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

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SWW317+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 : n020.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 11:01:14 AM UTC 2026

% Result   : Theorem 79.71s 16.16s
% Output   : CNFRefutation 79.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :  187
% Syntax   : Number of formulae    : 1767 (1333 unt;   0 typ;   0 def)
%            Number of atoms       : 7975 (4927 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives : 30632 (2538   ~;1798   |;  39   &;25996   @)
%                                         (  72 <=>; 189  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  533 ( 530 usr;  54 con; 0-10 aty)
%            Number of variables   : 7375 (   0   ^;7372   !;   3   ?;7375   :)

% 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_Ocom_OAss,type,
    c_Com_Ocom_OAss: $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__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 ).

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__image__simple__idem,type,
    c_Finite__Set_Ofolding__image__simple__idem: $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,type,
    c_Finite__Set_Ofun__left__comm: $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_Ois__measure,type,
    c_FunDef_Ois__measure: $i > $i > $o ).

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_HOL_Oequal__class_Oequal,type,
    c_HOL_Oequal__class_Oequal: $i > $i ).

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

thf(tp_c_Lazy__Sequence_Obind,type,
    c_Lazy__Sequence_Obind: $i > $i > $i > $i > $i ).

thf(tp_c_Lazy__Sequence_Oempty,type,
    c_Lazy__Sequence_Oempty: $i > $i ).

thf(tp_c_Lazy__Sequence_Ohb__bind,type,
    c_Lazy__Sequence_Ohb__bind: $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_Lazy__Sequence_Ohit__bound,type,
    c_Lazy__Sequence_Ohit__bound: $i > $i ).

thf(tp_c_Lazy__Sequence_Olazy__sequence_OInsert,type,
    c_Lazy__Sequence_Olazy__sequence_OInsert: $i > $i > $i > $i ).

thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case,type,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size,type,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size: $i > $i > $i ).

thf(tp_c_Lazy__Sequence_Oyield,type,
    c_Lazy__Sequence_Oyield: $i > $i ).

thf(tp_c_Lazy__Sequence_Oyieldn,type,
    c_Lazy__Sequence_Oyieldn: $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__all,type,
    c_List_Olist__all: $i > $i > $i > $o ).

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__ex1,type,
    c_List_Olist__ex1: $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__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 > $i > $i > $i > $o ).

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

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

thf(tp_c_New__DSequence_Oneg__bind,type,
    c_New__DSequence_Oneg__bind: $i > $i > $i > $i > $i ).

thf(tp_c_New__DSequence_Oneg__decr__bind,type,
    c_New__DSequence_Oneg__decr__bind: $i > $i > $i > $i > $i ).

thf(tp_c_New__DSequence_Opos__decr__bind,type,
    c_New__DSequence_Opos__decr__bind: $i > $i > $i > $i > $i ).

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

thf(tp_c_New__Random__Sequence_Oneg__bind,type,
    c_New__Random__Sequence_Oneg__bind: $i > $i > $i > $i > $i ).

thf(tp_c_New__Random__Sequence_Oneg__decr__bind,type,
    c_New__Random__Sequence_Oneg__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_New__Random__Sequence_Oneg__map,type,
    c_New__Random__Sequence_Oneg__map: $i > $i > $i > $i > $i ).

thf(tp_c_New__Random__Sequence_Oneg__single,type,
    c_New__Random__Sequence_Oneg__single: $i > $i ).

thf(tp_c_New__Random__Sequence_Opos__decr__bind,type,
    c_New__Random__Sequence_Opos__decr__bind: $i > $i > $i > $i > $i > $i > $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_ORep__Frac,type,
    c_Nitpick_ORep__Frac: $i > $i ).

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

thf(tp_c_Nitpick_Odenom,type,
    c_Nitpick_Odenom: $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 ).

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_Oinverse__frac,type,
    c_Nitpick_Oinverse__frac: $i > $i > $i ).

thf(tp_c_Nitpick_Oless__eq__frac,type,
    c_Nitpick_Oless__eq__frac: $i > $i > $i > $o ).

thf(tp_c_Nitpick_Oless__frac,type,
    c_Nitpick_Oless__frac: $i > $i > $i > $o ).

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_Onum,type,
    c_Nitpick_Onum: $i > $i ).

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

thf(tp_c_Nitpick_Oof__frac,type,
    c_Nitpick_Oof__frac: $i > $i > $i > $i ).

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

thf(tp_c_Nitpick_Oplus__frac,type,
    c_Nitpick_Oplus__frac: $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_Otimes__frac,type,
    c_Nitpick_Otimes__frac: $i > $i > $i > $i ).

thf(tp_c_Nitpick_Ouminus__frac,type,
    c_Nitpick_Ouminus__frac: $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_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_Oorder__class_Ostrict__mono,type,
    c_Orderings_Oorder__class_Ostrict__mono: $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_Partial__Function_Omk__less,type,
    c_Partial__Function_Omk__less: $i > $i > $i > $i > $o ).

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_Oinv__imagep,type,
    c_Predicate_Oinv__imagep: $i > $i > $i > $i > $i > $i > $o ).

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_Ointernal__split,type,
    c_Product__Type_Ointernal__split: $i > $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_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_Nat_Osize,type,
    class_Nat_Osize: $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_Oinverse,type,
    class_Rings_Oinverse: $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_sK1_SY1248,type,
    sK1_SY1248: $i > $i > $i ).

thf(tp_sK2_SY1626,type,
    sK2_SY1626: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK3_SY1341,type,
    sK3_SY1341: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK4_SY1696,type,
    sK4_SY1696: $i > $i > $i > $i > $i > $i ).

thf(tp_sK5_SY1776,type,
    sK5_SY1776: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK6_SY1707,type,
    sK6_SY1707: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK7_SY1777,type,
    sK7_SY1777: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK8_SY1778,type,
    sK8_SY1778: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK9_SY1781,type,
    sK9_SY1781: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_t_a,type,
    t_a: $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_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_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_G,type,
    v_G: $i ).

thf(tp_v_Ga,type,
    v_Ga: $i ).

thf(tp_v_P,type,
    v_P: $i ).

thf(16,axiom,
    ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ 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_b: $i,T_d: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ 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_d: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ 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(65,axiom,
    ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

thf(66,axiom,
    ! [T_1: $i] : ( class_HOL_Oequal @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__HOL_Oequal) ).

thf(93,axiom,
    class_Nat_Osize @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).

thf(94,axiom,
    class_Enum_Oenum @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

thf(95,axiom,
    class_HOL_Oequal @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__HOL_Oequal) ).

thf(96,axiom,
    class_Groups_Ominus @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

thf(97,axiom,
    class_Groups_Ouminus @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

thf(98,axiom,
    class_Orderings_Obot @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).

thf(99,axiom,
    class_Orderings_Oord @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

thf(100,axiom,
    class_Orderings_Otop @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

thf(101,axiom,
    class_Orderings_Oorder @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

thf(102,axiom,
    class_Lattices_Olattice @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).

thf(103,axiom,
    class_Finite__Set_Ofinite @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

thf(104,axiom,
    class_Orderings_Opreorder @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

thf(105,axiom,
    class_Lattices_Oboolean__algebra @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

thf(106,axiom,
    class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).

thf(107,axiom,
    class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).

thf(108,axiom,
    class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).

thf(109,axiom,
    class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).

thf(110,axiom,
    class_Lattices_Obounded__lattice__top @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).

thf(111,axiom,
    class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).

thf(234,axiom,
    ! [T_1: $i,T_2: $i] :
      ( ( ( class_Enum_Oenum @ T_2 )
        & ( class_Enum_Oenum @ T_1 ) )
     => ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

thf(236,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Groups_Ominus @ T_1 )
     => ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

thf(237,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Groups_Ouminus @ T_1 )
     => ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

thf(238,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Orderings_Obot @ T_1 )
     => ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).

thf(239,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Orderings_Oord @ T_1 )
     => ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

thf(240,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Orderings_Otop @ T_1 )
     => ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

thf(241,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Orderings_Oorder @ T_1 )
     => ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

thf(242,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Lattices_Olattice @ T_1 )
     => ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).

thf(243,axiom,
    ! [T_1: $i,T_2: $i] :
      ( ( ( class_Finite__Set_Ofinite @ T_2 )
        & ( class_Finite__Set_Ofinite @ T_1 ) )
     => ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

thf(244,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Orderings_Opreorder @ T_1 )
     => ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

thf(245,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Lattices_Oboolean__algebra @ T_1 )
     => ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

thf(246,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Lattices_Odistrib__lattice @ T_1 )
     => ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

thf(251,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
     => ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(252,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Lattices_Obounded__lattice @ T_1 )
     => ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

thf(253,axiom,
    class_Lattices_Obounded__lattice @ tc_HOL_Obool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).

thf(341,axiom,
    ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_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__image__simple__idem_Oidem) ).

thf(360,axiom,
    ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
     => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
        = ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

thf(397,axiom,
    ! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
      = V_z_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__empty) ).

thf(439,axiom,
    ! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
      ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).

thf(453,axiom,
    ! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).

thf(476,axiom,
    ! [V_r_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
      = V_r_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).

thf(599,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(600,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(618,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(930,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(931,axiom,
    ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
        = V_ys_2 )
    <=> ( V_xs_2
        = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).

thf(932,axiom,
    ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
        = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
    <=> ( V_xs_2 = V_ys_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

thf(1186,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(1187,axiom,
    ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
    <=> ? [B_us: $i] :
          ( ( ( V_xs_2
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
            & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
              = V_tsa_2 ) )
          | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
              = V_zs_2 )
            & ( V_ys_2
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

thf(1188,axiom,
    ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
    <=> ( V_ys_2 = V_zs_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).

thf(1189,axiom,
    ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
    <=> ( V_ys_2 = V_zs_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).

thf(1190,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(1404,axiom,
    ! [T_b: $i] :
      ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__empty) ).

thf(1459,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(1460,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(1618,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(1619,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(1620,axiom,
    ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
        = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ 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(1710,axiom,
    ! [V_a_2: $i,V_f_2: $i,T_b: $i] :
      ( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
      = V_a_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton) ).

thf(1711,axiom,
    ! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
      ( ( V_g_2
        = ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
     => ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
        = V_a_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).

thf(1757,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(1758,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(1913,axiom,
    ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
      = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).

thf(2081,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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(2082,axiom,
    ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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(2705,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(2914,axiom,
    ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
      ( ( V_p_2 = V_q_2 )
     => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).

thf(2916,axiom,
    ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ 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(2917,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(3968,axiom,
    ! [V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__empty) ).

thf(3975,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(3977,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(3978,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(3979,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(4156,axiom,
    ! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
      = V_z_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__empty) ).

thf(4183,axiom,
    ! [T_b: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).

thf(4249,axiom,
    ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).

thf(4286,axiom,
    ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofolding__one__idem @ T_b @ 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(4419,axiom,
    ! [V_R_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).

thf(4426,axiom,
    ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
     => ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
        = V_x_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).

thf(4427,axiom,
    ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
        = ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
    <=> ( V_a_2 = V_a_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Oinject) ).

thf(4435,axiom,
    ! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
     => ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
        = V_z_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).

thf(4517,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
        = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
    <=> ( V_A_2 = V_B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).

thf(4518,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
      = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).

thf(4561,axiom,
    ! [V_r_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__empty) ).

thf(4562,axiom,
    ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
        = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
    <=> ( V_A_2
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).

thf(4563,axiom,
    ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
    <=> ( V_A_2
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty) ).

thf(4572,axiom,
    ! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).

thf(4575,axiom,
    ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ 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(4640,axiom,
    ! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).

thf(4702,axiom,
    ! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

thf(4703,axiom,
    ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

thf(4705,axiom,
    ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
      ( ( ( V_x_2 = V_a_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ 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(4707,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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(4708,axiom,
    ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
      = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

thf(4709,axiom,
    ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ 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(4710,axiom,
    ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
      ( ( ( V_z_2 = V_x_2 )
       => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ 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(4711,axiom,
    ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
      ( ( V_a_2 != V_c_2 )
     => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

thf(4712,axiom,
    ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
      ( ( V_z_2 != V_x_2 )
     => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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(4713,axiom,
    ! [T_b: $i,T_c: $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_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
        = V_f_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

thf(4736,axiom,
    ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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(4770,axiom,
    ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).

thf(4771,axiom,
    ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).

thf(4772,axiom,
    ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).

thf(4796,axiom,
    ! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).

thf(4801,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__right) ).

thf(4802,axiom,
    ! [V_B_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).

thf(4803,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).

thf(4804,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
      = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).

thf(4805,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).

thf(4846,axiom,
    ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).

thf(4848,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
      = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).

thf(4850,axiom,
    ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).

thf(4851,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).

thf(4852,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).

thf(4853,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
      = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).

thf(4928,axiom,
    ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__is__Un) ).

thf(4963,axiom,
    ! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__left) ).

thf(4964,axiom,
    ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).

thf(4965,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
    <=> ( ( V_A_2
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        & ( V_B_2
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty) ).

thf(4966,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
      = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).

thf(4967,axiom,
    ! [V_B_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
      = V_B_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).

thf(4972,axiom,
    ! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).

thf(4973,axiom,
    ! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
      ( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
    <=> ( V_A_2
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).

thf(4974,axiom,
    ! [V_f_2: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__empty) ).

thf(4975,axiom,
    ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
        = ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
    <=> ( V_A_2
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).

thf(4998,axiom,
    ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__assoc) ).

thf(5001,axiom,
    ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__commute) ).

thf(5003,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__absorb) ).

thf(5004,axiom,
    ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__commute) ).

thf(5006,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
      = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).

thf(5034,axiom,
    ! [T_b: $i] :
      ( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__empty) ).

thf(5038,axiom,
    ! [V_A_2: $i,T_b: $i] :
      ( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__not__empty) ).

thf(5039,axiom,
    ! [V_P_2: $i,T_b: $i] :
      ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
      = V_P_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).

thf(5055,axiom,
    ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
      ( ( c_Fun_Ooverride__on @ T_b @ T_c @ V_f_2 @ V_g_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
      = V_f_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__emptyset) ).

thf(5056,axiom,
    ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $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_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
        = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).

thf(5065,axiom,
    ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
     => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
        = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).

thf(5066,axiom,
    ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
        = V_c_2 )
     => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
        = ( hAPP @ V_c_2 @ V_v_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

thf(5067,axiom,
    ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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(5068,axiom,
    ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
      = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).

thf(5073,axiom,
    ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).

thf(5074,axiom,
    ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
      ( ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).

thf(5086,axiom,
    ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).

thf(5108,axiom,
    ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).

thf(5109,axiom,
    ! [V_t: $i,V_n: $i,V_s: $i] :
      ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
     => ( V_t = V_s ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).

thf(5121,axiom,
    ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
        = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
     => ! [B_v: $i] :
          ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
          = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).

thf(5124,axiom,
    ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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(5132,axiom,
    ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
      ( ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).

thf(5133,axiom,
    ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).

thf(5153,axiom,
    ! [V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
      ( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ c_Com_Ocom_OSKIP )
      = V_f1_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I64_J) ).

thf(5167,axiom,
    ! [V_com_H_2: $i,V_fun_H_2: $i] :
      ( ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).

thf(5168,axiom,
    ! [V_com_H_2: $i,V_fun_H_2: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).

thf(5171,axiom,
    ! [V_fun_H_2: $i,V_vname_H_2: $i] :
      ( ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).

thf(5172,axiom,
    ! [V_fun_H_2: $i,V_vname_H_2: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).

thf(5173,axiom,
    ! [V_com2_H: $i,V_com1_H: $i] :
      ( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).

thf(5174,axiom,
    ! [V_com2_H: $i,V_com1_H: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).

