,SV508: $i,SV237: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV237 @ SV508 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6488]) ).

thf(6574,plain,
    ! [SV121: $i,SV240: $i,SV331: $i,SV402: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $false )
      | ( ( ~ ! [SY1224: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6491]) ).

thf(6575,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ( ~ ! [SY1225: $i] :
                ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6492]) ).

thf(6576,plain,
    ! [SV122: $i,SV241: $i,SV332: $i,SV403: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false )
      | ( ( ~ ! [SY1547: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6493]) ).

thf(6577,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ! [SY1548: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6494]) ).

thf(6578,plain,
    ! [SV333: $i,SV124: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6495]) ).

thf(6579,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i,SV496: $i,SV502: $i,SV509: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV509 @ SV502 @ SV496 @ SV482 ) @ SV452 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SV502 @ SV496 @ SV334 ) @ SV244 ) )
        | ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
          = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6496]) ).

thf(6580,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
          | ~ ! [SY1662: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6497]) ).

thf(6581,plain,
    ! [SV38: $i,SV159: $i,SV263: $i,SV351: $i,SV417: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
              | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6498]) ).

thf(6582,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
              | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6499]) ).

thf(6583,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( ~ ! [SY1286: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6501]) ).

thf(6584,plain,
    ! [SV161: $i,SV40: $i,SV265: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6502]) ).

thf(6585,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ! [SY1287: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1287 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1287 ) @ SV40 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6503]) ).

thf(6586,plain,
    ! [SV486: $i,SV267: $i,SV42: $i,SV163: $i] :
      ( ( ( SV163
          = ( c_Hilbert__Choice_OEps @ SV42 @ SV267 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV267 @ SV163 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV267 @ SV486 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6504]) ).

thf(6587,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
         != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        | ~ ( ~ ~ ( ( SV463 != SV268 )
                  | ( SV420 != SV164 ) )
            | ( SV354 != SV43 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6505]) ).

thf(6588,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                    | ( SV420 != SV164 ) )
              | ( SV354 != SV43 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6506]) ).

thf(6589,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( SV465 != SV422 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = SV45 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6508]) ).

thf(6590,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( ~ ( ( SV465 != SV422 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = ( hAPP @ SV166 @ SV465 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6509]) ).

thf(6591,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ~ ( ( SV47 != SV168 )
              | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6510]) ).

thf(6592,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ~ ( ( SV47 != SV168 )
              | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6511]) ).

thf(6593,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1479: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6511]) ).

thf(6594,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i,SV504: $i,SV510: $i] :
      ( ( ! [SY1666: $i] :
            ( ( ( hAPP @ SY1666 @ ( hAPP @ SV510 @ SV504 ) )
             != ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SY1666 ) @ SV510 ) @ SV504 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6512]) ).

thf(6595,plain,
    ! [SV273: $i,SV50: $i,SV171: $i,SV359: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV359 ) @ SV171 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6513]) ).

thf(6596,plain,
    ! [SV359: $i,SV171: $i,SV50: $i,SV273: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ ( sK4_SY1487 @ SV50 @ SV273 @ SV171 @ SV359 ) ) @ SV50 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV359 @ SV273 ) ) @ SV171 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6514]) ).

thf(6597,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true )
      | ( ( ~ ( ( SV360 != SV172 )
              | ( SV274 != SV51 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6515]) ).

thf(6598,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( ~ ~ ( ( SV360 != SV172 )
                | ( SV274 != SV51 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6516]) ).

thf(6599,plain,
    ! [SV54: $i,SV175: $i,SV277: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false )
      | ( ( ~ ! [SY1584: $i] :
                ~ ( ~ ( ( SV363
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                       != SV54 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                       != SV175 )
                      | ( SV277
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6520]) ).

thf(6600,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ! [SY1585: $i] :
                ~ ( ~ ( ( SV363
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                       != SV54 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                       != SV175 )
                      | ( SV277
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6521]) ).

thf(6601,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6522]) ).

thf(6602,plain,
    ! [SV364: $i,SV278: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6523]) ).

thf(6603,plain,
    ! [SV59: $i,SV180: $i,SV281: $i,SV366: $i,SV428: $i,SV470: $i,SV491: $i] :
      ( ( ( SV491 = SV470 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV491 ) @ SV180 ) ) @ SV470 ) @ SV59 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV428 @ SV366 ) @ SV281 ) @ SV470 ) @ SV59 ) ) @ SV491 ) @ SV180 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6525]) ).

thf(6604,plain,
    ! [SV367: $i,SV181: $i,SV60: $i,SV282: $i] :
      ( ( ( SV282 = SV60 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV181 @ SV60 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6526]) ).

thf(6605,plain,
    ! [SV181: $i,SV367: $i,SV60: $i,SV282: $i] :
      ( ( ( SV282 = SV60 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6527]) ).

thf(6606,plain,
    ! [SV282: $i,SV367: $i,SV60: $i,SV181: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV181 @ SV60 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV367 ) @ SV282 ) @ SV181 ) @ SV60 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6527]) ).

thf(6607,plain,
    ! [SV368: $i,SV63: $i,SV184: $i,SV285: $i,SV429: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6528]) ).

thf(6608,plain,
    ! [SV286: $i,SV369: $i,SV185: $i,SV65: $i] :
      ( ( ( SV65 = SV185 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
              | ! [SY1503: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6529]) ).

thf(6609,plain,
    ! [SV65: $i,SV286: $i,SV185: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
          | ! [SY1503: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6530]) ).

thf(6610,plain,
    ! [SV287: $i,SV66: $i,SV505: $i,SV186: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SV505 ) @ SV66 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV505 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6531]) ).

thf(6611,plain,
    ! [SV66: $i,SV287: $i,SV186: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ ( sK6_SY1342 @ SV287 @ SV66 @ SV186 ) ) @ SV66 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6532]) ).

thf(6612,plain,
    ! [SV66: $i,SV186: $i,SV287: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ ( sK6_SY1342 @ SV287 @ SV66 @ SV186 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6532]) ).

thf(6613,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ~ ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        | ~ ! [SY1507: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6533]) ).

thf(6614,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ~ ~ ! [SY1508: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) )
        | ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6534]) ).

thf(6615,plain,
    ! [SV291: $i,SV71: $i,SV506: $i,SV191: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SV506 ) @ SV71 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV506 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6535]) ).

thf(6616,plain,
    ! [SV71: $i,SV291: $i,SV191: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ ( sK7_SY1351 @ SV291 @ SV71 @ SV191 ) ) @ SV71 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6536]) ).

thf(6617,plain,
    ! [SV71: $i,SV191: $i,SV291: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ ( sK7_SY1351 @ SV291 @ SV71 @ SV191 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6536]) ).

thf(6618,plain,
    ! [SV294: $i,SV374: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6538]) ).

thf(6619,plain,
    ! [SV374: $i,SV294: $i,SV74: $i,SV194: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6539]) ).

thf(6620,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
              | ( ( hAPP @ SV76 @ SV499 )
                = ( hAPP @ SV76 @ SV507 ) ) )
          | ~ ( ( ( hAPP @ SV76 @ SV499 )
               != ( hAPP @ SV76 @ SV507 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6540]) ).

thf(6621,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
          | ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6541]) ).

thf(6622,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ( ! [SY1115: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1115 ) @ SV77 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6542]) ).

thf(6623,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV197: $i] :
      ( ( ( ! [SY1116: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SY1116 ) @ SV77 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6543]) ).

thf(6624,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV79: $i,SV199: $i,SV433: $i] :
      ( ( ( ~ ( ( ( hAPP @ SV433 @ SV199 )
               != ( hAPP @ SV433 @ SV79 ) )
              | ( SV199 = SV79 ) )
          | ~ ( ( SV199 != SV79 )
              | ( ( hAPP @ SV433 @ SV199 )
                = ( hAPP @ SV433 @ SV79 ) ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6544]) ).

thf(6625,plain,
    ! [SV81: $i,SV201: $i,SV300: $i,SV378: $i,SV434: $i,SV474: $i,SV494: $i,SV500: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV500 @ SV494 @ SV474 @ SV434 ) @ SV378 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SV494 @ SV474 @ SV201 ) @ SV81 ) )
        = $false )
      | ( ( ! [SY1600: $i] :
              ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SY1600 ) )
              = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SY1600 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6545]) ).