thf(5180,axiom,
    ! [V_Q_2: $i,V_P_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
     => ( ! [B_Z: $i,B_s: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
           => ! [B_s_H: $i] :
                ( ! [B_Z_H: $i] :
                    ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z_H ) @ B_s ) )
                   => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z_H ) @ B_s_H ) ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s_H ) ) ) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conseq12) ).

thf(5184,axiom,
    ! [V_R_2: $i,V_d_2: $i,V_Q_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
     => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_Q_2 @ V_d_2 @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ ( c_Com_Ocom_OSemi @ V_c_2 @ V_d_2 ) @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Comp) ).

thf(5185,axiom,
    ! [V_Q_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
     => ( ! [B_Z: $i,B_s: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z ) @ B_s ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s ) ) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conseq2) ).

thf(5186,axiom,
    ! [V_P_2: $i,V_Q_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
     => ( ! [B_Z: $i,B_s: $i] :
            ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
           => ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z ) @ B_s ) ) )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conseq1) ).

thf(5188,axiom,
    ! [V_x_2: $i,T_b: $i] :
      ( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
      = V_x_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).

thf(5189,axiom,
    ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).

thf(5190,axiom,
    ! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
    <=> ( ( ( V_a_2 = V_c_2 )
          & ( V_b_2 = V_d_2 ) )
        | ( ( V_a_2 = V_d_2 )
          & ( V_b_2 = V_c_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).

thf(5191,axiom,
    ! [V_b_2: $i,V_a_2: $i,T_b: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
     => ( V_a_2 = V_b_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).

thf(5192,axiom,
    ! [V_x_2: $i,T_c: $i,T_b: $i] :
      ( ( class_Orderings_Obot @ T_b )
     => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
        = ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).

thf(5203,axiom,
    ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).

thf(5204,axiom,
    ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

thf(5205,axiom,
    ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ 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(5219,axiom,
    ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
     != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).

thf(5224,axiom,
    ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).

thf(5225,axiom,
    ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
      = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Orecs) ).

thf(5226,axiom,
    ! [V_x_2: $i,T_c: $i,T_b: $i] :
      ( ( class_Orderings_Obot @ T_b )
     => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
        = ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).

thf(5231,axiom,
    ! [V_tsa_2: $i,V_t_2: $i,V_G_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
     => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ V_tsa_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).

thf(5232,axiom,
    ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
     => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
       => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut) ).

thf(5235,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_b: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_fun1_2 @ V_com_2 @ V_fun2_2 )
        = ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ 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(5236,axiom,
    ! [V_a2_2: $i,V_a1_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a1_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_a2_2 @ c_Com_Ocom_OSKIP @ V_a2_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

thf(5237,axiom,
    ! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

thf(5238,axiom,
    ! [V_P_2: $i,V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ c_Com_Ocom_OSKIP @ V_P_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).

thf(5239,axiom,
    ! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty) ).

thf(5240,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(5242,conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(5243,negated_conjecture,
    ( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5242]) ).

thf(5244,plain,
    ( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5243]) ).

thf(5245,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ 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(5246,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ 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(5247,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ 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(5248,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(5249,plain,
    ( ( ! [V_P: $i,T_a: $i] :
          ( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
          = V_P ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(5250,plain,
    ( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[65]) ).

thf(5251,plain,
    ( ( ! [T_1: $i] : ( class_HOL_Oequal @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[66]) ).

thf(5252,plain,
    ( ( class_Nat_Osize @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[93]) ).

thf(5253,plain,
    ( ( class_Enum_Oenum @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[94]) ).

thf(5254,plain,
    ( ( class_HOL_Oequal @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[95]) ).

thf(5255,plain,
    ( ( class_Groups_Ominus @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[96]) ).

thf(5256,plain,
    ( ( class_Groups_Ouminus @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[97]) ).

thf(5257,plain,
    ( ( class_Orderings_Obot @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[98]) ).

thf(5258,plain,
    ( ( class_Orderings_Oord @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[99]) ).

thf(5259,plain,
    ( ( class_Orderings_Otop @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[100]) ).

thf(5260,plain,
    ( ( class_Orderings_Oorder @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[101]) ).

thf(5261,plain,
    ( ( class_Lattices_Olattice @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[102]) ).

thf(5262,plain,
    ( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[103]) ).

thf(5263,plain,
    ( ( class_Orderings_Opreorder @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[104]) ).

thf(5264,plain,
    ( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[105]) ).

thf(5265,plain,
    ( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[106]) ).

thf(5266,plain,
    ( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[107]) ).

thf(5267,plain,
    ( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[108]) ).

thf(5268,plain,
    ( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[109]) ).

thf(5269,plain,
    ( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[110]) ).

thf(5270,plain,
    ( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[111]) ).

thf(5271,plain,
    ( ( ! [T_1: $i,T_2: $i] :
          ( ( ( class_Enum_Oenum @ T_2 )
            & ( class_Enum_Oenum @ T_1 ) )
         => ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[234]) ).

thf(5272,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Groups_Ominus @ T_1 )
         => ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[236]) ).

thf(5273,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Groups_Ouminus @ T_1 )
         => ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[237]) ).

thf(5274,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Obot @ T_1 )
         => ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[238]) ).

thf(5275,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Oord @ T_1 )
         => ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[239]) ).

thf(5276,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Otop @ T_1 )
         => ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[240]) ).

thf(5277,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Oorder @ T_1 )
         => ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[241]) ).

thf(5278,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Olattice @ T_1 )
         => ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[242]) ).

thf(5279,plain,
    ( ( ! [T_1: $i,T_2: $i] :
          ( ( ( class_Finite__Set_Ofinite @ T_2 )
            & ( class_Finite__Set_Ofinite @ T_1 ) )
         => ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[243]) ).

thf(5280,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Opreorder @ T_1 )
         => ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[244]) ).

thf(5281,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Oboolean__algebra @ T_1 )
         => ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[245]) ).

thf(5282,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Odistrib__lattice @ T_1 )
         => ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[246]) ).

thf(5283,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
         => ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[251]) ).

thf(5284,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Obounded__lattice @ T_1 )
         => ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[252]) ).

thf(5285,plain,
    ( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
    = $true ),
    inference(unfold_def,[status(thm)],[253]) ).

thf(5286,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
            = V_x_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[341]) ).

thf(5287,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
            = ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[360]) ).

thf(5288,plain,
    ( ( ! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = V_z_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[397]) ).

thf(5289,plain,
    ( ( ! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
          ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[439]) ).

thf(5290,plain,
    ( ( ! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[453]) ).

thf(5291,plain,
    ( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
          = V_r_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[476]) ).

thf(5292,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)],[599]) ).

thf(5293,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)],[600]) ).

thf(5294,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)],[618]) ).

thf(5295,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)],[930]) ).

thf(5296,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
            = V_ys_2 )
        <=> ( V_xs_2
            = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[931]) ).

thf(5297,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
            = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
        <=> ( V_xs_2 = V_ys_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[932]) ).

thf(5298,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)],[1186]) ).

thf(5299,plain,
    ( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
        <=> ? [B_us: $i] :
              ( ( ( V_xs_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
                & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
                  = V_tsa_2 ) )
              | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
                  = V_zs_2 )
                & ( V_ys_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1187]) ).

thf(5300,plain,
    ( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1188]) ).

thf(5301,plain,
    ( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1189]) ).

thf(5302,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)],[1190]) ).

thf(5303,plain,
    ( ( ! [T_b: $i] :
          ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1404]) ).

thf(5304,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)],[1459]) ).

thf(5305,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)],[1460]) ).

thf(5306,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)],[1618]) ).

thf(5307,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)],[1619]) ).

thf(5308,plain,
    ( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ 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)],[1620]) ).

thf(5309,plain,
    ( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
          = V_a_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1710]) ).

thf(5310,plain,
    ( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
          ( ( V_g_2
            = ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
         => ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = V_a_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1711]) ).

thf(5311,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)],[1757]) ).

thf(5312,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
          = V_x ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1758]) ).

thf(5313,plain,
    ( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
          = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1913]) ).

thf(5314,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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)],[2081]) ).

thf(5315,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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)],[2082]) ).

thf(5316,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)],[2705]) ).

thf(5317,plain,
    ( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
          ( ( V_p_2 = V_q_2 )
         => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2914]) ).

thf(5318,plain,
    ( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ 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)],[2916]) ).

thf(5319,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)],[2917]) ).

thf(5320,plain,
    ( ( ! [V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3968]) ).

thf(5321,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)],[3975]) ).

thf(5322,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)],[3977]) ).

thf(5323,plain,
    ( ( ! [V_n: $i] :
          ( ( hAPP @ c_Nat_OSuc @ V_n )
         != V_n ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3978]) ).

thf(5324,plain,
    ( ( ! [V_n: $i] :
          ( V_n
         != ( hAPP @ c_Nat_OSuc @ V_n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3979]) ).

thf(5325,plain,
    ( ( ! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = V_z_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4156]) ).

thf(5326,plain,
    ( ( ! [T_b: $i] :
          ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4183]) ).

thf(5327,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
          ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4249]) ).

thf(5328,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__one__idem @ T_b @ 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)],[4286]) ).

thf(5329,plain,
    ( ( ! [V_R_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4419]) ).

thf(5330,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
         => ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = V_x_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4426]) ).

thf(5331,plain,
    ( ( ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
            = ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
        <=> ( V_a_2 = V_a_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4427]) ).

thf(5332,plain,
    ( ( ! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
         => ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
            = V_z_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4435]) ).

thf(5333,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
            = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
        <=> ( V_A_2 = V_B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4517]) ).

thf(5334,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
          = V_A_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4518]) ).

thf(5335,plain,
    ( ( ! [V_r_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4561]) ).

thf(5336,plain,
    ( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
            = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4562]) ).

thf(5337,plain,
    ( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4563]) ).

thf(5338,plain,
    ( ( ! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4572]) ).

thf(5339,plain,
    ( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ 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)],[4575]) ).

thf(5340,plain,
    ( ( ! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4640]) ).

thf(5341,plain,
    ( ( ! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4702]) ).

thf(5342,plain,
    ( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4703]) ).

thf(5343,plain,
    ( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
          ( ( ( V_x_2 = V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ 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)],[4705]) ).

thf(5344,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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)],[4707]) ).

thf(5345,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4708]) ).

thf(5346,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
          = V_y_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4709]) ).

thf(5347,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
          ( ( ( V_z_2 = V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ 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)],[4710]) ).

thf(5348,plain,
    ( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
          ( ( V_a_2 != V_c_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4711]) ).

thf(5349,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
          ( ( V_z_2 != V_x_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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)],[4712]) ).

thf(5350,plain,
    ( ( ! [T_b: $i,T_c: $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_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4713]) ).

thf(5351,plain,
    ( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
          = V_f_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4736]) ).

thf(5352,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4770]) ).

thf(5353,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4771]) ).

thf(5354,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4772]) ).

thf(5355,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4796]) ).

thf(5356,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4801]) ).

thf(5357,plain,
    ( ( ! [V_B_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4802]) ).

thf(5358,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4803]) ).

thf(5359,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_A_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4804]) ).

thf(5360,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4805]) ).

thf(5361,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4846]) ).

thf(5362,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4848]) ).

thf(5363,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4850]) ).

thf(5364,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4851]) ).

thf(5365,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4852]) ).

thf(5366,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = V_A_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4853]) ).

thf(5367,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4928]) ).

thf(5368,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4963]) ).

thf(5369,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4964]) ).

thf(5370,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        <=> ( ( V_A_2
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
            & ( V_B_2
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4965]) ).

thf(5371,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_A_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4966]) ).

thf(5372,plain,
    ( ( ! [V_B_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
          = V_B_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4967]) ).

thf(5373,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4972]) ).

thf(5374,plain,
    ( ( ! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4973]) ).

thf(5375,plain,
    ( ( ! [V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4974]) ).

thf(5376,plain,
    ( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
            = ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4975]) ).

thf(5377,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4998]) ).

thf(5378,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5001]) ).

thf(5379,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5003]) ).

thf(5380,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5004]) ).

thf(5381,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = V_A_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5006]) ).

thf(5382,plain,
    ( ( ! [T_b: $i] :
          ( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5034]) ).

thf(5383,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5038]) ).

thf(5384,plain,
    ( ( ! [V_P_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
          = V_P_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5039]) ).

thf(5385,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Fun_Ooverride__on @ T_b @ T_c @ V_f_2 @ V_g_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_f_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5055]) ).

thf(5386,plain,
    ( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $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_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
            = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5056]) ).

thf(5387,plain,
    ( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5065]) ).

thf(5388,plain,
    ( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = V_c_2 )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5066]) ).

thf(5389,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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)],[5067]) ).

thf(5390,plain,
    ( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
          = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5068]) ).

thf(5391,plain,
    ( ( ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5073]) ).

thf(5392,plain,
    ( ( ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
          ( ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5074]) ).

thf(5393,plain,
    ( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5086]) ).

thf(5394,plain,
    ( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5108]) ).

thf(5395,plain,
    ( ( ! [V_t: $i,V_n: $i,V_s: $i] :
          ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
         => ( V_t = V_s ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5109]) ).

thf(5396,plain,
    ( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
         => ! [B_v: $i] :
              ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
              = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5121]) ).

thf(5397,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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)],[5124]) ).

thf(5398,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
          ( ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5132]) ).

thf(5399,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5133]) ).

thf(5400,plain,
    ( ( ! [V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
          ( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ c_Com_Ocom_OSKIP )
          = V_f1_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5153]) ).

thf(5401,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i] :
          ( ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5167]) ).

thf(5402,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5168]) ).

thf(5403,plain,
    ( ( ! [V_fun_H_2: $i,V_vname_H_2: $i] :
          ( ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5171]) ).

thf(5404,plain,
    ( ( ! [V_fun_H_2: $i,V_vname_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5172]) ).

thf(5405,plain,
    ( ( ! [V_com2_H: $i,V_com1_H: $i] :
          ( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5173]) ).

thf(5406,plain,
    ( ( ! [V_com2_H: $i,V_com1_H: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5174]) ).

thf(5407,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
               => ! [B_s_H: $i] :
                    ( ! [B_Z_H: $i] :
                        ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z_H ) @ B_s ) )
                       => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z_H ) @ B_s_H ) ) )
                   => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s_H ) ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5180]) ).

thf(5408,plain,
    ( ( ! [V_R_2: $i,V_d_2: $i,V_Q_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_Q_2 @ V_d_2 @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ ( c_Com_Ocom_OSemi @ V_c_2 @ V_d_2 ) @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5184]) ).

thf(5409,plain,
    ( ( ! [V_Q_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z ) @ B_s ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5185]) ).

thf(5410,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z ) @ B_s ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5186]) ).

thf(5411,plain,
    ( ( ! [V_x_2: $i,T_b: $i] :
          ( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
          = V_x_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5188]) ).

thf(5412,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5189]) ).

thf(5413,plain,
    ( ( ! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
        <=> ( ( ( V_a_2 = V_c_2 )
              & ( V_b_2 = V_d_2 ) )
            | ( ( V_a_2 = V_d_2 )
              & ( V_b_2 = V_c_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5190]) ).

thf(5414,plain,
    ( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
         => ( V_a_2 = V_b_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5191]) ).

thf(5415,plain,
    ( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
          ( ( class_Orderings_Obot @ T_b )
         => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
            = ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5192]) ).

thf(5416,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5203]) ).

thf(5417,plain,
    ( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5204]) ).

thf(5418,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ 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)],[5205]) ).

thf(5419,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5219]) ).

thf(5420,plain,
    ( ( ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
          ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5224]) ).

thf(5421,plain,
    ( ( ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
          ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5225]) ).

thf(5422,plain,
    ( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
          ( ( class_Orderings_Obot @ T_b )
         => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
            = ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5226]) ).

thf(5423,plain,
    ( ( ! [V_tsa_2: $i,V_t_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ V_tsa_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5231]) ).

thf(5424,plain,
    ( ( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5232]) ).