thf(6626,plain,
    ! [SV82: $i,SV202: $i,SV301: $i,SV379: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6546]) ).

thf(6627,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6547]) ).

thf(6628,plain,
    ! [SV308: $i,SV439: $i,SV89: $i,SV383: $i,SV476: $i,SV209: $i] :
      ( ( ( SV209
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV383 ) @ SV89 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV209 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV308 ) @ SV89 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV476 ) @ SV439 ) @ SV383 )
          = SV308 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6548]) ).

thf(6629,plain,
    ! [SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV440: $i,SV477: $i,SV495: $i,SV501: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV501 @ SV495 ) @ SV477 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
          | ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SV501 @ SV440 @ SV495 @ SV384 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6549]) ).

thf(6630,plain,
    ! [SV92: $i,SV441: $i,SV211: $i,SV385: $i,SV310: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV310 ) @ SV385 ) @ SV211 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV441 @ SV92 @ SV310 ) ) @ SV385 ) @ SV211 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV441 @ SV385 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6550]) ).

thf(6631,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ ( sK12_SY1392 @ SV93 @ SV212 @ SV311 ) ) @ SV93 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6551]) ).

thf(6632,plain,
    ! [SV93: $i,SV511: $i,SV212: $i,SV311: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SV511 ) @ SV93 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6552]) ).

thf(6633,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( SV478 != SV442 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = SV94 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6553]) ).

thf(6634,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( ~ ( ( SV478 != SV442 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = ( hAPP @ SV213 @ SV478 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6554]) ).

thf(6635,plain,
    ! [SV95: $i,SV214: $i,SV313: $i,SV387: $i,SV443: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
          = SV313 )
        = $false )
      | ( ( ( hAPP @ SV313 @ SV214 )
          = SV95 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6555]) ).

thf(6636,plain,
    ! [SV387: $i,SV443: $i,SV95: $i,SV214: $i,SV313: $i] :
      ( ( ( ( hAPP @ SV313 @ SV214 )
          = SV95 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV443 @ SV387 ) @ SV313 ) @ SV214 ) @ SV95 )
          = SV313 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6556]) ).

thf(6637,plain,
    ! [SV314: $i,SV96: $i,SV388: $i,SV215: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6557]) ).

thf(6638,plain,
    ! [SV388: $i,SV96: $i,SV314: $i,SV215: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6558]) ).

thf(6639,plain,
    ! [SV512: $i,SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( ! [SY1667: $i] : ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SV512 ) @ SY1667 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV318 @ ( sK9_SY1403 @ SV101 @ SV220 @ SV318 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6561]) ).

thf(6640,plain,
    ! [SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ ( sK10_SY1406 @ SV101 @ SV220 @ SV318 ) ) @ ( sK13_SY1665 @ SV101 @ SV220 @ SV318 ) ) ) )
        = $false )
      | ( ( ! [SY1408: $i] : ( hBOOL @ ( hAPP @ SV318 @ SY1408 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6562]) ).

thf(6641,plain,
    ! [SV106: $i,SV225: $i,SV321: $i,SV394: $i,SV445: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6564]) ).

thf(6642,plain,
    ! [SV394: $i,SV445: $i,SV106: $i,SV321: $i,SV225: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV225 @ ( hAPP @ SV321 @ SV106 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV445 @ SV394 @ SV321 ) @ SV225 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6565]) ).

thf(6643,plain,
    ! [SV107: $i,SV226: $i,SV322: $i,SV395: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6566]) ).

thf(6644,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
          | ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6567]) ).

thf(6645,plain,
    ! [SV109: $i,SV323: $i,SV447: $i,SV480: $i,SV228: $i,SV396: $i] :
      ( ( ( SV396 != SV228 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6568]) ).

thf(6646,plain,
    ! [SV228: $i,SV396: $i,SV447: $i,SV480: $i,SV109: $i,SV323: $i] :
      ( ( ( SV323 != SV109 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6568]) ).

thf(6647,plain,
    ! [SV448: $i,SV324: $i,SV110: $i,SV229: $i,SV397: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6569]) ).

thf(6648,plain,
    ! [SV113: $i,SV232: $i,SV326: $i,SV399: $i,SV450: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false )
      | ( ( ~ ( ( SV399 != SV232 )
              | ( SV326 != SV113 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6570]) ).

thf(6649,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( ~ ( ( SV399 != SV232 )
              | ( SV326 != SV113 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6571]) ).

thf(6650,plain,
    ! [SV118: $i,SV237: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV237 @ ( sK11_SY1219 @ SV118 @ SV237 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6572]) ).

thf(6651,plain,
    ! [SV118: $i,SV508: $i,SV237: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV237 @ SV508 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV237 @ ( c_Hilbert__Choice_OEps @ SV118 @ SV237 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6573]) ).

thf(6652,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ( ! [SY1224: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1224 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6574]) ).

thf(6653,plain,
    ! [SV331: $i,SV402: $i,SV121: $i,SV240: $i] :
      ( ( ( ! [SY1225: $i] :
              ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SY1225 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6575]) ).

thf(6654,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ( ! [SY1547: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1547 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1547 ) @ SV122 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6576]) ).

thf(6655,plain,
    ! [SV122: $i,SV332: $i,SV241: $i,SV403: $i] :
      ( ( ( ! [SY1548: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SY1548 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SY1548 ) @ SV122 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6577]) ).

thf(6656,plain,
    ! [SV404: $i,SV124: $i,SV333: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6578]) ).

thf(6657,plain,
    ! [SV333: $i,SV451: $i,SV124: $i,SV243: $i,SV404: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6578]) ).

thf(6658,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i,SV496: $i,SV502: $i,SV509: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV509 @ SV502 @ SV496 @ SV482 ) @ SV452 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SV502 @ SV496 @ SV334 ) @ SV244 ) )
        = $true )
      | ( ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
          = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6579]) ).

thf(6659,plain,
    ! [SV126: $i,SV245: $i,SV335: $i,SV406: $i,SV453: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
          | ~ ! [SY1662: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6580]) ).

thf(6660,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
          | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6581]) ).

thf(6661,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
          | ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6582]) ).

thf(6662,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ! [SY1286: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SY1286 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SY1286 ) @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6583]) ).

thf(6663,plain,
    ! [SV265: $i,SV513: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6585]) ).

thf(6664,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
         != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ( SV463 != SV268 )
                    | ( SV420 != SV164 ) )
              | ( SV354 != SV43 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6587]) ).

thf(6665,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ( SV463 != SV268 )
                      | ( SV420 != SV164 ) )
                | ( SV354 != SV43 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6588]) ).

thf(6666,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( SV465 = SV422 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = SV45 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6589]) ).

thf(6667,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( SV465 != SV422 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = ( hAPP @ SV166 @ SV465 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6590]) ).

thf(6668,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ( SV47 != SV168 )
          | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6591]) ).

thf(6669,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( ( SV47 != SV168 )
          | ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6592]) ).

thf(6670,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
          | ~ ~ ! [SY1479: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6593]) ).

thf(6671,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i,SV504: $i,SV510: $i,SV514: $i] :
      ( ( ( ( hAPP @ SV514 @ ( hAPP @ SV510 @ SV504 ) )
         != ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SV514 ) @ SV510 ) @ SV504 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6594]) ).

thf(6672,plain,
    ! [SV51: $i,SV172: $i,SV274: $i,SV360: $i,SV424: $i,SV467: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false )
      | ( ( ~ ( ( SV360 != SV172 )
              | ( SV274 != SV51 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6597]) ).

thf(6673,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( ~ ( ( SV360 != SV172 )
              | ( SV274 != SV51 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6598]) ).

thf(6674,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ! [SY1584: $i] :
              ~ ( ~ ( ( SV363
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1584 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV277 )
                     != SV54 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1584 )
                     != SV175 )
                    | ( SV277
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1584 ) @ SV54 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6599]) ).

thf(6675,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ! [SY1585: $i] :
              ~ ( ~ ( ( SV363
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SY1585 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV277 )
                     != SV54 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SY1585 )
                     != SV175 )
                    | ( SV277
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SY1585 ) @ SV54 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6600]) ).