thf(5425,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_b: $i] :
          ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_fun1_2 @ V_com_2 @ V_fun2_2 )
            = ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ 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)],[5235]) ).

thf(5426,plain,
    ( ( ! [V_a2_2: $i,V_a1_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a1_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_a2_2 @ c_Com_Ocom_OSKIP @ V_a2_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5236]) ).

thf(5427,plain,
    ( ( ! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5237]) ).

thf(5428,plain,
    ( ( ! [V_P_2: $i,V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ c_Com_Ocom_OSKIP @ V_P_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5238]) ).

thf(5429,plain,
    ( ( ! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5239]) ).

thf(5430,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)],[5240]) ).

thf(5431,plain,
    ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5244]) ).

thf(5432,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)],[5430]) ).

thf(5433,plain,
    ( ( ! [V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5429]) ).

thf(5434,plain,
    ( ( ! [V_P_2: $i,V_G_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ c_Com_Ocom_OSKIP @ V_P_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5428]) ).

thf(5435,plain,
    ( ( ! [V_a_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5427]) ).

thf(5436,plain,
    ( ( ! [V_a2_2: $i,V_a1_2: $i,T_b: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_a1_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_a2_2 @ c_Com_Ocom_OSKIP @ V_a2_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5426]) ).

thf(5437,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_b: $i] :
          ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_fun1_2 @ V_com_2 @ V_fun2_2 )
            = ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ 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)],[5425]) ).

thf(5438,plain,
    ( ( ! [V_G_2: $i,V_tsa_2: $i,V_G_Ha_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_Ha_2 @ V_tsa_2 )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_G_Ha_2 )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5424]) ).

thf(5439,plain,
    ( ( ! [V_tsa_2: $i,V_t_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ V_tsa_2 )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ V_t_2 ) @ V_tsa_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5423]) ).

thf(5440,plain,
    ( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
          ( ( class_Orderings_Obot @ T_b )
         => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
            = ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5422]) ).

thf(5441,plain,
    ( ( ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
          ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5421]) ).

thf(5442,plain,
    ( ( ! [V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,V_f1_2: $i,T_b: $i,T_c: $i] :
          ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ T_c @ T_b @ V_f1_2 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_c @ V_fun1_2 @ V_com_2 @ V_fun2_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ V_f1_2 @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5420]) ).

thf(5443,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5419]) ).

thf(5444,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
          ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ 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)],[5418]) ).

thf(5445,plain,
    ( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5417]) ).

thf(5446,plain,
    ( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5416]) ).

thf(5447,plain,
    ( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
          ( ( class_Orderings_Obot @ T_b )
         => ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
            = ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5415]) ).

thf(5448,plain,
    ( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
         => ( V_a_2 = V_b_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5414]) ).

thf(5449,plain,
    ( ( ! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
        <=> ( ( ( V_a_2 = V_c_2 )
              & ( V_b_2 = V_d_2 ) )
            | ( ( V_a_2 = V_d_2 )
              & ( V_b_2 = V_c_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5413]) ).

thf(5450,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5412]) ).

thf(5451,plain,
    ( ( ! [V_x_2: $i,T_b: $i] :
          ( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
          = V_x_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5411]) ).

thf(5452,plain,
    ( ( ! [V_P_2: $i,V_Q_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z ) @ B_s ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5410]) ).

thf(5453,plain,
    ( ( ! [V_Q_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z ) @ B_s ) )
               => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5409]) ).

thf(5454,plain,
    ( ( ! [V_R_2: $i,V_d_2: $i,V_Q_2: $i,V_c_2: $i,V_P_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_Q_2 @ V_d_2 @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ ( c_Com_Ocom_OSemi @ V_c_2 @ V_d_2 ) @ V_R_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5408]) ).

thf(5455,plain,
    ( ( ! [V_Q_2: $i,V_P_2: $i,V_Q_H_2: $i,V_c_2: $i,V_P_H_2: $i,V_G_2: $i,T_b: $i] :
          ( ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_H_2 @ V_c_2 @ V_Q_H_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) )
         => ( ! [B_Z: $i,B_s: $i] :
                ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ B_Z ) @ B_s ) )
               => ! [B_s_H: $i] :
                    ( ! [B_Z_H: $i] :
                        ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H_2 @ B_Z_H ) @ B_s ) )
                       => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H_2 @ B_Z_H ) @ B_s_H ) ) )
                   => ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ B_Z ) @ B_s_H ) ) ) )
           => ( c_Hoare__Mirabelle_Ohoare__derivs @ T_b @ V_G_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b @ V_P_2 @ V_c_2 @ V_Q_2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) @ tc_HOL_Obool ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5407]) ).

thf(5456,plain,
    ( ( ! [V_com2_H: $i,V_com1_H: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[5406]) ).

thf(5457,plain,
    ( ( ! [V_com2_H: $i,V_com1_H: $i] :
          ( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(copy,[status(thm)],[5405]) ).

thf(5458,plain,
    ( ( ! [V_fun_H_2: $i,V_vname_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5404]) ).

thf(5459,plain,
    ( ( ! [V_fun_H_2: $i,V_vname_H_2: $i] :
          ( ( c_Com_Ocom_OAss @ V_vname_H_2 @ V_fun_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(copy,[status(thm)],[5403]) ).

thf(5460,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5402]) ).

thf(5461,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i] :
          ( ( c_Com_Ocom_OWhile @ V_fun_H_2 @ V_com_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(copy,[status(thm)],[5401]) ).

thf(5462,plain,
    ( ( ! [V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
          ( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ c_Com_Ocom_OSKIP )
          = V_f1_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5400]) ).

thf(5463,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5399]) ).

thf(5464,plain,
    ( ( ! [V_com_H_2: $i,V_fun_H_2: $i,V_loc_H_2: $i] :
          ( ( c_Com_Ocom_OLocal @ V_loc_H_2 @ V_fun_H_2 @ V_com_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(copy,[status(thm)],[5398]) ).

thf(5465,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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)],[5397]) ).

thf(5466,plain,
    ( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
         => ! [B_v: $i] :
              ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
              = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5396]) ).

thf(5467,plain,
    ( ( ! [V_t: $i,V_n: $i,V_s: $i] :
          ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
         => ( V_t = V_s ) ) )
    = $true ),
    inference(copy,[status(thm)],[5395]) ).

thf(5468,plain,
    ( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
    = $true ),
    inference(copy,[status(thm)],[5394]) ).

thf(5469,plain,
    ( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
    = $true ),
    inference(copy,[status(thm)],[5393]) ).

thf(5470,plain,
    ( ( ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
          ( ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(copy,[status(thm)],[5392]) ).

thf(5471,plain,
    ( ( ! [V_com2_H_2: $i,V_com1_H_2: $i,V_fun_H_2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OCond @ V_fun_H_2 @ V_com1_H_2 @ V_com2_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5391]) ).

thf(5472,plain,
    ( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
          = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5390]) ).

thf(5473,plain,
    ( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ 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)],[5389]) ).

thf(5474,plain,
    ( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = V_c_2 )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5388]) ).

thf(5475,plain,
    ( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
          ( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
         => ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
            = ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5387]) ).

thf(5476,plain,
    ( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $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_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
            = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5386]) ).

thf(5477,plain,
    ( ( ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Fun_Ooverride__on @ T_b @ T_c @ V_f_2 @ V_g_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_f_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5385]) ).

thf(5478,plain,
    ( ( ! [V_P_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
          = V_P_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5384]) ).

thf(5479,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5383]) ).

thf(5480,plain,
    ( ( ! [T_b: $i] :
          ( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5382]) ).

thf(5481,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = V_A_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5381]) ).

thf(5482,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5380]) ).

thf(5483,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5379]) ).

thf(5484,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5378]) ).

thf(5485,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5377]) ).

thf(5486,plain,
    ( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
            = ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5376]) ).

thf(5487,plain,
    ( ( ! [V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5375]) ).

thf(5488,plain,
    ( ( ! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5374]) ).

thf(5489,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5373]) ).

thf(5490,plain,
    ( ( ! [V_B_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
          = V_B_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5372]) ).

thf(5491,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_A_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5371]) ).

thf(5492,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
        <=> ( ( V_A_2
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
            & ( V_B_2
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5370]) ).

thf(5493,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5369]) ).

thf(5494,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5368]) ).

thf(5495,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5367]) ).

thf(5496,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = V_A_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5366]) ).

thf(5497,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5365]) ).

thf(5498,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5364]) ).

thf(5499,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5363]) ).

thf(5500,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5362]) ).

thf(5501,plain,
    ( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
          = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5361]) ).

thf(5502,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5360]) ).

thf(5503,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = V_A_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5359]) ).

thf(5504,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5358]) ).

thf(5505,plain,
    ( ( ! [V_B_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5357]) ).

thf(5506,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5356]) ).

thf(5507,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5355]) ).

thf(5508,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5354]) ).

thf(5509,plain,
    ( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5353]) ).

thf(5510,plain,
    ( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5352]) ).

thf(5511,plain,
    ( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
          = V_f_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5351]) ).

thf(5512,plain,
    ( ( ! [T_b: $i,T_c: $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_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
            = V_f_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5350]) ).

thf(5513,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
          ( ( V_z_2 != V_x_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
            = ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5349]) ).

thf(5514,plain,
    ( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
          ( ( V_a_2 != V_c_2 )
         => ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5348]) ).

thf(5515,plain,
    ( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
          ( ( ( V_z_2 = V_x_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
              = ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5347]) ).

thf(5516,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
          = V_y_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5346]) ).

thf(5517,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5345]) ).

thf(5518,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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)],[5344]) ).

thf(5519,plain,
    ( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
          ( ( ( V_x_2 = V_a_2 )
           => ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ 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_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
              = ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5343]) ).

thf(5520,plain,
    ( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5342]) ).

thf(5521,plain,
    ( ( ! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5341]) ).

thf(5522,plain,
    ( ( ! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5340]) ).

thf(5523,plain,
    ( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ 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)],[5339]) ).

thf(5524,plain,
    ( ( ! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[5338]) ).

thf(5525,plain,
    ( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5337]) ).

thf(5526,plain,
    ( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
            = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
        <=> ( V_A_2
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5336]) ).

thf(5527,plain,
    ( ( ! [V_r_2: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5335]) ).

thf(5528,plain,
    ( ( ! [V_A_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
          = V_A_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5334]) ).

thf(5529,plain,
    ( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
            = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
        <=> ( V_A_2 = V_B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5333]) ).

thf(5530,plain,
    ( ( ! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
         => ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
            = V_z_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5332]) ).

thf(5531,plain,
    ( ( ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
            = ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
        <=> ( V_a_2 = V_a_H_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5331]) ).

thf(5532,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
         => ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = V_x_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5330]) ).

thf(5533,plain,
    ( ( ! [V_R_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5329]) ).

thf(5534,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__one__idem @ T_b @ 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)],[5328]) ).

thf(5535,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
          ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5327]) ).

thf(5536,plain,
    ( ( ! [T_b: $i] :
          ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5326]) ).

thf(5537,plain,
    ( ( ! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = V_z_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5325]) ).

thf(5538,plain,
    ( ( ! [V_n: $i] :
          ( V_n
         != ( hAPP @ c_Nat_OSuc @ V_n ) ) )
    = $true ),
    inference(copy,[status(thm)],[5324]) ).

thf(5539,plain,
    ( ( ! [V_n: $i] :
          ( ( hAPP @ c_Nat_OSuc @ V_n )
         != V_n ) )
    = $true ),
    inference(copy,[status(thm)],[5323]) ).

thf(5540,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)],[5322]) ).

thf(5541,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)],[5321]) ).

thf(5542,plain,
    ( ( ! [V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5320]) ).

thf(5543,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)],[5319]) ).

thf(5544,plain,
    ( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ 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)],[5318]) ).

thf(5545,plain,
    ( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
          ( ( V_p_2 = V_q_2 )
         => ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
            = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5317]) ).

thf(5546,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)],[5316]) ).

thf(5547,plain,
    ( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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)],[5315]) ).

thf(5548,plain,
    ( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Typedef_Otype__definition @ T_b @ T_c @ 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)],[5314]) ).

thf(5549,plain,
    ( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
          = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5313]) ).

thf(5550,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
          = V_x ) )
    = $true ),
    inference(copy,[status(thm)],[5312]) ).

thf(5551,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)],[5311]) ).

thf(5552,plain,
    ( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
          ( ( V_g_2
            = ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
         => ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
            = V_a_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5310]) ).

thf(5553,plain,
    ( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i] :
          ( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
          = V_a_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5309]) ).

thf(5554,plain,
    ( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ 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)],[5308]) ).

thf(5555,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)],[5307]) ).

thf(5556,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)],[5306]) ).

thf(5557,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)],[5305]) ).

thf(5558,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)],[5304]) ).

thf(5559,plain,
    ( ( ! [T_b: $i] :
          ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5303]) ).

thf(5560,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)],[5302]) ).

thf(5561,plain,
    ( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5301]) ).

thf(5562,plain,
    ( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
        <=> ( V_ys_2 = V_zs_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5300]) ).

thf(5563,plain,
    ( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
        <=> ? [B_us: $i] :
              ( ( ( V_xs_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
                & ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
                  = V_tsa_2 ) )
              | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
                  = V_zs_2 )
                & ( V_ys_2
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5299]) ).

thf(5564,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)],[5298]) ).

thf(5565,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
            = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
        <=> ( V_xs_2 = V_ys_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5297]) ).

thf(5566,plain,
    ( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
          ( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
            = V_ys_2 )
        <=> ( V_xs_2
            = ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5296]) ).

thf(5567,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)],[5295]) ).

thf(5568,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)],[5294]) ).

thf(5569,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)],[5293]) ).

thf(5570,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)],[5292]) ).

thf(5571,plain,
    ( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
          = V_r_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5291]) ).

thf(5572,plain,
    ( ( ! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5290]) ).

thf(5573,plain,
    ( ( ! [V_x_2: $i,V_n_2: $i,T_b: $i,V_f_2: $i] :
          ( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5289]) ).

thf(5574,plain,
    ( ( ! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
          = V_z_2 ) )
    = $true ),
    inference(copy,[status(thm)],[5288]) ).

thf(5575,plain,
    ( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
         => ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
            = ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5287]) ).

thf(5576,plain,
    ( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
          ( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_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(5577,plain,
    ( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5285]) ).

thf(5578,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Obounded__lattice @ T_1 )
         => ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5284]) ).

thf(5579,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
         => ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5283]) ).

thf(5580,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Odistrib__lattice @ T_1 )
         => ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5282]) ).

thf(5581,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Oboolean__algebra @ T_1 )
         => ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5281]) ).

thf(5582,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Opreorder @ T_1 )
         => ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5280]) ).

thf(5583,plain,
    ( ( ! [T_1: $i,T_2: $i] :
          ( ( ( class_Finite__Set_Ofinite @ T_2 )
            & ( class_Finite__Set_Ofinite @ T_1 ) )
         => ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5279]) ).

thf(5584,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Lattices_Olattice @ T_1 )
         => ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5278]) ).

thf(5585,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Oorder @ T_1 )
         => ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5277]) ).

thf(5586,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Otop @ T_1 )
         => ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5276]) ).

thf(5587,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Oord @ T_1 )
         => ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5275]) ).

thf(5588,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Orderings_Obot @ T_1 )
         => ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5274]) ).

thf(5589,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Groups_Ouminus @ T_1 )
         => ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5273]) ).

thf(5590,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Groups_Ominus @ T_1 )
         => ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5272]) ).

thf(5591,plain,
    ( ( ! [T_1: $i,T_2: $i] :
          ( ( ( class_Enum_Oenum @ T_2 )
            & ( class_Enum_Oenum @ T_1 ) )
         => ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5271]) ).

thf(5592,plain,
    ( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5270]) ).

thf(5593,plain,
    ( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5269]) ).

thf(5594,plain,
    ( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5268]) ).