thf(6676,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6601]) ).

thf(6677,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6602]) ).

thf(6678,plain,
    ! [SV368: $i,SV63: $i,SV184: $i,SV285: $i,SV429: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV184 ) @ SV63 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV429 @ SV285 ) ) @ SV368 ) @ SV63 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV285 ) @ SV368 ) @ SV184 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV429 @ SV368 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6607]) ).

thf(6679,plain,
    ! [SV65: $i,SV286: $i,SV185: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
          | ! [SY1503: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6608]) ).

thf(6680,plain,
    ! [SV65: $i,SV286: $i,SV185: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6609]) ).

thf(6681,plain,
    ! [SV65: $i,SV369: $i,SV185: $i,SV286: $i] :
      ( ( ( ! [SY1503: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6609]) ).

thf(6682,plain,
    ! [SV287: $i,SV66: $i,SV505: $i,SV186: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ SV505 ) @ SV66 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV505 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6610]) ).

thf(6683,plain,
    ! [SV66: $i,SV287: $i,SV186: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV186 @ ( sK6_SY1342 @ SV287 @ SV66 @ SV186 ) ) @ SV66 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV287 @ SV186 ) @ SV66 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6611]) ).

thf(6684,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ( ~ ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 ) )
        = $true )
      | ( ( ~ ! [SY1507: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6613]) ).

thf(6685,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ~ ! [SY1508: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6614]) ).

thf(6686,plain,
    ! [SV291: $i,SV71: $i,SV506: $i,SV191: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ SV506 ) @ SV71 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV506 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6615]) ).

thf(6687,plain,
    ! [SV71: $i,SV291: $i,SV191: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV191 @ ( sK7_SY1351 @ SV291 @ SV71 @ SV191 ) ) @ SV71 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV291 @ SV191 ) @ SV71 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6616]) ).

thf(6688,plain,
    ! [SV294: $i,SV374: $i,SV74: $i,SV194: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6618]) ).

thf(6689,plain,
    ! [SV374: $i,SV294: $i,SV74: $i,SV194: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV294 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV194 ) @ SV74 ) @ SV374 ) )
        = $true )
      | ( ( SV374 = SV294 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6619]) ).

thf(6690,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
              | ( ( hAPP @ SV76 @ SV499 )
                = ( hAPP @ SV76 @ SV507 ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6620]) ).

thf(6691,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( ( ( hAPP @ SV76 @ SV499 )
               != ( hAPP @ SV76 @ SV507 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6620]) ).

thf(6692,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
                = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6621]) ).

thf(6693,plain,
    ! [SV77: $i,SV375: $i,SV296: $i,SV197: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ ( sK14_SY1115 @ SV296 @ SV375 @ SV77 @ SV197 ) ) @ SV77 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6622]) ).

thf(6694,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV515: $i,SV197: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SV515 ) @ SV77 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6623]) ).

thf(6695,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV79: $i,SV199: $i,SV433: $i] :
      ( ( ( ~ ( ( ( hAPP @ SV433 @ SV199 )
               != ( hAPP @ SV433 @ SV79 ) )
              | ( SV199 = SV79 ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6624]) ).

thf(6696,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV433: $i,SV79: $i,SV199: $i] :
      ( ( ( ~ ( ( SV199 != SV79 )
              | ( ( hAPP @ SV433 @ SV199 )
                = ( hAPP @ SV433 @ SV79 ) ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6624]) ).

thf(6697,plain,
    ! [SV300: $i,SV474: $i,SV494: $i,SV500: $i,SV81: $i,SV201: $i,SV516: $i,SV378: $i,SV434: $i] :
      ( ( ( ( hAPP @ SV434 @ ( hAPP @ SV378 @ SV516 ) )
          = ( hAPP @ SV201 @ ( hAPP @ SV81 @ SV516 ) ) )
        = $true )
      | ( ( ( hAPP @ ( c_Fun_Ocomp @ SV500 @ SV494 @ SV474 @ SV434 ) @ SV378 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV300 @ SV494 @ SV474 @ SV201 ) @ SV81 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6625]) ).

thf(6698,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6626]) ).

thf(6699,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6627]) ).

thf(6700,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6627]) ).

thf(6701,plain,
    ! [SV495: $i,SV501: $i,SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV477: $i,SV440: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SV501 @ SV440 @ SV495 @ SV384 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV501 @ SV495 ) @ SV477 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6629]) ).

thf(6702,plain,
    ! [SV93: $i,SV212: $i,SV311: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ ( sK12_SY1392 @ SV93 @ SV212 @ SV311 ) ) @ SV93 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6631]) ).

thf(6703,plain,
    ! [SV93: $i,SV511: $i,SV212: $i,SV311: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV311 ) @ SV212 ) @ SV511 ) @ SV93 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV311 ) @ SV212 ) @ SV93 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6632]) ).

thf(6704,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( SV478 = SV442 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = SV94 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6633]) ).

thf(6705,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( SV478 != SV442 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = ( hAPP @ SV213 @ SV478 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6634]) ).

thf(6706,plain,
    ! [SV314: $i,SV96: $i,SV388: $i,SV215: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6637]) ).

thf(6707,plain,
    ! [SV388: $i,SV96: $i,SV314: $i,SV215: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV314 ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV388 ) @ SV96 ) )
        = $true )
      | ( ( SV388 = SV314 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6638]) ).

thf(6708,plain,
    ! [SV517: $i,SV512: $i,SV101: $i,SV220: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ SV512 ) @ SV517 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV318 @ ( sK9_SY1403 @ SV101 @ SV220 @ SV318 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6639]) ).

thf(6709,plain,
    ! [SV101: $i,SV220: $i,SV518: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV318 @ SV518 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV318 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV220 @ SV101 ) @ ( sK10_SY1406 @ SV101 @ SV220 @ SV318 ) ) @ ( sK13_SY1665 @ SV101 @ SV220 @ SV318 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6640]) ).

thf(6710,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6643]) ).

thf(6711,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6644]) ).

thf(6712,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6644]) ).

thf(6713,plain,
    ! [SV109: $i,SV323: $i,SV447: $i,SV480: $i,SV228: $i,SV396: $i] :
      ( ( ( SV396 = SV228 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6645]) ).

thf(6714,plain,
    ! [SV228: $i,SV396: $i,SV447: $i,SV480: $i,SV109: $i,SV323: $i] :
      ( ( ( SV323 = SV109 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV396 ) @ SV323 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV480 @ SV447 ) @ SV228 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6646]) ).

thf(6715,plain,
    ! [SV448: $i,SV324: $i,SV110: $i,SV229: $i,SV397: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV229 ) @ SV110 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV110 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV397 @ SV324 ) @ SV229 ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV448 @ SV397 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6647]) ).

thf(6716,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( ( SV399 != SV232 )
          | ( SV326 != SV113 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6648]) ).

thf(6717,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( ( SV399 != SV232 )
          | ( SV326 != SV113 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6649]) ).

thf(6718,plain,
    ! [SV402: $i,SV331: $i,SV121: $i,SV240: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ ( sK15_SY1224 @ SV331 @ SV402 @ SV121 @ SV240 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6652]) ).

thf(6719,plain,
    ! [SV331: $i,SV402: $i,SV519: $i,SV121: $i,SV240: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SV519 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6653]) ).

thf(6720,plain,
    ! [SV332: $i,SV122: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) @ SV122 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6654]) ).

thf(6721,plain,
    ! [SV122: $i,SV332: $i,SV520: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6655]) ).

thf(6722,plain,
    ! [SV404: $i,SV124: $i,SV333: $i,SV243: $i,SV451: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6656]) ).

thf(6723,plain,
    ! [SV333: $i,SV451: $i,SV124: $i,SV243: $i,SV404: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6657]) ).

thf(6724,plain,
    ! [SV125: $i,SV244: $i,SV334: $i,SV405: $i,SV452: $i,SV482: $i,SV496: $i,SV502: $i,SV509: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV509 @ SV502 @ SV496 @ SV482 ) @ SV452 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV405 @ SV502 @ SV496 @ SV334 ) @ SV244 ) )
        = $false )
      | ( ( ( hAPP @ SV482 @ ( hAPP @ SV452 @ SV125 ) )
          = ( hAPP @ SV334 @ ( hAPP @ SV244 @ SV125 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6658]) ).