thf(5595,plain,
    ( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5267]) ).

thf(5596,plain,
    ( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5266]) ).

thf(5597,plain,
    ( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5265]) ).

thf(5598,plain,
    ( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5264]) ).

thf(5599,plain,
    ( ( class_Orderings_Opreorder @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5263]) ).

thf(5600,plain,
    ( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5262]) ).

thf(5601,plain,
    ( ( class_Lattices_Olattice @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5261]) ).

thf(5602,plain,
    ( ( class_Orderings_Oorder @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5260]) ).

thf(5603,plain,
    ( ( class_Orderings_Otop @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5259]) ).

thf(5604,plain,
    ( ( class_Orderings_Oord @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5258]) ).

thf(5605,plain,
    ( ( class_Orderings_Obot @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5257]) ).

thf(5606,plain,
    ( ( class_Groups_Ouminus @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5256]) ).

thf(5607,plain,
    ( ( class_Groups_Ominus @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5255]) ).

thf(5608,plain,
    ( ( class_HOL_Oequal @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5254]) ).

thf(5609,plain,
    ( ( class_Enum_Oenum @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5253]) ).

thf(5610,plain,
    ( ( class_Nat_Osize @ tc_HOL_Obool )
    = $true ),
    inference(copy,[status(thm)],[5252]) ).

thf(5611,plain,
    ( ( ! [T_1: $i] : ( class_HOL_Oequal @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5251]) ).

thf(5612,plain,
    ( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5250]) ).

thf(5613,plain,
    ( ( ! [V_P: $i,T_a: $i] :
          ( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
          = V_P ) )
    = $true ),
    inference(copy,[status(thm)],[5249]) ).

thf(5614,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)],[5248]) ).

thf(5615,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ 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)],[5247]) ).

thf(5616,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ 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)],[5246]) ).

thf(5617,plain,
    ( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
          ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ 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)],[5245]) ).

thf(5618,plain,
    ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5431]) ).

thf(5619,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)],[5570]) ).

thf(5620,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)],[5544]) ).

thf(5621,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)],[5476]) ).

thf(5622,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)],[5558]) ).

thf(5623,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)],[5562]) ).

thf(5624,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
                 != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) )
                | ( SX1 = SX0 ) )
            | ~ ( ( SX1 != SX0 )
                | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
                  = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5529]) ).

thf(5625,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
                | ( SX1
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SX1
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5525]) ).

thf(5626,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX6 @ SX5 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX4 @ SX3 @ SX2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) @ tc_HOL_Obool ) ) ) )
          | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX6 @ SX5 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX2 @ SX1 @ SX0 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) @ tc_HOL_Obool ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX6 @ SX5 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX4 @ ( c_Com_Ocom_OSemi @ SX3 @ SX1 ) @ SX0 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5454]) ).

thf(5627,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX3 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) )
                 != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) ) )
                | ~ ( ( SX3 != SX1 )
                    | ( SX2 != SX0 ) )
                | ~ ( ( SX3 != SX0 )
                    | ( SX2 != SX1 ) ) )
            | ~ ( ~ ( ~ ( ( SX3 != SX1 )
                        | ( SX2 != SX0 ) )
                    | ~ ( ( SX3 != SX0 )
                        | ( SX2 != SX1 ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX3 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) )
                  = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5449]) ).

thf(5628,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)],[5474]) ).

thf(5629,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Lattices_Obounded__lattice @ SX1 )
          | ( class_Lattices_Obounded__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5578]) ).

thf(5630,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)],[5548]) ).

thf(5631,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                 != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 ) )
                | ( SX1
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SX1
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                  = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5526]) ).

thf(5632,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OAss @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5458]) ).

thf(5633,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OSemi @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5456]) ).

thf(5634,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SX1 )
          | ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5579]) ).

thf(5635,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5450]) ).

thf(5636,plain,
    ( ( ! [SX0: $i] :
          ( SX0
         != ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5538]) ).

thf(5637,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)],[5566]) ).

thf(5638,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SX2 @ SX1 @ SX0 )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5467]) ).

thf(5639,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Lattices_Oboolean__algebra @ SX1 )
          | ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5581]) ).

thf(5640,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)],[5561]) ).

thf(5641,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)],[5546]) ).

thf(5642,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)],[5540]) ).

thf(5643,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( c_Finite__Set_Ofun__left__comm @ SX5 @ SX4 @ SX3 )
          | ( ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
            = ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5575]) ).

thf(5644,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SX3 @ SX2 @ SX1 ) @ SX0 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                | ( SX0
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SX0
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) )
                | ( ( hAPP @ ( c_Set_Oimage @ SX3 @ SX2 @ SX1 ) @ SX0 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5488]) ).

thf(5645,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)],[5569]) ).

thf(5646,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)],[5534]) ).

thf(5647,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) )
                 != ( hAPP @ ( c_Set_Oimage @ SX2 @ SX3 @ SX1 ) @ SX0 ) )
                | ( SX0
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SX0
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) )
                  = ( hAPP @ ( c_Set_Oimage @ SX2 @ SX3 @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5486]) ).

thf(5648,plain,
    ( ( ! [SX0: $i] :
          ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SX0 @ tc_HOL_Obool ) )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5536]) ).

thf(5649,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)],[5475]) ).

thf(5650,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ SX1 )
          | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX0 @ SX2 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5438]) ).

thf(5651,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( c_Com_Ocom_OWhile @ SX1 @ SX0 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5461]) ).

thf(5652,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( class_Orderings_Obot @ SX2 )
          | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ SX2 ) ) @ SX0 )
            = ( c_Orderings_Obot__class_Obot @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5440]) ).

thf(5653,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Orderings_Opreorder @ SX1 )
          | ( class_Orderings_Opreorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5582]) ).

thf(5654,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
         != SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5555]) ).

thf(5655,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ( hAPP @ SX1 @ SX2 )
                = ( hAPP @ SX0 @ SX2 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5432]) ).

thf(5656,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
           != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5448]) ).

thf(5657,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Orderings_Obot @ SX1 )
          | ( class_Orderings_Obot @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5588]) ).

thf(5658,plain,
    ( ( ! [SX0: $i] :
          ( ( hAPP @ c_Nat_OSuc @ SX0 )
         != SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5539]) ).

thf(5659,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Orderings_Oord @ SX1 )
          | ( class_Orderings_Oord @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5587]) ).

thf(5660,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( c_Finite__Set_Ofolding__one @ SX3 @ SX2 @ SX1 )
          | ( ( hAPP @ SX1 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5532]) ).

thf(5661,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5443]) ).

thf(5662,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OWhile @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5460]) ).

thf(5663,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)],[5512]) ).

thf(5664,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)],[5568]) ).

thf(5665,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( SX2
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5556]) ).

thf(5666,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( c_Com_Ocom_OAss @ SX1 @ SX0 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5459]) ).

thf(5667,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SX1 )
                | ~ ( class_Finite__Set_Ofinite @ SX0 ) )
          | ( class_Finite__Set_Ofinite @ ( tc_fun @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5583]) ).

thf(5668,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( hAPP @ ( c_Set_OPow @ SX1 ) @ SX0 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX1 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5479]) ).

thf(5669,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
          | ( ( hAPP @ ( hAPP @ SX4 @ SX0 ) @ SX0 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5576]) ).

thf(5670,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( c_Finite__Set_Ofolding__image__simple @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
          | ( ( hAPP @ SX0 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) )
            = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5530]) ).

thf(5671,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)],[5514]) ).

thf(5672,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( c_Com_Ocom_OSemi @ SX1 @ SX0 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5457]) ).

thf(5673,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)],[5519]) ).

thf(5674,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)],[5563]) ).

thf(5675,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Orderings_Oorder @ SX1 )
          | ( class_Orderings_Oorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5585]) ).

thf(5676,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)],[5543]) ).

thf(5677,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( class_Enum_Oenum @ SX1 )
                | ~ ( class_Enum_Oenum @ SX0 ) )
          | ( class_Enum_Oenum @ ( tc_fun @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5591]) ).

thf(5678,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)],[5513]) ).

thf(5679,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                | ~ ( ( SX1
                     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                    | ( SX0
                     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
            | ~ ( ~ ~ ( ( SX1
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
                      | ( SX0
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5492]) ).

thf(5680,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OCond @ SX2 @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5471]) ).

thf(5681,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX5 @ SX4 @ SX3 )
                 != ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX2 @ SX1 @ SX0 ) )
                | ~ ( ~ ~ ( ( SX5 != SX2 )
                          | ( SX4 != SX1 ) )
                    | ( SX3 != SX0 ) ) )
            | ~ ( ~ ~ ( ~ ~ ( ( SX5 != SX2 )
                            | ( SX4 != SX1 ) )
                      | ( SX3 != SX0 ) )
                | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX5 @ SX4 @ SX3 )
                  = ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX2 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5437]) ).

thf(5682,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Orderings_Otop @ SX1 )
          | ( class_Orderings_Otop @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5586]) ).

thf(5683,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX5 @ SX4 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX5 @ SX3 @ SX2 @ SX1 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) @ tc_HOL_Obool ) ) ) )
          | ~ ! [SX6: $i,SX7: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX6 ) @ SX7 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX6 ) @ SX7 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX5 @ SX4 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX5 @ SX0 @ SX2 @ SX1 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5452]) ).

thf(5684,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Lattices_Odistrib__lattice @ SX1 )
          | ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5580]) ).

thf(5685,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Groups_Ominus @ SX1 )
          | ( class_Groups_Ominus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5590]) ).

thf(5686,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Lattices_Olattice @ SX1 )
          | ( class_Lattices_Olattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5584]) ).

thf(5687,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)],[5531]) ).

thf(5688,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)],[5565]) ).

thf(5689,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX6 @ SX5 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX4 @ SX3 @ SX2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) @ tc_HOL_Obool ) ) ) )
          | ~ ! [SX7: $i,SX8: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX7 ) @ SX8 ) )
                | ! [SX9: $i] :
                    ( ~ ! [SX10: $i] :
                          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX10 ) @ SX8 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX10 ) @ SX9 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX7 ) @ SX9 ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX6 @ SX5 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 @ SX1 @ SX3 @ SX0 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX6 ) @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5455]) ).

thf(5690,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP @ c_Nat_OSuc @ SX1 )
           != ( hAPP @ c_Nat_OSuc @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5541]) ).

thf(5691,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)],[5466]) ).

thf(5692,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)],[5523]) ).

thf(5693,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX3 ) ) @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX3 ) @ tc_HOL_Obool ) ) ) )
          | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ SX0 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX3 @ SX2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX3 ) ) @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5439]) ).

thf(5694,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)],[5560]) ).

thf(5695,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)],[5554]) ).

thf(5696,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( class_Groups_Ouminus @ SX1 )
          | ( class_Groups_Ouminus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5589]) ).

thf(5697,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)],[5518]) ).

thf(5698,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( class_Orderings_Obot @ SX2 )
          | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ SX2 ) ) @ SX0 )
            = ( c_Orderings_Obot__class_Obot @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5447]) ).

thf(5699,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( c_Com_Ocom_OCond @ SX2 @ SX1 @ SX0 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5470]) ).

thf(5700,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( c_Com_Ocom_OLocal @ SX2 @ SX1 @ SX0 )
         != c_Com_Ocom_OSKIP ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5464]) ).

thf(5701,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SX5 @ SX4 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX5 @ SX3 @ SX2 @ SX1 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) @ tc_HOL_Obool ) ) ) )
          | ~ ! [SX6: $i,SX7: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX6 ) @ SX7 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX6 ) @ SX7 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SX5 @ SX4 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX5 @ SX3 @ SX2 @ SX0 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SX5 ) @ tc_HOL_Obool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5453]) ).

thf(5702,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( c_Com_Ocom_OSKIP
         != ( c_Com_Ocom_OLocal @ SX2 @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5463]) ).

thf(5703,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)],[5515]) ).

thf(5704,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( SX3
           != ( c_Finite__Set_Ofold1 @ SX2 @ SX1 ) )
          | ( ( hAPP @ SX3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5552]) ).

thf(5705,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)],[5444]) ).

thf(5706,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)],[5545]) ).

thf(5707,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)],[5547]) ).

thf(5708,plain,
    ! [SV1: $i] :
      ( ( ! [SY616: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY616 @ SV1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY616 ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5433]) ).

thf(5709,plain,
    ! [SV2: $i] :
      ( ( ! [SY617: $i,SY618: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY618 @ SY617 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY618 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY618 @ SV2 @ c_Com_Ocom_OSKIP @ SV2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY618 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5434]) ).

thf(5710,plain,
    ! [SV3: $i] :
      ( ( ! [SY619: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY619 @ SV3 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY619 ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5435]) ).

thf(5711,plain,
    ! [SV4: $i] :
      ( ( ! [SY620: $i,SY621: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY621 @ SY620 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY621 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY621 @ SV4 @ c_Com_Ocom_OSKIP @ SV4 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY621 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5436]) ).

thf(5712,plain,
    ! [SV5: $i] :
      ( ( ! [SY622: $i,SY623: $i,SY624: $i,SY625: $i,SY626: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SY626 @ SY625 @ SY624 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY626 @ SY623 @ SY622 @ SV5 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY624 @ SY623 ) @ SY622 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5441]) ).

thf(5713,plain,
    ! [SV6: $i] :
      ( ( ! [SY627: $i,SY628: $i,SY629: $i,SY630: $i,SY631: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY631 @ SY630 @ SY629 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY631 @ SY628 @ SY627 @ SV6 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY629 @ SY628 ) @ SY627 ) @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5442]) ).

thf(5714,plain,
    ! [SV7: $i] :
      ( ( ! [SY632: $i,SY633: $i,SY634: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY634 ) @ SY633 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY634 ) @ SY632 ) @ SV7 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY634 ) @ SY632 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY634 ) @ SY633 ) @ SV7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5445]) ).

thf(5715,plain,
    ! [SV8: $i] :
      ( ( ! [SY635: $i,SY636: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY636 ) @ SY635 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY636 ) @ SY635 ) @ SV8 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY636 ) @ SY635 ) @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5446]) ).

thf(5716,plain,
    ! [SV9: $i] :
      ( ( ! [SY637: $i] :
            ( ( c_Set_Othe__elem @ SY637 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY637 ) @ SV9 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY637 @ tc_HOL_Obool ) ) ) )
            = SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5451]) ).

thf(5717,plain,
    ! [SV10: $i] :
      ( ( ! [SY638: $i,SY639: $i,SY640: $i,SY641: $i,SY642: $i,SY643: $i,SY644: $i,SY645: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY645 @ SY644 @ SY643 @ SY642 @ SY641 @ SY640 @ SY639 @ SY638 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY644 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5462]) ).

thf(5718,plain,
    ! [SV11: $i] :
      ( ( ! [SY646: $i,SY647: $i,SY648: $i,SY649: $i,SY650: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY650 @ SY649 @ SY648 @ SY647 ) @ SY646 ) @ SV11 )
            = ( hAPP @ SY647 @ ( hAPP @ SY646 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5465]) ).

thf(5719,plain,
    ! [SV12: $i] :
      ( ( ! [SY651: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY651 @ SV12 @ SY651 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5468]) ).

thf(5720,plain,
    ! [SV13: $i] :
      ( ( ! [SY652: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY652 @ SV13 @ SY652 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5469]) ).

thf(5721,plain,
    ! [SV14: $i] :
      ( ( ! [SY653: $i,SY654: $i,SY655: $i,SY656: $i,SY657: $i,SY658: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY658 @ SY657 @ SY656 @ SY655 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY654 @ SY658 @ SY656 @ SY653 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SY654 @ SY657 @ SY656 @ ( hAPP @ ( c_Fun_Ocomp @ SY658 @ SY657 @ SY654 @ SY655 ) @ SY653 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5472]) ).