thf(6725,plain,
    ! [SV483: $i,SV453: $i,SV497: $i,SV503: $i,SV126: $i,SV245: $i,SV335: $i,SV406: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) ) )
        = $true )
      | ( ( ~ ! [SY1662: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6659]) ).

thf(6726,plain,
    ! [SV263: $i,SV417: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6660]) ).

thf(6727,plain,
    ! [SV159: $i,SV351: $i,SV417: $i,SV38: $i,SV263: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6660]) ).

thf(6728,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6661]) ).

thf(6729,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6662]) ).

thf(6730,plain,
    ! [SV265: $i,SV513: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6663]) ).

thf(6731,plain,
    ! [SV43: $i,SV164: $i,SV268: $i,SV354: $i,SV420: $i,SV463: $i,SV487: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ( SV463 != SV268 )
                    | ( SV420 != SV164 ) )
              | ( SV354 != SV43 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6664]) ).

thf(6732,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ( ~ ~ ( ( SV463 != SV268 )
                    | ( SV420 != SV164 ) )
              | ( SV354 != SV43 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6665]) ).

thf(6733,plain,
    ! [SV45: $i,SV166: $i,SV270: $i,SV356: $i,SV422: $i,SV465: $i] :
      ( ( ( SV465 = SV422 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV356 @ SV270 ) @ SV166 ) @ SV422 ) @ SV45 ) @ SV465 )
          = ( hAPP @ SV166 @ SV465 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6667]) ).

thf(6734,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( SV47 != SV168 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6668]) ).

thf(6735,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6668]) ).

thf(6736,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( SV47 != SV168 )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6669]) ).

thf(6737,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY1479: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6670]) ).

thf(6738,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i,SV504: $i,SV510: $i,SV514: $i] :
      ( ( ( ( hAPP @ SV514 @ ( hAPP @ SV510 @ SV504 ) )
         != ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SV514 ) @ SV510 ) @ SV504 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6671]) ).

thf(6739,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( ( SV360 != SV172 )
          | ( SV274 != SV51 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6672]) ).

thf(6740,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( ( SV360 != SV172 )
          | ( SV274 != SV51 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6673]) ).

thf(6741,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ~ ( ( SV363
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
                   != SV54 ) )
              | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
                   != SV175 )
                  | ( SV277
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6674]) ).

thf(6742,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ~ ( ( SV363
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
                   != SV54 ) )
              | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
                   != SV175 )
                  | ( SV277
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6675]) ).

thf(6743,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6676]) ).

thf(6744,plain,
    ! [SV364: $i,SV278: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6676]) ).

thf(6745,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6677]) ).

thf(6746,plain,
    ! [SV364: $i,SV278: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6677]) ).

thf(6747,plain,
    ! [SV286: $i,SV65: $i,SV185: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV369 @ SV185 ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6679]) ).

thf(6748,plain,
    ! [SV65: $i,SV369: $i,SV185: $i,SV286: $i] :
      ( ( ( ! [SY1503: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ SY1503 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SY1503 ) @ SV65 ) ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6679]) ).

thf(6749,plain,
    ! [SV65: $i,SV286: $i,SV185: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6680]) ).

thf(6750,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6681]) ).

thf(6751,plain,
    ! [SV68: $i,SV188: $i,SV289: $i,SV370: $i,SV430: $i,SV471: $i,SV492: $i] :
      ( ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false )
      | ( ( ~ ! [SY1507: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6684]) ).

thf(6752,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ! [SY1508: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6685]) ).

thf(6753,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
          | ( ( hAPP @ SV76 @ SV499 )
            = ( hAPP @ SV76 @ SV507 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6690]) ).

thf(6754,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ( ( hAPP @ SV76 @ SV499 )
           != ( hAPP @ SV76 @ SV507 ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6691]) ).

thf(6755,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
          | ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
            = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6692]) ).

thf(6756,plain,
    ! [SV77: $i,SV375: $i,SV296: $i,SV197: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ ( sK14_SY1115 @ SV296 @ SV375 @ SV77 @ SV197 ) ) @ SV77 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6693]) ).

thf(6757,plain,
    ! [SV296: $i,SV375: $i,SV77: $i,SV515: $i,SV197: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV197 @ SV515 ) @ SV77 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV375 @ SV296 @ SV197 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6694]) ).

thf(6758,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV79: $i,SV199: $i,SV433: $i] :
      ( ( ( ( ( hAPP @ SV433 @ SV199 )
           != ( hAPP @ SV433 @ SV79 ) )
          | ( SV199 = SV79 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6695]) ).

thf(6759,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV433: $i,SV79: $i,SV199: $i] :
      ( ( ( ( SV199 != SV79 )
          | ( ( hAPP @ SV433 @ SV199 )
            = ( hAPP @ SV433 @ SV79 ) ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6696]) ).

thf(6760,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6698]) ).

thf(6761,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6699]) ).

thf(6762,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6700]) ).

thf(6763,plain,
    ! [SV495: $i,SV501: $i,SV91: $i,SV210: $i,SV309: $i,SV384: $i,SV477: $i,SV440: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV440 @ SV477 ) @ SV384 ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV309 @ SV210 @ SV91 @ SV501 @ SV440 @ SV495 @ SV384 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV501 @ SV495 ) @ SV477 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6701]) ).

thf(6764,plain,
    ! [SV94: $i,SV213: $i,SV312: $i,SV386: $i,SV442: $i,SV478: $i] :
      ( ( ( SV478 = SV442 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV386 @ SV312 ) @ SV213 ) @ SV442 ) @ SV94 ) @ SV478 )
          = ( hAPP @ SV213 @ SV478 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6705]) ).

thf(6765,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6710]) ).

thf(6766,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6711]) ).

thf(6767,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6712]) ).

thf(6768,plain,
    ! [SV113: $i,SV326: $i,SV450: $i,SV232: $i,SV399: $i] :
      ( ( ( SV399 != SV232 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6716]) ).

thf(6769,plain,
    ! [SV232: $i,SV399: $i,SV450: $i,SV113: $i,SV326: $i] :
      ( ( ( SV326 != SV113 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6716]) ).

thf(6770,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( SV399 != SV232 )
        = $true )
      | ( ( SV326 != SV113 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6717]) ).

thf(6771,plain,
    ! [SV402: $i,SV331: $i,SV121: $i,SV240: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ ( sK15_SY1224 @ SV331 @ SV402 @ SV121 @ SV240 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6718]) ).

thf(6772,plain,
    ! [SV331: $i,SV402: $i,SV519: $i,SV121: $i,SV240: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV240 @ SV121 ) @ SV519 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV331 @ SV240 ) @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6719]) ).

thf(6773,plain,
    ! [SV332: $i,SV122: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) @ SV122 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6720]) ).

thf(6774,plain,
    ! [SV122: $i,SV332: $i,SV520: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6721]) ).

thf(6775,plain,
    ! [SV404: $i,SV124: $i,SV333: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6722]) ).

thf(6776,plain,
    ! [SV404: $i,SV124: $i,SV333: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6723]) ).

thf(6777,plain,
    ! [SV483: $i,SV453: $i,SV497: $i,SV503: $i,SV126: $i,SV245: $i,SV335: $i,SV406: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( ~ ! [SY1662: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6725]) ).

thf(6778,plain,
    ! [SV263: $i,SV417: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6726]) ).

thf(6779,plain,
    ! [SV159: $i,SV351: $i,SV417: $i,SV38: $i,SV263: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV263 @ SV38 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6727]) ).

thf(6780,plain,
    ! [SV417: $i,SV263: $i,SV38: $i,SV159: $i,SV351: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV263 @ SV38 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6728]) ).

thf(6781,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) @ SV40 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6729]) ).

thf(6782,plain,
    ! [SV265: $i,SV513: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6730]) ).

thf(6783,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ~ ( ( SV463 != SV268 )
                | ( SV420 != SV164 ) )
          | ( SV354 != SV43 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6731]) ).

thf(6784,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ~ ( ( SV463 != SV268 )
                | ( SV420 != SV164 ) )
          | ( SV354 != SV43 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6732]) ).

thf(6785,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( SV47 = SV168 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6734]) ).