thf(5722,plain,
    ! [SV15: $i] :
      ( ( ! [SY659: $i,SY660: $i,SY661: $i,SY662: $i,SY663: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY663 @ SY662 @ SY661 @ SY660 ) @ SY659 ) @ SV15 )
            = ( hAPP @ SY660 @ ( hAPP @ SY659 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5473]) ).

thf(5723,plain,
    ! [SV16: $i] :
      ( ( ! [SY664: $i,SY665: $i,SY666: $i] :
            ( ( c_Fun_Ooverride__on @ SY666 @ SY665 @ SY664 @ SV16 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY666 @ tc_HOL_Obool ) ) )
            = SY664 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5477]) ).

thf(5724,plain,
    ! [SV17: $i] :
      ( ( ! [SY667: $i] :
            ( ( hAPP @ ( c_Set_OCollect @ SY667 ) @ SV17 )
            = SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5478]) ).

thf(5725,plain,
    ! [SV18: $i] :
      ( ( ( hAPP @ ( c_Set_OPow @ SV18 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV18 @ tc_HOL_Obool ) ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ SV18 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV18 @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV18 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5480]) ).

thf(5726,plain,
    ! [SV19: $i] :
      ( ( ! [SY668: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY668 @ tc_HOL_Obool ) ) @ SV19 ) @ SV19 )
            = SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5481]) ).

thf(5727,plain,
    ! [SV20: $i] :
      ( ( ! [SY669: $i,SY670: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY670 @ tc_HOL_Obool ) ) @ SY669 ) @ SV20 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY670 @ tc_HOL_Obool ) ) @ SV20 ) @ SY669 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5482]) ).

thf(5728,plain,
    ! [SV21: $i] :
      ( ( ! [SY671: $i,SY672: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY672 @ tc_HOL_Obool ) ) @ SY671 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY672 @ tc_HOL_Obool ) ) @ SY671 ) @ SV21 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY672 @ tc_HOL_Obool ) ) @ SY671 ) @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5483]) ).

thf(5729,plain,
    ! [SV22: $i] :
      ( ( ! [SY673: $i,SY674: $i,SY675: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY675 @ tc_HOL_Obool ) ) @ SY674 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY675 @ tc_HOL_Obool ) ) @ SY673 ) @ SV22 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY675 @ tc_HOL_Obool ) ) @ SY673 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY675 @ tc_HOL_Obool ) ) @ SY674 ) @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5484]) ).

thf(5730,plain,
    ! [SV23: $i] :
      ( ( ! [SY676: $i,SY677: $i,SY678: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY678 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY678 @ tc_HOL_Obool ) ) @ SY677 ) @ SY676 ) ) @ SV23 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY678 @ tc_HOL_Obool ) ) @ SY677 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY678 @ tc_HOL_Obool ) ) @ SY676 ) @ SV23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5485]) ).

thf(5731,plain,
    ! [SV24: $i] :
      ( ( ! [SY679: $i,SY680: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY680 @ SY679 @ SV24 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY680 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY679 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5487]) ).

thf(5732,plain,
    ! [SV25: $i] :
      ( ( ! [SY681: $i,SY682: $i,SY683: $i,SY684: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY684 @ SY683 @ SY682 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY684 ) @ SY681 ) @ SV25 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY683 ) @ ( hAPP @ SY682 @ SY681 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY684 @ SY683 @ SY682 ) @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5489]) ).

thf(5733,plain,
    ! [SV26: $i] :
      ( ( ! [SY685: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY685 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY685 @ tc_HOL_Obool ) ) ) @ SV26 )
            = SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5490]) ).

thf(5734,plain,
    ! [SV27: $i] :
      ( ( ! [SY686: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY686 @ tc_HOL_Obool ) ) @ SV27 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY686 @ tc_HOL_Obool ) ) )
            = SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5491]) ).

thf(5735,plain,
    ! [SV28: $i] :
      ( ( ! [SY687: $i,SY688: $i,SY689: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY689 @ tc_HOL_Obool ) ) @ SY688 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY689 ) @ SY687 ) @ SV28 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY689 ) @ SY687 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY689 @ tc_HOL_Obool ) ) @ SY688 ) @ SV28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5493]) ).

thf(5736,plain,
    ! [SV29: $i] :
      ( ( ! [SY690: $i,SY691: $i,SY692: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY692 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY692 ) @ SY691 ) @ SY690 ) ) @ SV29 )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY692 ) @ SY691 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY692 @ tc_HOL_Obool ) ) @ SY690 ) @ SV29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5494]) ).

thf(5737,plain,
    ! [SV30: $i] :
      ( ( ! [SY693: $i,SY694: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY694 ) @ SY693 ) @ SV30 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY694 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY694 ) @ SY693 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY694 @ tc_HOL_Obool ) ) ) ) @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5495]) ).

thf(5738,plain,
    ! [SV31: $i] :
      ( ( ! [SY695: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY695 @ tc_HOL_Obool ) ) @ SV31 ) @ SV31 )
            = SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5496]) ).

thf(5739,plain,
    ! [SV32: $i] :
      ( ( ! [SY696: $i,SY697: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY697 @ tc_HOL_Obool ) ) @ SY696 ) @ SV32 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY697 @ tc_HOL_Obool ) ) @ SV32 ) @ SY696 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5497]) ).

thf(5740,plain,
    ! [SV33: $i] :
      ( ( ! [SY698: $i,SY699: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY699 @ tc_HOL_Obool ) ) @ SY698 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY699 @ tc_HOL_Obool ) ) @ SY698 ) @ SV33 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY699 @ tc_HOL_Obool ) ) @ SY698 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5498]) ).

thf(5741,plain,
    ! [SV34: $i] :
      ( ( ! [SY700: $i,SY701: $i,SY702: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY702 @ tc_HOL_Obool ) ) @ SY701 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY702 @ tc_HOL_Obool ) ) @ SY700 ) @ SV34 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY702 @ tc_HOL_Obool ) ) @ SY700 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY702 @ tc_HOL_Obool ) ) @ SY701 ) @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5499]) ).

thf(5742,plain,
    ! [SV35: $i] :
      ( ( ! [SY703: $i,SY704: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY704 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY704 @ tc_HOL_Obool ) ) @ SY703 ) @ SV35 ) ) @ SV35 )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY704 @ tc_HOL_Obool ) ) @ SY703 ) @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5500]) ).

thf(5743,plain,
    ! [SV36: $i] :
      ( ( ! [SY705: $i,SY706: $i,SY707: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY707 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY707 @ tc_HOL_Obool ) ) @ SY706 ) @ SY705 ) ) @ SV36 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY707 @ tc_HOL_Obool ) ) @ SY706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY707 @ tc_HOL_Obool ) ) @ SY705 ) @ SV36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5501]) ).

thf(5744,plain,
    ! [SV37: $i] :
      ( ( ! [SY708: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY708 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY708 @ tc_HOL_Obool ) ) ) @ SV37 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY708 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5502]) ).

thf(5745,plain,
    ! [SV38: $i] :
      ( ( ! [SY709: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY709 @ tc_HOL_Obool ) ) @ SV38 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY709 @ tc_HOL_Obool ) ) )
            = SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5503]) ).

thf(5746,plain,
    ! [SV39: $i] :
      ( ( ! [SY710: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY710 @ tc_HOL_Obool ) ) @ SV39 ) @ SV39 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY710 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5504]) ).

thf(5747,plain,
    ! [SV40: $i] :
      ( ( ! [SY711: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY711 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY711 @ tc_HOL_Obool ) ) ) @ SV40 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY711 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5505]) ).

thf(5748,plain,
    ! [SV41: $i] :
      ( ( ! [SY712: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY712 @ tc_HOL_Obool ) ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY712 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY712 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5506]) ).

thf(5749,plain,
    ! [SV42: $i] :
      ( ( ! [SY713: $i,SY714: $i,SY715: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY715 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY715 ) @ SY714 ) @ SY713 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY715 ) @ SY714 ) @ SV42 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY715 ) @ SY714 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY715 @ tc_HOL_Obool ) ) @ SY713 ) @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5507]) ).

thf(5750,plain,
    ! [SV43: $i] :
      ( ( ! [SY716: $i,SY717: $i,SY718: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY718 @ tc_HOL_Obool ) ) @ SY717 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY718 ) @ SY716 ) @ SV43 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY718 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY718 @ tc_HOL_Obool ) ) @ SY717 ) @ SV43 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY718 ) @ SY716 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY718 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5508]) ).

thf(5751,plain,
    ! [SV44: $i] :
      ( ( ! [SY719: $i,SY720: $i,SY721: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY721 @ tc_HOL_Obool ) ) @ SY720 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY721 ) @ SY719 ) @ SV44 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY721 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY721 @ tc_HOL_Obool ) ) @ SY720 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY721 ) @ SY719 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY721 @ tc_HOL_Obool ) ) ) ) ) @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5509]) ).

thf(5752,plain,
    ! [SV45: $i] :
      ( ( ! [SY722: $i,SY723: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY723 ) @ SY722 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY723 @ tc_HOL_Obool ) ) @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY723 ) @ SY722 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY723 @ tc_HOL_Obool ) ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY723 ) @ SY722 ) @ SV45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5510]) ).

thf(5753,plain,
    ! [SV46: $i] :
      ( ( ! [SY724: $i,SY725: $i,SY726: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY726 @ SY725 ) @ SY724 ) @ SV46 ) @ ( hAPP @ SY724 @ SV46 ) )
            = SY724 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5511]) ).

thf(5754,plain,
    ! [SV47: $i] :
      ( ( ! [SY727: $i,SY728: $i,SY729: $i,SY730: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY730 @ SY729 ) @ SY728 ) @ SY727 ) @ SV47 ) @ SY727 )
            = SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5516]) ).

thf(5755,plain,
    ! [SV48: $i] :
      ( ( ! [SY731: $i,SY732: $i,SY733: $i,SY734: $i,SY735: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY735 @ SY734 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY735 @ SY734 ) @ SY733 ) @ SY732 ) @ SY731 ) ) @ SY732 ) @ SV48 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY735 @ SY734 ) @ SY733 ) @ SY732 ) @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5517]) ).

thf(5756,plain,
    ! [SV49: $i] :
      ( ( ! [SY736: $i,SY737: $i,SY738: $i] : ( c_Nitpick_Ofold__graph_H @ SY738 @ SY737 @ SY736 @ SV49 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY738 @ tc_HOL_Obool ) ) @ SV49 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5520]) ).

thf(5757,plain,
    ! [SV50: $i] :
      ( ( ! [SY739: $i,SY740: $i,SY741: $i] : ( c_Nitpick_Ofold__graph_H @ SY741 @ SY740 @ SY739 @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY741 @ tc_HOL_Obool ) ) @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5521]) ).

thf(5758,plain,
    ! [SV51: $i] :
      ( ( ! [SY742: $i,SY743: $i] : ( c_Fun_Oinj__on @ SY743 @ SY742 @ SV51 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY743 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5522]) ).

thf(5759,plain,
    ! [SV52: $i] :
      ( ( c_Finite__Set_Ofun__left__comm__idem @ SV52 @ ( tc_fun @ SV52 @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ SV52 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5524]) ).

thf(5760,plain,
    ! [SV53: $i] :
      ( ( ! [SY744: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY744 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY744 @ tc_HOL_Obool ) ) ) @ SV53 )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY744 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5527]) ).

thf(5761,plain,
    ! [SV54: $i] :
      ( ( ! [SY745: $i] :
            ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY745 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY745 @ tc_HOL_Obool ) ) @ SV54 ) )
            = SV54 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5528]) ).

thf(5762,plain,
    ! [SV55: $i] :
      ( ( ! [SY746: $i,SY747: $i] :
            ( ( hAPP @ ( c_Relation_OImage @ SY747 @ SY746 @ SV55 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY747 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY746 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5533]) ).

thf(5763,plain,
    ! [SV56: $i] :
      ( ( ! [SY748: $i,SY749: $i,SY750: $i] :
            ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY750 @ ( tc_fun @ SY749 @ tc_HOL_Obool ) ) ) @ SY748 ) @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5535]) ).

thf(5764,plain,
    ! [SV57: $i] :
      ( ( ! [SY751: $i,SY752: $i,SY753: $i,SY754: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY754 @ SY753 @ SY752 ) @ SY751 ) @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY753 @ tc_HOL_Obool ) ) )
            = SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5537]) ).

thf(5765,plain,
    ! [SV58: $i] :
      ( ( ! [SY755: $i,SY756: $i] :
            ( ( hAPP @ ( c_Set_Ovimage @ SY756 @ SY755 @ SV58 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY755 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY756 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5542]) ).

thf(5766,plain,
    ! [SV59: $i] :
      ( ( ! [SY757: $i,SY758: $i,SY759: $i,SY760: $i,SY761: $i,SY762: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY762 @ SY761 @ SY760 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY762 @ SY759 @ SY761 ) @ SY758 ) @ SY757 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY762 @ SY759 @ SY760 ) @ SY758 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY759 @ SY761 @ SY760 ) @ SY757 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5549]) ).

thf(5767,plain,
    ! [SV60: $i] :
      ( ( ! [SY763: $i] :
            ( ( hAPP @ ( c_Fun_Oid @ SY763 ) @ SV60 )
            = SV60 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5550]) ).

thf(5768,plain,
    ! [SV61: $i] :
      ( ( ! [SY764: $i] :
            ( ( hAPP @ ( c_Fun_Oid @ SY764 ) @ SV61 )
            = SV61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5551]) ).

thf(5769,plain,
    ! [SV62: $i] :
      ( ( ! [SY765: $i,SY766: $i] :
            ( ( hAPP @ ( c_Finite__Set_Ofold1 @ SY766 @ SY765 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY766 ) @ SV62 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY766 @ tc_HOL_Obool ) ) ) )
            = SV62 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5553]) ).

thf(5770,plain,
    ! [SV63: $i] :
      ( ( ! [SY767: $i,SY768: $i,SY769: $i,SY770: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY770 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY770 @ SY769 ) @ SY768 ) @ SY767 ) ) @ SY768 ) @ SV63 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY770 @ SY769 ) @ SY768 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5557]) ).

thf(5771,plain,
    ! [SV64: $i] :
      ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV64 @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV64 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV64 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5559]) ).

thf(5772,plain,
    ! [SV65: $i] :
      ( ( ! [SY771: $i,SY772: $i,SY773: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ SY771 ) ) @ SV65 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY771 ) @ SV65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5564]) ).

thf(5773,plain,
    ! [SV66: $i] :
      ( ( ! [SY774: $i] :
            ( ( hAPP @ ( c_List_Orev @ SY774 ) @ ( hAPP @ ( c_List_Orev @ SY774 ) @ SV66 ) )
            = SV66 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5567]) ).

thf(5774,plain,
    ! [SV67: $i] :
      ( ( ! [SY775: $i,SY776: $i] :
            ( ( hAPP @ ( c_Relation_Oconverse @ SY776 @ SY775 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY775 @ SY776 ) @ SV67 ) )
            = SV67 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5571]) ).

thf(5775,plain,
    ! [SV68: $i] :
      ( ( ! [SY777: $i] : ( c_Relation_Ototal__on @ SY777 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY777 @ tc_HOL_Obool ) ) @ SV68 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5572]) ).