thf(6786,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6735]) ).

thf(6787,plain,
    ! [SV271: $i,SV357: $i,SV168: $i,SV47: $i] :
      ( ( ( SV47 = SV168 )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6736]) ).

thf(6788,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( ~ ~ ! [SY1479: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6737]) ).

thf(6789,plain,
    ! [SV49: $i,SV170: $i,SV272: $i,SV358: $i,SV423: $i,SV466: $i,SV488: $i,SV498: $i,SV504: $i,SV510: $i,SV514: $i] :
      ( ( ( ( hAPP @ SV514 @ ( hAPP @ SV510 @ SV504 ) )
          = ( hAPP @ SV498 @ ( hAPP @ SV488 @ SV466 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV423 @ SV358 @ SV272 @ SV514 ) @ SV510 ) @ SV504 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV170 @ SV358 @ SV49 @ SV498 ) @ SV488 ) @ SV466 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6738]) ).

thf(6790,plain,
    ! [SV51: $i,SV274: $i,SV424: $i,SV467: $i,SV172: $i,SV360: $i] :
      ( ( ( SV360 != SV172 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6739]) ).

thf(6791,plain,
    ! [SV172: $i,SV360: $i,SV424: $i,SV467: $i,SV51: $i,SV274: $i] :
      ( ( ( SV274 != SV51 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6739]) ).

thf(6792,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( SV360 != SV172 )
        = $true )
      | ( ( SV274 != SV51 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6740]) ).

thf(6793,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ( SV363
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
               != SV54 ) )
          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6741]) ).

thf(6794,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ( SV363
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
               != SV54 ) )
          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6742]) ).

thf(6795,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6743]) ).

thf(6796,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6745]) ).

thf(6797,plain,
    ! [SV286: $i,SV65: $i,SV185: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $true )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6747]) ).

thf(6798,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6748]) ).

thf(6799,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6750]) ).

thf(6800,plain,
    ! [SV185: $i,SV65: $i,SV286: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6750]) ).

thf(6801,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ( ! [SY1507: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1507 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1507 ) @ SV68 ) ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6751]) ).

thf(6802,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV188: $i,SV370: $i] :
      ( ( ( ! [SY1508: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SY1508 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SY1508 ) @ SV68 ) ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6752]) ).

thf(6803,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) ) )
        = $true )
      | ( ( ( hAPP @ SV76 @ SV499 )
          = ( hAPP @ SV76 @ SV507 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6753]) ).

thf(6804,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ SV499 )
         != ( hAPP @ SV76 @ SV507 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6754]) ).

thf(6805,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6755]) ).

thf(6806,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6755]) ).

thf(6807,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV79: $i,SV199: $i,SV433: $i] :
      ( ( ( ( hAPP @ SV433 @ SV199 )
         != ( hAPP @ SV433 @ SV79 ) )
        = $true )
      | ( ( SV199 = SV79 )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6758]) ).

thf(6808,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV433: $i,SV79: $i,SV199: $i] :
      ( ( ( SV199 != SV79 )
        = $true )
      | ( ( ( hAPP @ SV433 @ SV199 )
          = ( hAPP @ SV433 @ SV79 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6759]) ).

thf(6809,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6760]) ).

thf(6810,plain,
    ! [SV301: $i,SV435: $i,SV82: $i,SV202: $i,SV379: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6760]) ).

thf(6811,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6761]) ).

thf(6812,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6762]) ).

thf(6813,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6765]) ).

thf(6814,plain,
    ! [SV322: $i,SV446: $i,SV107: $i,SV226: $i,SV395: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6765]) ).

thf(6815,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6766]) ).

thf(6816,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6767]) ).

thf(6817,plain,
    ! [SV113: $i,SV326: $i,SV450: $i,SV232: $i,SV399: $i] :
      ( ( ( SV399 = SV232 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6768]) ).

thf(6818,plain,
    ! [SV232: $i,SV399: $i,SV450: $i,SV113: $i,SV326: $i] :
      ( ( ( SV326 = SV113 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6769]) ).

thf(6819,plain,
    ! [SV450: $i,SV113: $i,SV326: $i,SV232: $i,SV399: $i] :
      ( ( ( SV399 = SV232 )
        = $false )
      | ( ( SV326 != SV113 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6770]) ).

thf(6820,plain,
    ! [SV332: $i,SV122: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) @ SV122 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6773]) ).

thf(6821,plain,
    ! [SV122: $i,SV332: $i,SV520: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6774]) ).

thf(6822,plain,
    ! [SV124: $i,SV333: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6775]) ).

thf(6823,plain,
    ! [SV404: $i,SV451: $i,SV124: $i,SV243: $i,SV333: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6775]) ).

thf(6824,plain,
    ! [SV333: $i,SV124: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6776]) ).

thf(6825,plain,
    ! [SV451: $i,SV404: $i,SV124: $i,SV243: $i,SV333: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6776]) ).

thf(6826,plain,
    ! [SV483: $i,SV245: $i,SV126: $i,SV335: $i,SV406: $i,SV453: $i,SV497: $i,SV503: $i] :
      ( ( ( ! [SY1662: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SY1662 ) @ SV453 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SY1662 ) @ SV126 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6777]) ).

thf(6827,plain,
    ! [SV417: $i,SV159: $i,SV351: $i,SV38: $i,SV263: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV263 @ SV38 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV351 @ SV159 ) @ SV38 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV417 @ SV351 @ SV263 ) @ SV159 ) @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6780]) ).

thf(6828,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) @ SV40 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6781]) ).

thf(6829,plain,
    ! [SV265: $i,SV513: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6782]) ).

thf(6830,plain,
    ! [SV43: $i,SV354: $i,SV487: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ~ ( ( SV463 != SV268 )
                | ( SV420 != SV164 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6783]) ).

thf(6831,plain,
    ! [SV164: $i,SV268: $i,SV420: $i,SV463: $i,SV487: $i,SV43: $i,SV354: $i] :
      ( ( ( SV354 != SV43 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6783]) ).

thf(6832,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ~ ( ( SV463 != SV268 )
                | ( SV420 != SV164 ) ) )
        = $true )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6784]) ).

thf(6833,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
          | ~ ~ ! [SY1478: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6785]) ).

thf(6834,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
              | ~ ~ ! [SY1478: $i] :
                      ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6786]) ).

thf(6835,plain,
    ! [SV271: $i,SV47: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6787]) ).

thf(6836,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ! [SY1479: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6788]) ).

thf(6837,plain,
    ! [SV51: $i,SV274: $i,SV424: $i,SV467: $i,SV172: $i,SV360: $i] :
      ( ( ( SV360 = SV172 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6790]) ).

thf(6838,plain,
    ! [SV172: $i,SV360: $i,SV424: $i,SV467: $i,SV51: $i,SV274: $i] :
      ( ( ( SV274 = SV51 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6791]) ).

thf(6839,plain,
    ! [SV424: $i,SV467: $i,SV51: $i,SV274: $i,SV172: $i,SV360: $i] :
      ( ( ( SV360 = SV172 )
        = $false )
      | ( ( SV274 != SV51 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6792]) ).

thf(6840,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ( SV363
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
               != SV54 ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6793]) ).

thf(6841,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ~ ( ( SV363
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
               != SV54 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6794]) ).

thf(6842,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV521: $i,SV363: $i,SV426: $i] :
      ( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6794]) ).

thf(6843,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6795]) ).

thf(6844,plain,
    ! [SV278: $i,SV364: $i,SV55: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV364 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV176 ) @ SV55 ) @ SV278 ) )
        = $true )
      | ( ( SV364 = SV278 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6796]) ).

thf(6845,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6798]) ).

thf(6846,plain,
    ! [SV185: $i,SV65: $i,SV286: $i,SV369: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) ) )
        = $false )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6798]) ).

thf(6847,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6799]) ).

thf(6848,plain,
    ! [SV185: $i,SV65: $i,SV286: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK19_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV369 @ SV185 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6800]) ).

thf(6849,plain,
    ! [SV289: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) @ SV68 ) ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6801]) ).

thf(6850,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV522: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6802]) ).

thf(6851,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
        = $false )
      | ( ( ( hAPP @ SV76 @ SV499 )
          = ( hAPP @ SV76 @ SV507 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6803]) ).