thf(5776,plain,
    ! [SV69: $i] :
      ( ( ! [SY778: $i,SY779: $i,SY780: $i] :
            ( ( hAPP @ SY780 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY779 @ SY779 ) @ SY778 ) @ SY780 ) @ SV69 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY779 @ SY779 ) @ SY778 ) @ SY780 ) @ ( hAPP @ SY780 @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5573]) ).

thf(5777,plain,
    ! [SV70: $i] :
      ( ( ! [SY781: $i,SY782: $i,SY783: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY783 @ SY782 @ SY781 ) @ SV70 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY783 @ tc_HOL_Obool ) ) )
            = SV70 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5574]) ).

thf(5778,plain,
    ! [SV71: $i] :
      ( ( class_HOL_Oequal @ ( tc_Hoare__Mirabelle_Otriple @ SV71 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5611]) ).

thf(5779,plain,
    ! [SV72: $i] :
      ( ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ SV72 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5612]) ).

thf(5780,plain,
    ! [SV73: $i] :
      ( ( ! [SY784: $i] :
            ( ( hAPP @ ( c_COMBI @ SY784 ) @ SV73 )
            = SV73 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5613]) ).

thf(5781,plain,
    ! [SV74: $i] :
      ( ( ! [SY785: $i,SY786: $i,SY787: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY787 @ SY786 ) @ SY785 ) @ SV74 )
            = SY785 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5614]) ).

thf(5782,plain,
    ! [SV75: $i] :
      ( ( ! [SY788: $i,SY789: $i,SY790: $i,SY791: $i,SY792: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY792 @ SY791 @ SY790 ) @ SY789 ) @ SY788 ) @ SV75 )
            = ( hAPP @ SY789 @ ( hAPP @ SY788 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5615]) ).

thf(5783,plain,
    ! [SV76: $i] :
      ( ( ! [SY793: $i,SY794: $i,SY795: $i,SY796: $i,SY797: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY797 @ SY796 @ SY795 ) @ SY794 ) @ SY793 ) @ SV76 )
            = ( hAPP @ ( hAPP @ SY794 @ SV76 ) @ SY793 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5616]) ).

thf(5784,plain,
    ! [SV77: $i] :
      ( ( ! [SY798: $i,SY799: $i,SY800: $i,SY801: $i,SY802: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY802 @ SY801 @ SY800 ) @ SY799 ) @ SY798 ) @ SV77 )
            = ( hAPP @ ( hAPP @ SY799 @ SV77 ) @ ( hAPP @ SY798 @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5617]) ).

thf(5785,plain,
    ( ( c_Hoare__Mirabelle_Ohoare__derivs @ t_a @ v_Ga @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a @ v_P @ c_Com_Ocom_OSKIP @ v_P ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_HOL_Obool ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5618]) ).

thf(5786,plain,
    ! [SV78: $i] :
      ( ( ! [SY803: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY803 )
                   != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
                  | ( SY803 = SV78 ) )
              | ~ ( ( SY803 != SV78 )
                  | ( ( hAPP @ c_Code__Numeral_Onat__of @ SY803 )
                    = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5619]) ).

thf(5787,plain,
    ! [SV79: $i] :
      ( ( ! [SY804: $i,SY805: $i,SY806: $i,SY807: $i,SY808: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY808 @ SY807 ) @ SY806 ) @ SY805 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY808 @ SY807 ) @ SY804 ) @ SV79 ) )
                  | ~ ( ( SY806 != SY804 )
                      | ( SY805 != SV79 ) ) )
              | ~ ( ~ ~ ( ( SY806 != SY804 )
                        | ( SY805 != SV79 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY808 @ SY807 ) @ SY806 ) @ SY805 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY808 @ SY807 ) @ SY804 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5620]) ).

thf(5788,plain,
    ! [SV80: $i] :
      ( ( ! [SY809: $i,SY810: $i,SY811: $i,SY812: $i,SY813: $i,SY814: $i,SY815: $i,SY816: $i,SY817: $i,SY818: $i] :
            ( ( ( hAPP @ SY818 @ ( hAPP @ SY817 @ SY816 ) )
             != ( hAPP @ SY815 @ ( hAPP @ SY814 @ SY813 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY812 @ SY811 @ SY810 @ SY818 ) @ SY817 ) @ SY816 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY809 @ SY811 @ SV80 @ SY815 ) @ SY814 ) @ SY813 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5621]) ).

thf(5789,plain,
    ! [SV81: $i] :
      ( ( ! [SY819: $i,SY820: $i,SY821: $i,SY822: $i,SY823: $i] :
            ( ~ ( ( SY823 != SY822 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY821 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY821 @ SY820 ) @ SY823 ) @ SY819 ) ) @ SY822 ) @ SV81 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY821 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY821 @ SY820 ) @ SY822 ) @ SV81 ) ) @ SY823 ) @ SY819 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5622]) ).

thf(5790,plain,
    ! [SV82: $i] :
      ( ( ! [SY824: $i,SY825: $i,SY826: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY826 ) @ SY825 ) @ SY824 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY826 ) @ SY825 ) @ SV82 ) )
                  | ( SY824 = SV82 ) )
              | ~ ( ( SY824 != SV82 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY826 ) @ SY825 ) @ SY824 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY826 ) @ SY825 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5623]) ).

thf(5791,plain,
    ! [SV83: $i] :
      ( ( ! [SY827: $i,SY828: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY828 @ tc_HOL_Obool ) ) @ SY827 )
                   != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY828 @ tc_HOL_Obool ) ) @ SV83 ) )
                  | ( SY827 = SV83 ) )
              | ~ ( ( SY827 != SV83 )
                  | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY828 @ tc_HOL_Obool ) ) @ SY827 )
                    = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY828 @ tc_HOL_Obool ) ) @ SV83 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5624]) ).

thf(5792,plain,
    ! [SV84: $i] :
      ( ( ! [SY829: $i,SY830: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY830 ) @ SY829 ) @ SV84 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY830 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
                  | ( SY829
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY830 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SY829
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY830 @ tc_HOL_Obool ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY830 ) @ SY829 ) @ SV84 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY830 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5625]) ).

thf(5793,plain,
    ! [SV85: $i] :
      ( ( ! [SY831: $i,SY832: $i,SY833: $i,SY834: $i,SY835: $i,SY836: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY836 @ SY835 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY836 @ SY834 @ SY833 @ SY832 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY836 @ SY835 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY836 @ SY832 @ SY831 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY836 @ SY835 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY836 @ SY834 @ ( c_Com_Ocom_OSemi @ SY833 @ SY831 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY836 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5626]) ).

thf(5794,plain,
    ! [SV86: $i] :
      ( ( ! [SY837: $i,SY838: $i,SY839: $i,SY840: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY839 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY838 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY840 @ tc_HOL_Obool ) ) ) )
                   != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY837 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY840 @ tc_HOL_Obool ) ) ) ) )
                  | ~ ( ( SY839 != SY837 )
                      | ( SY838 != SV86 ) )
                  | ~ ( ( SY839 != SV86 )
                      | ( SY838 != SY837 ) ) )
              | ~ ( ~ ( ~ ( ( SY839 != SY837 )
                          | ( SY838 != SV86 ) )
                      | ~ ( ( SY839 != SV86 )
                          | ( SY838 != SY837 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY839 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY838 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY840 @ tc_HOL_Obool ) ) ) )
                    = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SY837 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY840 @ tc_HOL_Obool ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5627]) ).

thf(5795,plain,
    ! [SV87: $i] :
      ( ( ! [SY841: $i,SY842: $i,SY843: $i,SY844: $i,SY845: $i,SY846: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY846 @ SY845 @ SY844 @ SY843 ) @ SY842 )
             != SY841 )
            | ( ( hAPP @ SY843 @ ( hAPP @ SY842 @ SV87 ) )
              = ( hAPP @ SY841 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5628]) ).

thf(5796,plain,
    ! [SV88: $i] :
      ( ( ! [SY847: $i] :
            ( ~ ( class_Lattices_Obounded__lattice @ SY847 )
            | ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV88 @ SY847 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5629]) ).

thf(5797,plain,
    ! [SV89: $i] :
      ( ( ! [SY848: $i,SY849: $i,SY850: $i,SY851: $i,SY852: $i,SY853: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY853 @ SY852 @ SY851 @ SY850 @ SY849 )
            | ~ ( ~ ( ( ( hAPP @ SY851 @ SY848 )
                     != ( hAPP @ SY851 @ SV89 ) )
                    | ( SY848 = SV89 ) )
                | ~ ( ( SY848 != SV89 )
                    | ( ( hAPP @ SY851 @ SY848 )
                      = ( hAPP @ SY851 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5630]) ).

thf(5798,plain,
    ! [SV90: $i] :
      ( ( ! [SY854: $i,SY855: $i] :
            ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY855 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                   != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY855 ) @ SY854 ) @ SV90 ) )
                  | ( SY854
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY855 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SY854
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY855 @ tc_HOL_Obool ) ) )
                  | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY855 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                    = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY855 ) @ SY854 ) @ SV90 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5631]) ).

thf(5799,plain,
    ! [SV91: $i] :
      ( ( ! [SY856: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OAss @ SY856 @ SV91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5632]) ).

thf(5800,plain,
    ! [SV92: $i] :
      ( ( ! [SY857: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OSemi @ SY857 @ SV92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5633]) ).

thf(5801,plain,
    ! [SV93: $i] :
      ( ( ! [SY858: $i] :
            ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY858 )
            | ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV93 @ SY858 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5634]) ).

thf(5802,plain,
    ! [SV94: $i] :
      ( ( ! [SY859: $i,SY860: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY860 ) @ SY859 ) @ SV94 )
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY860 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5635]) ).

thf(5803,plain,
    ! [SV95: $i] :
      ( ( SV95
       != ( hAPP @ c_Nat_OSuc @ SV95 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5636]) ).

thf(5804,plain,
    ! [SV96: $i] :
      ( ( ! [SY861: $i,SY862: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY862 ) @ SY861 )
                   != SV96 )
                  | ( SY861
                    = ( hAPP @ ( c_List_Orev @ SY862 ) @ SV96 ) ) )
              | ~ ( ( SY861
                   != ( hAPP @ ( c_List_Orev @ SY862 ) @ SV96 ) )
                  | ( ( hAPP @ ( c_List_Orev @ SY862 ) @ SY861 )
                    = SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5637]) ).

thf(5805,plain,
    ! [SV97: $i] :
      ( ( ! [SY863: $i,SY864: $i] :
            ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY864 @ SY863 @ SV97 )
            | ( SV97 = SY864 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5638]) ).

thf(5806,plain,
    ! [SV98: $i] :
      ( ( ! [SY865: $i] :
            ( ~ ( class_Lattices_Oboolean__algebra @ SY865 )
            | ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV98 @ SY865 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5639]) ).

thf(5807,plain,
    ! [SV99: $i] :
      ( ( ! [SY866: $i,SY867: $i,SY868: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY868 ) @ SY867 ) @ SY866 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY868 ) @ SV99 ) @ SY866 ) )
                  | ( SY867 = SV99 ) )
              | ~ ( ( SY867 != SV99 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY868 ) @ SY867 ) @ SY866 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY868 ) @ SV99 ) @ SY866 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5640]) ).

thf(5808,plain,
    ! [SV100: $i] :
      ( ( ! [SY869: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY869 )
                   != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
                  | ( SY869 = SV100 ) )
              | ~ ( ( SY869 != SV100 )
                  | ( ( hAPP @ c_Int_ORep__Integ @ SY869 )
                    = ( hAPP @ c_Int_ORep__Integ @ SV100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5641]) ).

thf(5809,plain,
    ! [SV101: $i] :
      ( ( ! [SY870: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY870 )
                   != ( hAPP @ c_Nat_OSuc @ SV101 ) )
                  | ( SY870 = SV101 ) )
              | ~ ( ( SY870 != SV101 )
                  | ( ( hAPP @ c_Nat_OSuc @ SY870 )
                    = ( hAPP @ c_Nat_OSuc @ SV101 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5642]) ).

thf(5810,plain,
    ! [SV102: $i] :
      ( ( ! [SY871: $i,SY872: $i,SY873: $i,SY874: $i,SY875: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm @ SY875 @ SY874 @ SY873 )
            | ( ( hAPP @ ( hAPP @ SY873 @ SY872 ) @ ( hAPP @ ( hAPP @ SY873 @ SY871 ) @ SV102 ) )
              = ( hAPP @ ( hAPP @ SY873 @ SY871 ) @ ( hAPP @ ( hAPP @ SY873 @ SY872 ) @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5643]) ).

thf(5811,plain,
    ! [SV103: $i] :
      ( ( ! [SY876: $i,SY877: $i,SY878: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY878 @ SY877 @ SY876 ) @ SV103 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY877 @ tc_HOL_Obool ) ) )
                  | ( SV103
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY878 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV103
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY878 @ tc_HOL_Obool ) ) )
                  | ( ( hAPP @ ( c_Set_Oimage @ SY878 @ SY877 @ SY876 ) @ SV103 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY877 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5644]) ).

thf(5812,plain,
    ! [SV104: $i] :
      ( ( ! [SY879: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY879 )
                   != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
                  | ( SY879 = SV104 ) )
              | ~ ( ( SY879 != SV104 )
                  | ( ( hAPP @ c_Code__Numeral_Onat__of @ SY879 )
                    = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5645]) ).

thf(5813,plain,
    ! [SV105: $i] :
      ( ( ! [SY880: $i,SY881: $i,SY882: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY882 @ SY881 @ SY880 )
            | ( ( hAPP @ ( hAPP @ SY881 @ SV105 ) @ SV105 )
              = SV105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5646]) ).

thf(5814,plain,
    ! [SV106: $i] :
      ( ( ! [SY883: $i,SY884: $i,SY885: $i] :
            ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY885 @ tc_HOL_Obool ) )
                   != ( hAPP @ ( c_Set_Oimage @ SY884 @ SY885 @ SY883 ) @ SV106 ) )
                  | ( SV106
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY884 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV106
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY884 @ tc_HOL_Obool ) ) )
                  | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY885 @ tc_HOL_Obool ) )
                    = ( hAPP @ ( c_Set_Oimage @ SY884 @ SY885 @ SY883 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5647]) ).

thf(5815,plain,
    ! [SV107: $i] :
      ( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV107 @ tc_HOL_Obool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV107 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5648]) ).

thf(5816,plain,
    ! [SV108: $i] :
      ( ( ! [SY886: $i,SY887: $i,SY888: $i,SY889: $i,SY890: $i,SY891: $i,SY892: $i,SY893: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY893 @ SY892 @ SY891 @ SY890 ) @ SY889 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY888 @ SY892 @ SY891 @ SY887 ) @ SY886 ) )
            | ( ( hAPP @ SY890 @ ( hAPP @ SY889 @ SV108 ) )
              = ( hAPP @ SY887 @ ( hAPP @ SY886 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5649]) ).

thf(5817,plain,
    ! [SV109: $i] :
      ( ( ! [SY894: $i,SY895: $i,SY896: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY896 @ SY895 @ SY894 )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY896 @ SV109 @ SY895 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY896 @ SV109 @ SY894 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5650]) ).

thf(5818,plain,
    ! [SV110: $i] :
      ( ( ! [SY897: $i] :
            ( ( c_Com_Ocom_OWhile @ SY897 @ SV110 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5651]) ).