thf(6852,plain,
    ! [SV196: $i,SV507: $i,SV499: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ SV499 )
          = ( hAPP @ SV76 @ SV507 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV499 ) @ SV507 ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6804]) ).

thf(6853,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
               != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6805]) ).

thf(6854,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
           != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
        = $false )
      | ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6806]) ).

thf(6855,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV79: $i,SV199: $i,SV433: $i] :
      ( ( ( ( hAPP @ SV433 @ SV199 )
          = ( hAPP @ SV433 @ SV79 ) )
        = $false )
      | ( ( SV199 = SV79 )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6807]) ).

thf(6856,plain,
    ! [SV298: $i,SV376: $i,SV473: $i,SV493: $i,SV433: $i,SV79: $i,SV199: $i] :
      ( ( ( SV199 = SV79 )
        = $false )
      | ( ( ( hAPP @ SV433 @ SV199 )
          = ( hAPP @ SV433 @ SV79 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV493 @ SV473 @ SV433 @ SV376 @ SV298 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6808]) ).

thf(6857,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6809]) ).

thf(6858,plain,
    ! [SV301: $i,SV435: $i,SV82: $i,SV202: $i,SV379: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6810]) ).

thf(6859,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6811]) ).

thf(6860,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6812]) ).

thf(6861,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6813]) ).

thf(6862,plain,
    ! [SV322: $i,SV446: $i,SV107: $i,SV226: $i,SV395: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6814]) ).

thf(6863,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6815]) ).

thf(6864,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6816]) ).

thf(6865,plain,
    ! [SV450: $i,SV232: $i,SV399: $i,SV113: $i,SV326: $i] :
      ( ( ( SV326 = SV113 )
        = $false )
      | ( ( SV399 = SV232 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV399 ) @ SV326 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV450 ) @ SV232 ) @ SV113 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6819]) ).

thf(6866,plain,
    ! [SV332: $i,SV122: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6820]) ).

thf(6867,plain,
    ! [SV403: $i,SV241: $i,SV122: $i,SV332: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) @ SV122 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6820]) ).

thf(6868,plain,
    ! [SV122: $i,SV332: $i,SV520: $i,SV241: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6821]) ).

thf(6869,plain,
    ! [SV124: $i,SV333: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6822]) ).

thf(6870,plain,
    ! [SV404: $i,SV451: $i,SV124: $i,SV243: $i,SV333: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6823]) ).

thf(6871,plain,
    ! [SV333: $i,SV124: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV451 @ SV243 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6824]) ).

thf(6872,plain,
    ! [SV451: $i,SV404: $i,SV124: $i,SV243: $i,SV333: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV333 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6825]) ).

thf(6873,plain,
    ! [SV453: $i,SV406: $i,SV335: $i,SV126: $i,SV245: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV453 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV126 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6826]) ).

thf(6874,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6828]) ).

thf(6875,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) @ SV40 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6828]) ).

thf(6876,plain,
    ! [SV265: $i,SV513: $i,SV40: $i,SV161: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6829]) ).

thf(6877,plain,
    ! [SV43: $i,SV354: $i,SV487: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ( ( SV463 != SV268 )
              | ( SV420 != SV164 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6830]) ).

thf(6878,plain,
    ! [SV164: $i,SV268: $i,SV420: $i,SV463: $i,SV487: $i,SV43: $i,SV354: $i] :
      ( ( ( SV354 = SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6831]) ).

thf(6879,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ~ ( ( SV463 != SV268 )
              | ( SV420 != SV164 ) ) )
        = $false )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6832]) ).

thf(6880,plain,
    ! [SV271: $i,SV47: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6833]) ).

thf(6881,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ~ ! [SY1478: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6833]) ).

thf(6882,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
          | ~ ~ ! [SY1478: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6834]) ).

thf(6883,plain,
    ! [SV271: $i,SV47: $i,SV168: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6835]) ).

thf(6884,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ! [SY1479: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1479 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1479 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6836]) ).

thf(6885,plain,
    ! [SV424: $i,SV467: $i,SV172: $i,SV360: $i,SV51: $i,SV274: $i] :
      ( ( ( SV274 = SV51 )
        = $false )
      | ( ( SV360 = SV172 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV360 ) @ SV274 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV467 @ SV424 ) @ SV172 ) @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6839]) ).

thf(6886,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ( SV363
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
           != SV54 ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6840]) ).

thf(6887,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( ( SV363
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
           != SV54 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6841]) ).

thf(6888,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV521: $i,SV363: $i,SV426: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
           != SV175 )
          | ( SV277
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6842]) ).

thf(6889,plain,
    ! [SV369: $i,SV65: $i,SV185: $i,SV286: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV286 ) @ SV185 ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) )
        = $true )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6845]) ).

thf(6890,plain,
    ! [SV185: $i,SV65: $i,SV286: $i,SV369: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ ( sK20_SY1503 @ SV65 @ SV369 @ SV185 @ SV286 ) ) @ SV65 ) )
        = $true )
      | ( ( SV65 = SV185 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV369 @ SV286 ) ) @ SV185 ) @ SV65 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6846]) ).

thf(6891,plain,
    ! [SV289: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) @ SV68 ) ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6849]) ).

thf(6892,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV522: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6850]) ).

thf(6893,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
           != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6853]) ).

thf(6894,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
         != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6854]) ).

thf(6895,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6854]) ).

thf(6896,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6857]) ).

thf(6897,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6858]) ).

thf(6898,plain,
    ! [SV301: $i,SV435: $i,SV82: $i,SV202: $i,SV379: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6859]) ).

thf(6899,plain,
    ! [SV379: $i,SV82: $i,SV301: $i,SV202: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6860]) ).

thf(6900,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6861]) ).

thf(6901,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6862]) ).

thf(6902,plain,
    ! [SV322: $i,SV446: $i,SV107: $i,SV226: $i,SV395: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6863]) ).

thf(6903,plain,
    ! [SV395: $i,SV107: $i,SV322: $i,SV226: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6864]) ).

thf(6904,plain,
    ! [SV332: $i,SV122: $i,SV241: $i,SV403: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6866]) ).

thf(6905,plain,
    ! [SV403: $i,SV241: $i,SV122: $i,SV332: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ ( sK16_SY1547 @ SV122 @ SV332 @ SV241 @ SV403 ) ) @ SV122 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6867]) ).

thf(6906,plain,
    ! [SV122: $i,SV332: $i,SV520: $i,SV241: $i,SV403: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6868]) ).

thf(6907,plain,
    ! [SV124: $i,SV333: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6869]) ).

thf(6908,plain,
    ! [SV333: $i,SV124: $i,SV404: $i,SV243: $i,SV451: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV451 @ SV243 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV404 ) @ SV243 ) @ SV124 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV451 @ SV404 @ SV333 ) ) @ SV243 ) @ SV124 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6871]) ).

thf(6909,plain,
    ! [SV453: $i,SV406: $i,SV335: $i,SV126: $i,SV245: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV453 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV126 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6873]) ).

thf(6910,plain,
    ! [SV265: $i,SV40: $i,SV161: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6874]) ).

thf(6911,plain,
    ! [SV40: $i,SV161: $i,SV265: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ ( sK17_SY1286 @ SV265 @ SV40 @ SV161 ) ) @ SV40 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV265 @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6875]) ).

thf(6912,plain,
    ! [SV40: $i,SV513: $i,SV161: $i,SV265: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV513 ) @ SV40 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV161 ) @ SV40 ) @ SV513 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV265 @ SV161 ) ) @ SV40 ) @ SV40 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6876]) ).

thf(6913,plain,
    ! [SV43: $i,SV354: $i,SV487: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ( SV463 != SV268 )
          | ( SV420 != SV164 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6877]) ).

thf(6914,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( ( SV463 != SV268 )
          | ( SV420 != SV164 ) )
        = $true )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6879]) ).

thf(6915,plain,
    ! [SV271: $i,SV47: $i,SV168: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6880]) ).

thf(6916,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ! [SY1478: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6881]) ).

thf(6917,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV357 @ SV168 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6882]) ).

thf(6918,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ~ ! [SY1478: $i] :
                  ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6882]) ).

thf(6919,plain,
    ! [SV47: $i,SV357: $i,SV523: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6884]) ).