thf(5819,plain,
    ! [SV111: $i] :
      ( ( ! [SY898: $i,SY899: $i] :
            ( ~ ( class_Orderings_Obot @ SY899 )
            | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY898 @ SY899 ) ) @ SV111 )
              = ( c_Orderings_Obot__class_Obot @ SY899 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5652]) ).

thf(5820,plain,
    ! [SV112: $i] :
      ( ( ! [SY900: $i] :
            ( ~ ( class_Orderings_Opreorder @ SY900 )
            | ( class_Orderings_Opreorder @ ( tc_fun @ SV112 @ SY900 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5653]) ).

thf(5821,plain,
    ! [SV113: $i] :
      ( ( ! [SY901: $i,SY902: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY902 ) @ SY901 ) @ SV113 )
           != SV113 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5654]) ).

thf(5822,plain,
    ! [SV114: $i] :
      ( ( ! [SY903: $i] :
            ( ~ ! [SY904: $i] :
                  ( ( hAPP @ SY903 @ SY904 )
                  = ( hAPP @ SV114 @ SY904 ) )
            | ( SY903 = SV114 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5655]) ).

thf(5823,plain,
    ! [SV115: $i] :
      ( ( ! [SY905: $i,SY906: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY906 ) @ SY905 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY906 @ tc_HOL_Obool ) ) )
             != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY906 ) @ SV115 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY906 @ tc_HOL_Obool ) ) ) )
            | ( SY905 = SV115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5656]) ).

thf(5824,plain,
    ! [SV116: $i] :
      ( ( ! [SY907: $i] :
            ( ~ ( class_Orderings_Obot @ SY907 )
            | ( class_Orderings_Obot @ ( tc_fun @ SV116 @ SY907 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5657]) ).

thf(5825,plain,
    ! [SV117: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ SV117 )
       != SV117 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5658]) ).

thf(5826,plain,
    ! [SV118: $i] :
      ( ( ! [SY908: $i] :
            ( ~ ( class_Orderings_Oord @ SY908 )
            | ( class_Orderings_Oord @ ( tc_fun @ SV118 @ SY908 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5659]) ).

thf(5827,plain,
    ! [SV119: $i] :
      ( ( ! [SY909: $i,SY910: $i,SY911: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one @ SY911 @ SY910 @ SY909 )
            | ( ( hAPP @ SY909 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY911 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY911 @ tc_HOL_Obool ) ) ) )
              = SV119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5660]) ).

thf(5828,plain,
    ! [SV120: $i] :
      ( ( ! [SY912: $i,SY913: $i] :
            ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY913 @ tc_HOL_Obool ) )
           != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY913 ) @ SY912 ) @ SV120 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5661]) ).

thf(5829,plain,
    ! [SV121: $i] :
      ( ( ! [SY914: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OWhile @ SY914 @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5662]) ).

thf(5830,plain,
    ! [SV122: $i] :
      ( ( ! [SY915: $i,SY916: $i,SY917: $i,SY918: $i] :
            ( ( ( hAPP @ SY918 @ SY917 )
             != SY916 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY915 @ SV122 ) @ SY918 ) @ SY917 ) @ SY916 )
              = SY918 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5663]) ).

thf(5831,plain,
    ! [SV123: $i] :
      ( ( ! [SY919: $i] :
            ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY919 )
                   != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
                  | ( SY919 = SV123 ) )
              | ~ ( ( SY919 != SV123 )
                  | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY919 )
                    = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5664]) ).

thf(5832,plain,
    ! [SV124: $i] :
      ( ( ! [SY920: $i,SY921: $i] :
            ( SY921
           != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY920 ) @ SV124 ) @ SY921 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5665]) ).

thf(5833,plain,
    ! [SV125: $i] :
      ( ( ! [SY922: $i] :
            ( ( c_Com_Ocom_OAss @ SY922 @ SV125 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5666]) ).

thf(5834,plain,
    ! [SV126: $i] :
      ( ( ! [SY923: $i] :
            ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SY923 )
                  | ~ ( class_Finite__Set_Ofinite @ SV126 ) )
            | ( class_Finite__Set_Ofinite @ ( tc_fun @ SY923 @ SV126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5667]) ).

thf(5835,plain,
    ! [SV127: $i] :
      ( ( ! [SY924: $i] :
            ( ( hAPP @ ( c_Set_OPow @ SY924 ) @ SV127 )
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY924 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5668]) ).

thf(5836,plain,
    ! [SV128: $i] :
      ( ( ! [SY925: $i,SY926: $i,SY927: $i,SY928: $i,SY929: $i,SY930: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY930 @ SY929 @ SY928 @ SY927 @ SY926 @ SY925 )
            | ( ( hAPP @ ( hAPP @ SY928 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5669]) ).

thf(5837,plain,
    ! [SV129: $i] :
      ( ( ! [SY931: $i,SY932: $i,SY933: $i,SY934: $i,SY935: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple @ SY935 @ SY934 @ SY933 @ SY932 @ SY931 @ SV129 )
            | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY934 @ tc_HOL_Obool ) ) )
              = SY932 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5670]) ).

thf(5838,plain,
    ! [SV130: $i] :
      ( ( ! [SY936: $i,SY937: $i,SY938: $i,SY939: $i,SY940: $i,SY941: $i] :
            ( ~ ( ( SY941 != SY940 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY939 @ SY938 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY939 @ SY938 ) @ SY937 ) @ SY941 ) @ SY936 ) ) @ SY940 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY939 @ SY938 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY939 @ SY938 ) @ SY937 ) @ SY940 ) @ SV130 ) ) @ SY941 ) @ SY936 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5671]) ).

thf(5839,plain,
    ! [SV131: $i] :
      ( ( ! [SY942: $i] :
            ( ( c_Com_Ocom_OSemi @ SY942 @ SV131 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5672]) ).

thf(5840,plain,
    ! [SV132: $i] :
      ( ( ! [SY943: $i,SY944: $i,SY945: $i,SY946: $i,SY947: $i] :
            ~ ( ~ ( ( SY947 != SY946 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY945 @ SY944 ) @ SY943 ) @ SY946 ) @ SV132 ) @ SY947 )
                    = SV132 ) )
              | ~ ( ~ ( ( SY947 != SY946 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY945 @ SY944 ) @ SY943 ) @ SY946 ) @ SV132 ) @ SY947 )
                    = ( hAPP @ SY943 @ SY947 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5673]) ).

thf(5841,plain,
    ! [SV133: $i] :
      ( ( ! [SY948: $i,SY949: $i,SY950: $i,SY951: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY950 ) @ SY949 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY948 ) @ SV133 ) )
                  | ~ ! [SY952: $i] :
                        ~ ( ~ ( ( SY950
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY948 ) @ SY952 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY952 ) @ SY949 )
                               != SV133 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY950 ) @ SY952 )
                               != SY948 )
                              | ( SY949
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY952 ) @ SV133 ) ) ) ) )
              | ~ ( ~ ~ ! [SY953: $i] :
                          ~ ( ~ ( ( SY950
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY948 ) @ SY953 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY953 ) @ SY949 )
                                 != SV133 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY950 ) @ SY953 )
                                 != SY948 )
                                | ( SY949
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY953 ) @ SV133 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY950 ) @ SY949 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY951 ) @ SY948 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5674]) ).

thf(5842,plain,
    ! [SV134: $i] :
      ( ( ! [SY954: $i] :
            ( ~ ( class_Orderings_Oorder @ SY954 )
            | ( class_Orderings_Oorder @ ( tc_fun @ SV134 @ SY954 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5675]) ).

thf(5843,plain,
    ! [SV135: $i] :
      ( ( ! [SY955: $i,SY956: $i,SY957: $i,SY958: $i,SY959: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY959 @ SY958 ) @ SY957 ) @ SY956 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY959 @ SY958 ) @ SY955 ) @ SV135 ) )
            | ~ ( ( SY957 != SY955 )
                | ( SY956 != SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5676]) ).

thf(5844,plain,
    ! [SV136: $i] :
      ( ( ! [SY960: $i] :
            ( ~ ~ ( ~ ( class_Enum_Oenum @ SY960 )
                  | ~ ( class_Enum_Oenum @ SV136 ) )
            | ( class_Enum_Oenum @ ( tc_fun @ SY960 @ SV136 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5677]) ).

thf(5845,plain,
    ! [SV137: $i] :
      ( ( ! [SY961: $i,SY962: $i,SY963: $i,SY964: $i,SY965: $i] :
            ( ~ ( ( SY965 != SY964 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY963 @ SY962 ) @ SY961 ) @ SY964 ) @ SV137 ) @ SY965 )
              = ( hAPP @ SY961 @ SY965 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5678]) ).

thf(5846,plain,
    ! [SV138: $i] :
      ( ( ! [SY966: $i,SY967: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) @ SY966 ) @ SV138 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) )
                  | ~ ( ( SY966
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) )
                      | ( SV138
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) ) ) )
              | ~ ( ~ ~ ( ( SY966
                         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) )
                        | ( SV138
                         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) @ SY966 ) @ SV138 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY967 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5679]) ).

thf(5847,plain,
    ! [SV139: $i] :
      ( ( ! [SY968: $i,SY969: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OCond @ SY969 @ SY968 @ SV139 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5680]) ).

thf(5848,plain,
    ! [SV140: $i] :
      ( ( ! [SY970: $i,SY971: $i,SY972: $i,SY973: $i,SY974: $i,SY975: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY975 @ SY974 @ SY973 @ SY972 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY975 @ SY971 @ SY970 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SY974 != SY971 )
                            | ( SY973 != SY970 ) )
                      | ( SY972 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY974 != SY971 )
                              | ( SY973 != SY970 ) )
                        | ( SY972 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY975 @ SY974 @ SY973 @ SY972 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY975 @ SY971 @ SY970 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5681]) ).

thf(5849,plain,
    ! [SV141: $i] :
      ( ( ! [SY976: $i] :
            ( ~ ( class_Orderings_Otop @ SY976 )
            | ( class_Orderings_Otop @ ( tc_fun @ SV141 @ SY976 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5682]) ).

thf(5850,plain,
    ! [SV142: $i] :
      ( ( ! [SY977: $i,SY978: $i,SY979: $i,SY980: $i,SY981: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY981 @ SY980 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY981 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY981 @ SY979 @ SY978 @ SY977 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY981 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY982: $i,SY983: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY982 ) @ SY983 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SY979 @ SY982 ) @ SY983 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY981 @ SY980 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY981 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY981 @ SV142 @ SY978 @ SY977 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY981 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5683]) ).

thf(5851,plain,
    ! [SV143: $i] :
      ( ( ! [SY984: $i] :
            ( ~ ( class_Lattices_Odistrib__lattice @ SY984 )
            | ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV143 @ SY984 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5684]) ).

thf(5852,plain,
    ! [SV144: $i] :
      ( ( ! [SY985: $i] :
            ( ~ ( class_Groups_Ominus @ SY985 )
            | ( class_Groups_Ominus @ ( tc_fun @ SV144 @ SY985 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5685]) ).

thf(5853,plain,
    ! [SV145: $i] :
      ( ( ! [SY986: $i] :
            ( ~ ( class_Lattices_Olattice @ SY986 )
            | ( class_Lattices_Olattice @ ( tc_fun @ SV145 @ SY986 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5686]) ).

thf(5854,plain,
    ! [SV146: $i] :
      ( ( ! [SY987: $i,SY988: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY988 ) @ SY987 )
                   != ( hAPP @ ( c_Option_Ooption_OSome @ SY988 ) @ SV146 ) )
                  | ( SY987 = SV146 ) )
              | ~ ( ( SY987 != SV146 )
                  | ( ( hAPP @ ( c_Option_Ooption_OSome @ SY988 ) @ SY987 )
                    = ( hAPP @ ( c_Option_Ooption_OSome @ SY988 ) @ SV146 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5687]) ).

thf(5855,plain,
    ! [SV147: $i] :
      ( ( ! [SY989: $i,SY990: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY990 ) @ SY989 )
                   != ( hAPP @ ( c_List_Orev @ SY990 ) @ SV147 ) )
                  | ( SY989 = SV147 ) )
              | ~ ( ( SY989 != SV147 )
                  | ( ( hAPP @ ( c_List_Orev @ SY990 ) @ SY989 )
                    = ( hAPP @ ( c_List_Orev @ SY990 ) @ SV147 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5688]) ).

thf(5856,plain,
    ! [SV148: $i] :
      ( ( ! [SY991: $i,SY992: $i,SY993: $i,SY994: $i,SY995: $i,SY996: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY996 @ SY995 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY996 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY996 @ SY994 @ SY993 @ SY992 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY996 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY997: $i,SY998: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY991 @ SY997 ) @ SY998 ) )
                  | ! [SY999: $i] :
                      ( ~ ! [SX10: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY994 @ SX10 ) @ SY998 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SY992 @ SX10 ) @ SY999 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY997 ) @ SY999 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY996 @ SY995 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY996 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY996 @ SY991 @ SY993 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY996 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5689]) ).

thf(5857,plain,
    ! [SV149: $i] :
      ( ( ! [SY1001: $i] :
            ( ( ( hAPP @ c_Nat_OSuc @ SY1001 )
             != ( hAPP @ c_Nat_OSuc @ SV149 ) )
            | ( SY1001 = SV149 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5690]) ).

thf(5858,plain,
    ! [SV150: $i] :
      ( ( ! [SY1002: $i,SY1003: $i,SY1004: $i,SY1005: $i,SY1006: $i,SY1007: $i,SY1008: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1008 @ SY1007 @ SY1006 @ SY1005 ) @ SY1004 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1003 @ SY1007 @ SY1006 @ SY1002 ) @ SV150 ) )
            | ! [SY1009: $i] :
                ( ( hAPP @ SY1005 @ ( hAPP @ SY1004 @ SY1009 ) )
                = ( hAPP @ SY1002 @ ( hAPP @ SV150 @ SY1009 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5691]) ).

thf(5859,plain,
    ! [SV151: $i] :
      ( ( ! [SY1010: $i,SY1011: $i,SY1012: $i,SY1013: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1013 @ SY1012 @ SY1011 )
            | ( ( hAPP @ ( hAPP @ SY1011 @ SY1010 ) @ ( hAPP @ ( hAPP @ SY1011 @ SY1010 ) @ SV151 ) )
              = ( hAPP @ ( hAPP @ SY1011 @ SY1010 ) @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5692]) ).

thf(5860,plain,
    ! [SV152: $i] :
      ( ( ! [SY1014: $i,SY1015: $i,SY1016: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1016 @ SY1015 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1016 ) ) @ SY1014 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1016 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1016 @ SY1015 @ SV152 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1016 @ SY1015 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1016 ) ) @ SY1014 ) @ SV152 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5693]) ).

thf(5861,plain,
    ! [SV153: $i] :
      ( ( ! [SY1017: $i,SY1018: $i,SY1019: $i,SY1020: $i,SY1021: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1021 ) @ SY1020 ) @ SY1019 )
             != SY1018 )
            | ( SY1017
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1021 ) @ SY1019 ) @ SV153 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1021 ) @ SY1020 ) @ SY1017 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1021 ) @ SY1018 ) @ SV153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5694]) ).

thf(5862,plain,
    ! [SV154: $i] :
      ( ( ! [SY1022: $i,SY1023: $i,SY1024: $i,SY1025: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1025 ) @ SY1024 ) @ SY1023 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1025 ) @ SY1022 ) @ SV154 ) )
                  | ~ ( ( SY1024 != SY1022 )
                      | ( SY1023 != SV154 ) ) )
              | ~ ( ~ ~ ( ( SY1024 != SY1022 )
                        | ( SY1023 != SV154 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1025 ) @ SY1024 ) @ SY1023 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1025 ) @ SY1022 ) @ SV154 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5695]) ).