thf(6920,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( SV363
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6886]) ).

thf(6921,plain,
    ! [SV363: $i,SV175: $i,SV277: $i,SV54: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
         != SV54 )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6886]) ).

thf(6922,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( SV363
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
         != SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6887]) ).

thf(6923,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV521: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
         != SV175 )
        = $true )
      | ( ( SV277
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6888]) ).

thf(6924,plain,
    ! [SV289: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) @ SV68 ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6891]) ).

thf(6925,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV522: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6892]) ).

thf(6926,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
         != ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6893]) ).

thf(6927,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6893]) ).

thf(6928,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $false )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6894]) ).

thf(6929,plain,
    ! [SV82: $i,SV301: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6896]) ).

thf(6930,plain,
    ! [SV379: $i,SV435: $i,SV82: $i,SV202: $i,SV301: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6896]) ).

thf(6931,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6897]) ).

thf(6932,plain,
    ! [SV435: $i,SV379: $i,SV82: $i,SV202: $i,SV301: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6897]) ).

thf(6933,plain,
    ! [SV379: $i,SV435: $i,SV82: $i,SV202: $i,SV301: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6899]) ).

thf(6934,plain,
    ! [SV107: $i,SV322: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6900]) ).

thf(6935,plain,
    ! [SV395: $i,SV446: $i,SV107: $i,SV226: $i,SV322: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6900]) ).

thf(6936,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6901]) ).

thf(6937,plain,
    ! [SV446: $i,SV395: $i,SV107: $i,SV226: $i,SV322: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6901]) ).

thf(6938,plain,
    ! [SV395: $i,SV446: $i,SV107: $i,SV226: $i,SV322: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6903]) ).

thf(6939,plain,
    ! [SV241: $i,SV403: $i,SV122: $i,SV520: $i,SV332: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV332 ) @ SV520 ) @ SV122 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV403 ) @ SV241 ) @ SV520 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV403 @ SV332 ) ) @ SV241 ) @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6906]) ).

thf(6940,plain,
    ! [SV453: $i,SV406: $i,SV335: $i,SV126: $i,SV245: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV453 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV126 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6909]) ).

thf(6941,plain,
    ! [SV43: $i,SV164: $i,SV354: $i,SV420: $i,SV487: $i,SV268: $i,SV463: $i] :
      ( ( ( SV463 != SV268 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6913]) ).

thf(6942,plain,
    ! [SV43: $i,SV268: $i,SV354: $i,SV463: $i,SV487: $i,SV164: $i,SV420: $i] :
      ( ( ( SV420 != SV164 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6913]) ).

thf(6943,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( SV463 != SV268 )
        = $true )
      | ( ( SV420 != SV164 )
        = $true )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6914]) ).

thf(6944,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ! [SY1478: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6916]) ).

thf(6945,plain,
    ! [SV47: $i,SV271: $i,SV168: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6917]) ).

thf(6946,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ! [SY1478: $i] :
                ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6918]) ).

thf(6947,plain,
    ! [SV47: $i,SV357: $i,SV523: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6919]) ).

thf(6948,plain,
    ! [SV277: $i,SV54: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6920]) ).

thf(6949,plain,
    ! [SV363: $i,SV175: $i,SV277: $i,SV54: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
               != SV175 )
              | ( SV277
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6921]) ).

thf(6950,plain,
    ! [SV54: $i,SV277: $i,SV521: $i,SV175: $i,SV426: $i,SV363: $i] :
      ( ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
         != SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6922]) ).

thf(6951,plain,
    ! [SV54: $i,SV277: $i,SV175: $i,SV521: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
          = SV175 )
        = $false )
      | ( ( SV277
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6923]) ).

thf(6952,plain,
    ! [SV289: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6924]) ).

thf(6953,plain,
    ! [SV370: $i,SV188: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV289: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) @ SV68 ) ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6924]) ).

thf(6954,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV522: $i,SV188: $i,SV370: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6925]) ).

thf(6955,plain,
    ! [SV196: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) )
          = ( hAPP @ SV76 @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ ( sK5_SY762 @ SV196 @ SV76 ) ) @ ( sK8_SY1659 @ SV196 @ SV76 ) ) )
        = $true )
      | ( ( c_Equiv__Relations_Oequivp @ SV196 @ SV76 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6926]) ).

thf(6956,plain,
    ! [SV82: $i,SV301: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6929]) ).

thf(6957,plain,
    ! [SV379: $i,SV435: $i,SV82: $i,SV202: $i,SV301: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6930]) ).

thf(6958,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV435 @ SV202 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6931]) ).

thf(6959,plain,
    ! [SV435: $i,SV379: $i,SV82: $i,SV202: $i,SV301: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV301 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6932]) ).

thf(6960,plain,
    ! [SV107: $i,SV322: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6934]) ).

thf(6961,plain,
    ! [SV395: $i,SV446: $i,SV107: $i,SV226: $i,SV322: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6935]) ).

thf(6962,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ SV226 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6936]) ).

thf(6963,plain,
    ! [SV446: $i,SV395: $i,SV107: $i,SV226: $i,SV322: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV322 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6937]) ).

thf(6964,plain,
    ! [SV453: $i,SV406: $i,SV335: $i,SV126: $i,SV245: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV453 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6940]) ).

thf(6965,plain,
    ! [SV503: $i,SV497: $i,SV453: $i,SV126: $i,SV245: $i,SV483: $i,SV335: $i,SV406: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV126 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6940]) ).

thf(6966,plain,
    ! [SV43: $i,SV164: $i,SV354: $i,SV420: $i,SV487: $i,SV268: $i,SV463: $i] :
      ( ( ( SV463 = SV268 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6941]) ).

thf(6967,plain,
    ! [SV43: $i,SV268: $i,SV354: $i,SV463: $i,SV487: $i,SV164: $i,SV420: $i] :
      ( ( ( SV420 = SV164 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6942]) ).

thf(6968,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i] :
      ( ( ( SV463 = SV268 )
        = $false )
      | ( ( SV420 != SV164 )
        = $true )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6943]) ).

thf(6969,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6944]) ).

thf(6970,plain,
    ! [SV47: $i,SV357: $i,SV168: $i,SV271: $i] :
      ( ( ( ! [SY1478: $i] :
              ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SY1478 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SY1478 ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6946]) ).

thf(6971,plain,
    ! [SV47: $i,SV357: $i,SV523: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6947]) ).

thf(6972,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
           != SV175 )
          | ( SV277
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) )
        = $false )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6948]) ).

thf(6973,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
           != SV175 )
          | ( SV277
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6949]) ).

thf(6974,plain,
    ! [SV175: $i,SV363: $i,SV54: $i,SV277: $i,SV521: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV277 )
          = SV54 )
        = $false )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV521 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6950]) ).

thf(6975,plain,
    ! [SV175: $i,SV363: $i,SV54: $i,SV521: $i,SV426: $i,SV277: $i] :
      ( ( ( SV277
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV521 ) @ SV54 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV521 )
          = SV175 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6951]) ).

thf(6976,plain,
    ! [SV289: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV188: $i,SV370: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6952]) ).

thf(6977,plain,
    ! [SV370: $i,SV188: $i,SV68: $i,SV492: $i,SV471: $i,SV430: $i,SV289: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ ( sK21_SY1507 @ SV430 @ SV471 @ SV492 @ SV68 @ SV289 @ SV188 @ SV370 ) ) @ SV68 ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6953]) ).

thf(6978,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV68: $i,SV289: $i,SV522: $i,SV188: $i,SV370: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) ) )
        = $true )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6954]) ).

thf(6979,plain,
    ! [SV82: $i,SV301: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6956]) ).

thf(6980,plain,
    ! [SV301: $i,SV82: $i,SV379: $i,SV202: $i,SV435: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV435 @ SV202 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV379 ) @ SV202 ) @ SV82 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV435 @ SV379 @ SV301 ) ) @ SV202 ) @ SV82 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6958]) ).

thf(6981,plain,
    ! [SV107: $i,SV322: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6960]) ).

thf(6982,plain,
    ! [SV322: $i,SV107: $i,SV395: $i,SV226: $i,SV446: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV446 @ SV226 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV395 ) @ SV226 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV446 @ SV395 @ SV322 ) ) @ SV226 ) @ SV107 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6962]) ).

thf(6983,plain,
    ! [SV453: $i,SV406: $i,SV335: $i,SV126: $i,SV245: $i,SV483: $i,SV497: $i,SV503: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV453 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6964]) ).

thf(6984,plain,
    ! [SV503: $i,SV497: $i,SV453: $i,SV126: $i,SV245: $i,SV483: $i,SV335: $i,SV406: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ ( sK22_SY1662 @ SV483 @ SV245 @ SV126 @ SV335 @ SV406 @ SV453 @ SV497 @ SV503 ) ) @ SV126 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV406 ) @ SV335 ) @ SV245 ) @ SV126 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV503 ) @ SV497 ) @ SV483 ) @ SV453 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6965]) ).

thf(6985,plain,
    ! [SV487: $i,SV43: $i,SV354: $i,SV268: $i,SV463: $i,SV164: $i,SV420: $i] :
      ( ( ( SV420 = SV164 )
        = $false )
      | ( ( SV463 = SV268 )
        = $false )
      | ( ( SV354 != SV43 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6968]) ).

thf(6986,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6969]) ).

thf(6987,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6970]) ).

thf(6988,plain,
    ! [SV47: $i,SV357: $i,SV523: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6971]) ).

thf(6989,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
         != SV175 )
        = $false )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6972]) ).

thf(6990,plain,
    ! [SV363: $i,SV175: $i,SV54: $i,SV426: $i,SV277: $i] :
      ( ( ( SV277
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) )
        = $false )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6972]) ).

thf(6991,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
         != SV175 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6973]) ).

thf(6992,plain,
    ! [SV363: $i,SV175: $i,SV54: $i,SV426: $i,SV277: $i] :
      ( ( ( SV277
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6973]) ).

thf(6993,plain,
    ! [SV430: $i,SV471: $i,SV492: $i,SV188: $i,SV370: $i,SV68: $i,SV522: $i,SV289: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV289 @ SV522 ) @ SV68 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV370 @ SV188 ) @ SV522 ) )
        = $false )
      | ( ( c_Predicate_Opred__comp @ SV492 @ SV471 @ SV430 @ SV370 @ SV289 @ SV188 @ SV68 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6978]) ).

thf(6994,plain,
    ! [SV487: $i,SV164: $i,SV420: $i,SV268: $i,SV463: $i,SV43: $i,SV354: $i] :
      ( ( ( SV354 = SV43 )
        = $false )
      | ( ( SV463 = SV268 )
        = $false )
      | ( ( SV420 = SV164 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV463 ) @ SV420 ) @ SV354 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV487 ) @ SV268 ) @ SV164 ) @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6985]) ).

thf(6995,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6986]) ).

thf(6996,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6987]) ).

thf(6997,plain,
    ! [SV47: $i,SV357: $i,SV523: $i,SV168: $i,SV271: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6988]) ).

thf(6998,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
          = SV175 )
        = $true )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6989]) ).

thf(6999,plain,
    ! [SV363: $i,SV175: $i,SV54: $i,SV426: $i,SV277: $i] :
      ( ( ( SV277
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) )
        = $true )
      | ( ( SV363
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6990]) ).

thf(7000,plain,
    ! [SV175: $i,SV277: $i,SV54: $i,SV363: $i,SV426: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) )
          = SV175 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6991]) ).

thf(7001,plain,
    ! [SV363: $i,SV175: $i,SV54: $i,SV426: $i,SV277: $i] :
      ( ( ( SV277
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV54 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ ( sK18_SY1584 @ SV54 @ SV277 @ SV175 @ SV426 @ SV363 ) ) @ SV277 )
          = SV54 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV363 ) @ SV277 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV426 ) @ SV175 ) @ SV54 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6992]) ).

thf(7002,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6995]) ).

thf(7003,plain,
    ! [SV168: $i,SV47: $i,SV271: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) )
        = $false )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6995]) ).

thf(7004,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6996]) ).

thf(7005,plain,
    ! [SV168: $i,SV47: $i,SV523: $i,SV271: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV523 ) @ SV47 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ SV523 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6997]) ).

thf(7006,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[7002]) ).

thf(7007,plain,
    ! [SV168: $i,SV47: $i,SV271: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK23_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) )
        = $true )
      | ( ( SV47 = SV168 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[7003]) ).

thf(7008,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[7004]) ).

thf(7009,plain,
    ! [SV168: $i,SV47: $i,SV271: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[7004]) ).

thf(7010,plain,
    ! [SV357: $i,SV47: $i,SV168: $i,SV271: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV168 ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[7008]) ).

thf(7011,plain,
    ! [SV168: $i,SV47: $i,SV271: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ ( sK24_SY1478 @ SV47 @ SV357 @ SV168 @ SV271 ) ) @ SV47 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV357 @ SV168 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV357 @ SV271 ) ) @ SV168 ) @ SV47 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[7009]) ).

thf(7012,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[5476,7011,7010,7007,7006,7005,7001,7000,6999,6998,6994,6993,6984,6983,6982,6981,6980,6979,6977,6976,6975,6974,6967,6966,6963,6961,6959,6957,6955,6945,6939,6938,6933,6928,6927,6915,6912,6911,6910,6908,6907,6905,6904,6902,6898,6895,6890,6889,6885,6883,6878,6872,6870,6865,6856,6855,6852,6851,6848,6847,6844,6843,6838,6837,6827,6818,6817,6797,6789,6779,6778,6772,6771,6764,6763,6757,6756,6749,6746,6744,6733,6724,6715,6714,6713,6709,6708,6707,6706,6704,6703,6702,6697,6689,6688,6687,6686,6683,6682,6678,6666,6651,6650,6642,6641,6636,6635,6630,6628,6617,6612,6606,6605,6604,6603,6596,6595,6586,6584,6563,6560,6559,6537,6524,6519,6518,6517,6507,6500,6490,6489,6486,6485,6475,6472,6458,6457,6456,6455,6450,6449,6444,6443,6437,6410,6401,6400,6393,6392,6389,6388,6383,6382,6379,6378,6373,6356,6354,6336,6333,6332,6321,6320,6298,6297,6263,6252,6242,6219,6193,6192,6191,6190,6189,6187,6185,6184,6151,6141,6132,6111,6100,6081,6076,6072,6054,6041,5999,5984,5982,5972,5970,5969,5968,5967,5965,5964,5963,5959,5958,5957,5950,5948,5857,5842,5831,5768,5741,5724,5721,5717,5716,5715,5616,5604,5580,5579]) ).

thf(7013,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[7012]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW349+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21  % Computer : n004.cluster.edu
% 0.09/0.21  % Model    : x86_64 x86_64
% 0.09/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21  % Memory   : 8046.5625MB
% 0.09/0.21  % OS       : Linux 6.8.0-71-generic
% 0.09/0.21  % CPULimit : 300
% 0.09/0.21  % WCLimit  : 300
% 0.09/0.21  % DateTime : Tue Oct  6 16:54:39 UTC 2026
% 0.09/0.21  % CPUTime  : 
% 0.09/0.21  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 119.26/24.13  ....................................
% 119.26/24.13  
% 119.26/24.13   No.of.Axioms: 128
% 119.26/24.13  
% 119.26/24.13   Length.of.Defs: 0
% 119.26/24.13  
% 119.26/24.13   Contains.Choice.Funs: false
% 119.26/24.13  ......................................................................................................................................
% 119.26/24.13  
% 119.26/24.13  ********************************
% 119.26/24.13  *   All subproblems solved!    *
% 119.26/24.13  ********************************
% 119.26/24.13  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:128,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:292,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7012,loop_count:0,foatp_calls:1,translation:fof_full)
% 119.26/24.13  
% 119.26/24.13  %**** Beginning of derivation protocol ****
% 119.26/24.13  % SZS output start CNFRefutation
% See solution above
% 24.06/24.16  
% 24.06/24.16  %**** End of derivation protocol ****
% 24.06/24.16  %**** no. of clauses in derivation: 1914 ****
% 24.06/24.16  %**** clause counter: 7012 ****
% 24.06/24.16  
% 24.06/24.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:128,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:292,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7012,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------