thf(5863,plain,
    ! [SV155: $i] :
      ( ( ! [SY1026: $i] :
            ( ~ ( class_Groups_Ouminus @ SY1026 )
            | ( class_Groups_Ouminus @ ( tc_fun @ SV155 @ SY1026 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5696]) ).

thf(5864,plain,
    ! [SV156: $i] :
      ( ( ! [SY1027: $i,SY1028: $i,SY1029: $i,SY1030: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1030 @ SY1029 ) @ SY1028 ) @ SY1027 ) @ SV156 )
                   != SY1028 )
                  | ( ( hAPP @ SY1028 @ SY1027 )
                    = SV156 ) )
              | ~ ( ( ( hAPP @ SY1028 @ SY1027 )
                   != SV156 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1030 @ SY1029 ) @ SY1028 ) @ SY1027 ) @ SV156 )
                    = SY1028 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5697]) ).

thf(5865,plain,
    ! [SV157: $i] :
      ( ( ! [SY1031: $i,SY1032: $i] :
            ( ~ ( class_Orderings_Obot @ SY1032 )
            | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1031 @ SY1032 ) ) @ SV157 )
              = ( c_Orderings_Obot__class_Obot @ SY1032 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5698]) ).

thf(5866,plain,
    ! [SV158: $i] :
      ( ( ! [SY1033: $i,SY1034: $i] :
            ( ( c_Com_Ocom_OCond @ SY1034 @ SY1033 @ SV158 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5699]) ).

thf(5867,plain,
    ! [SV159: $i] :
      ( ( ! [SY1035: $i,SY1036: $i] :
            ( ( c_Com_Ocom_OLocal @ SY1036 @ SY1035 @ SV159 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5700]) ).

thf(5868,plain,
    ! [SV160: $i] :
      ( ( ! [SY1037: $i,SY1038: $i,SY1039: $i,SY1040: $i,SY1041: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1041 @ SY1040 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1041 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1041 @ SY1039 @ SY1038 @ SY1037 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1041 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1042: $i,SY1043: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1037 @ SY1042 ) @ SY1043 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1042 ) @ SY1043 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1041 @ SY1040 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1041 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1041 @ SY1039 @ SY1038 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1041 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5701]) ).

thf(5869,plain,
    ! [SV161: $i] :
      ( ( ! [SY1044: $i,SY1045: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OLocal @ SY1045 @ SY1044 @ SV161 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5702]) ).

thf(5870,plain,
    ! [SV162: $i] :
      ( ( ! [SY1046: $i,SY1047: $i,SY1048: $i,SY1049: $i,SY1050: $i] :
            ~ ( ~ ( ( SY1050 != SY1049 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1048 @ SY1047 ) @ SY1046 ) @ SY1049 ) @ SV162 ) @ SY1050 )
                    = SV162 ) )
              | ~ ( ~ ( ( SY1050 != SY1049 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1048 @ SY1047 ) @ SY1046 ) @ SY1049 ) @ SV162 ) @ SY1050 )
                    = ( hAPP @ SY1046 @ SY1050 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5703]) ).

thf(5871,plain,
    ! [SV163: $i] :
      ( ( ! [SY1051: $i,SY1052: $i,SY1053: $i] :
            ( ( SY1053
             != ( c_Finite__Set_Ofold1 @ SY1052 @ SY1051 ) )
            | ( ( hAPP @ SY1053 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1052 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1052 @ tc_HOL_Obool ) ) ) )
              = SV163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5704]) ).

thf(5872,plain,
    ! [SV164: $i] :
      ( ( ! [SY1054: $i,SY1055: $i,SY1056: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1056 ) @ SY1055 ) @ SY1054 ) @ SV164 ) )
                  | ( SY1055 = SV164 )
                  | ( hBOOL @ ( hAPP @ SY1054 @ SV164 ) ) )
              | ~ ( ~ ( ( SY1055 = SV164 )
                      | ( hBOOL @ ( hAPP @ SY1054 @ SV164 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1056 ) @ SY1055 ) @ SY1054 ) @ SV164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5705]) ).

thf(5873,plain,
    ! [SV165: $i] :
      ( ( ! [SY1057: $i,SY1058: $i,SY1059: $i,SY1060: $i,SY1061: $i] :
            ( ( SY1061 != SY1060 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1059 @ SY1058 @ SY1057 ) @ SV165 ) @ SY1061 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1059 @ SY1058 @ SY1057 ) @ SV165 ) @ SY1060 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5706]) ).

thf(5874,plain,
    ! [SV166: $i] :
      ( ( ! [SY1062: $i,SY1063: $i,SY1064: $i,SY1065: $i,SY1066: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1066 @ SY1065 @ SY1064 @ SY1063 @ SY1062 )
            | ( ( hAPP @ SY1063 @ ( hAPP @ SY1064 @ SV166 ) )
              = SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5707]) ).

thf(5875,plain,
    ! [SV1: $i,SV167: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV167 @ SV1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV167 ) @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5708]) ).

thf(5876,plain,
    ! [SV2: $i,SV168: $i] :
      ( ( ! [SY1067: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1067 @ SV168 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1067 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1067 @ SV2 @ c_Com_Ocom_OSKIP @ SV2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1067 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5709]) ).

thf(5877,plain,
    ! [SV3: $i,SV169: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV169 @ SV3 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV169 ) @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5710]) ).

thf(5878,plain,
    ! [SV4: $i,SV170: $i] :
      ( ( ! [SY1068: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1068 @ SV170 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1068 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1068 @ SV4 @ c_Com_Ocom_OSKIP @ SV4 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1068 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5711]) ).

thf(5879,plain,
    ! [SV5: $i,SV171: $i] :
      ( ( ! [SY1069: $i,SY1070: $i,SY1071: $i,SY1072: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SY1072 @ SY1071 @ SY1070 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1072 @ SY1069 @ SV171 @ SV5 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY1070 @ SY1069 ) @ SV171 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5712]) ).

thf(5880,plain,
    ! [SV6: $i,SV172: $i] :
      ( ( ! [SY1073: $i,SY1074: $i,SY1075: $i,SY1076: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY1076 @ SY1075 @ SY1074 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1076 @ SY1073 @ SV172 @ SV6 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY1074 @ SY1073 ) @ SV172 ) @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5713]) ).

thf(5881,plain,
    ! [SV7: $i,SV173: $i] :
      ( ( ! [SY1077: $i,SY1078: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1078 ) @ SY1077 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1078 ) @ SV173 ) @ SV7 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1078 ) @ SV173 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1078 ) @ SY1077 ) @ SV7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5714]) ).

thf(5882,plain,
    ! [SV8: $i,SV174: $i] :
      ( ( ! [SY1079: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1079 ) @ SV174 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1079 ) @ SV174 ) @ SV8 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1079 ) @ SV174 ) @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5715]) ).

thf(5883,plain,
    ! [SV9: $i,SV175: $i] :
      ( ( ( c_Set_Othe__elem @ SV175 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV175 ) @ SV9 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV175 @ tc_HOL_Obool ) ) ) )
        = SV9 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5716]) ).

thf(5884,plain,
    ! [SV10: $i,SV176: $i] :
      ( ( ! [SY1080: $i,SY1081: $i,SY1082: $i,SY1083: $i,SY1084: $i,SY1085: $i,SY1086: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1086 @ SY1085 @ SY1084 @ SY1083 @ SY1082 @ SY1081 @ SY1080 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1085 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5717]) ).

thf(5885,plain,
    ! [SV11: $i,SV177: $i] :
      ( ( ! [SY1087: $i,SY1088: $i,SY1089: $i,SY1090: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1090 @ SY1089 @ SY1088 @ SY1087 ) @ SV177 ) @ SV11 )
            = ( hAPP @ SY1087 @ ( hAPP @ SV177 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5718]) ).

thf(5886,plain,
    ! [SV12: $i,SV178: $i] :
      ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV178 @ SV12 @ SV178 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5719]) ).

thf(5887,plain,
    ! [SV13: $i,SV179: $i] :
      ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV179 @ SV13 @ SV179 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5720]) ).

thf(5888,plain,
    ! [SV14: $i,SV180: $i] :
      ( ( ! [SY1091: $i,SY1092: $i,SY1093: $i,SY1094: $i,SY1095: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1095 @ SY1094 @ SY1093 @ SY1092 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1091 @ SY1095 @ SY1093 @ SV180 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SY1091 @ SY1094 @ SY1093 @ ( hAPP @ ( c_Fun_Ocomp @ SY1095 @ SY1094 @ SY1091 @ SY1092 ) @ SV180 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5721]) ).

thf(5889,plain,
    ! [SV15: $i,SV181: $i] :
      ( ( ! [SY1096: $i,SY1097: $i,SY1098: $i,SY1099: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1099 @ SY1098 @ SY1097 @ SY1096 ) @ SV181 ) @ SV15 )
            = ( hAPP @ SY1096 @ ( hAPP @ SV181 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5722]) ).

thf(5890,plain,
    ! [SV16: $i,SV182: $i] :
      ( ( ! [SY1100: $i,SY1101: $i] :
            ( ( c_Fun_Ooverride__on @ SY1101 @ SY1100 @ SV182 @ SV16 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1101 @ tc_HOL_Obool ) ) )
            = SV182 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5723]) ).

thf(5891,plain,
    ! [SV17: $i,SV183: $i] :
      ( ( ( hAPP @ ( c_Set_OCollect @ SV183 ) @ SV17 )
        = SV17 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5724]) ).

thf(5892,plain,
    ! [SV19: $i,SV184: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV184 @ tc_HOL_Obool ) ) @ SV19 ) @ SV19 )
        = SV19 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5726]) ).

thf(5893,plain,
    ! [SV20: $i,SV185: $i] :
      ( ( ! [SY1102: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1102 @ tc_HOL_Obool ) ) @ SV185 ) @ SV20 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1102 @ tc_HOL_Obool ) ) @ SV20 ) @ SV185 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5727]) ).

thf(5894,plain,
    ! [SV21: $i,SV186: $i] :
      ( ( ! [SY1103: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1103 @ tc_HOL_Obool ) ) @ SV186 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1103 @ tc_HOL_Obool ) ) @ SV186 ) @ SV21 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1103 @ tc_HOL_Obool ) ) @ SV186 ) @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5728]) ).

thf(5895,plain,
    ! [SV22: $i,SV187: $i] :
      ( ( ! [SY1104: $i,SY1105: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1105 @ tc_HOL_Obool ) ) @ SY1104 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1105 @ tc_HOL_Obool ) ) @ SV187 ) @ SV22 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1105 @ tc_HOL_Obool ) ) @ SV187 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1105 @ tc_HOL_Obool ) ) @ SY1104 ) @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5729]) ).

thf(5896,plain,
    ! [SV23: $i,SV188: $i] :
      ( ( ! [SY1106: $i,SY1107: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1107 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1107 @ tc_HOL_Obool ) ) @ SY1106 ) @ SV188 ) ) @ SV23 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1107 @ tc_HOL_Obool ) ) @ SY1106 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1107 @ tc_HOL_Obool ) ) @ SV188 ) @ SV23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5730]) ).

thf(5897,plain,
    ! [SV24: $i,SV189: $i] :
      ( ( ! [SY1108: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY1108 @ SV189 @ SV24 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1108 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5731]) ).

thf(5898,plain,
    ! [SV25: $i,SV190: $i] :
      ( ( ! [SY1109: $i,SY1110: $i,SY1111: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY1111 @ SY1110 @ SY1109 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1111 ) @ SV190 ) @ SV25 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1110 ) @ ( hAPP @ SY1109 @ SV190 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1111 @ SY1110 @ SY1109 ) @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5732]) ).

thf(5899,plain,
    ! [SV26: $i,SV191: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV191 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_HOL_Obool ) ) ) @ SV26 )
        = SV26 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5733]) ).

thf(5900,plain,
    ! [SV27: $i,SV192: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV192 @ tc_HOL_Obool ) ) @ SV27 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_HOL_Obool ) ) )
        = SV27 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5734]) ).

thf(5901,plain,
    ! [SV28: $i,SV193: $i] :
      ( ( ! [SY1112: $i,SY1113: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1113 @ tc_HOL_Obool ) ) @ SY1112 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1113 ) @ SV193 ) @ SV28 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1113 ) @ SV193 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1113 @ tc_HOL_Obool ) ) @ SY1112 ) @ SV28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5735]) ).

thf(5902,plain,
    ! [SV29: $i,SV194: $i] :
      ( ( ! [SY1114: $i,SY1115: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1115 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1115 ) @ SY1114 ) @ SV194 ) ) @ SV29 )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1115 ) @ SY1114 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1115 @ tc_HOL_Obool ) ) @ SV194 ) @ SV29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5736]) ).

thf(5903,plain,
    ! [SV30: $i,SV195: $i] :
      ( ( ! [SY1116: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1116 ) @ SV195 ) @ SV30 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1116 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1116 ) @ SV195 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1116 @ tc_HOL_Obool ) ) ) ) @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5737]) ).

thf(5904,plain,
    ! [SV31: $i,SV196: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV196 @ tc_HOL_Obool ) ) @ SV31 ) @ SV31 )
        = SV31 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5738]) ).

thf(5905,plain,
    ! [SV32: $i,SV197: $i] :
      ( ( ! [SY1117: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1117 @ tc_HOL_Obool ) ) @ SV197 ) @ SV32 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1117 @ tc_HOL_Obool ) ) @ SV32 ) @ SV197 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5739]) ).

thf(5906,plain,
    ! [SV33: $i,SV198: $i] :
      ( ( ! [SY1118: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1118 @ tc_HOL_Obool ) ) @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1118 @ tc_HOL_Obool ) ) @ SV198 ) @ SV33 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1118 @ tc_HOL_Obool ) ) @ SV198 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5740]) ).

thf(5907,plain,
    ! [SV34: $i,SV199: $i] :
      ( ( ! [SY1119: $i,SY1120: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1120 @ tc_HOL_Obool ) ) @ SY1119 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1120 @ tc_HOL_Obool ) ) @ SV199 ) @ SV34 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1120 @ tc_HOL_Obool ) ) @ SV199 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1120 @ tc_HOL_Obool ) ) @ SY1119 ) @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5741]) ).

thf(5908,plain,
    ! [SV35: $i,SV200: $i] :
      ( ( ! [SY1121: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1121 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1121 @ tc_HOL_Obool ) ) @ SV200 ) @ SV35 ) ) @ SV35 )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1121 @ tc_HOL_Obool ) ) @ SV200 ) @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5742]) ).

thf(5909,plain,
    ! [SV36: $i,SV201: $i] :
      ( ( ! [SY1122: $i,SY1123: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1123 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1123 @ tc_HOL_Obool ) ) @ SY1122 ) @ SV201 ) ) @ SV36 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1123 @ tc_HOL_Obool ) ) @ SY1122 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1123 @ tc_HOL_Obool ) ) @ SV201 ) @ SV36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5743]) ).

thf(5910,plain,
    ! [SV37: $i,SV202: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV202 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_HOL_Obool ) ) ) @ SV37 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV202 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5744]) ).

thf(5911,plain,
    ! [SV38: $i,SV203: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SV38 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) )
        = SV38 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5745]) ).

thf(5912,plain,
    ! [SV39: $i,SV204: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV204 @ tc_HOL_Obool ) ) @ SV39 ) @ SV39 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV204 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5746]) ).

thf(5913,plain,
    ! [SV40: $i,SV205: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV205 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_HOL_Obool ) ) ) @ SV40 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5747]) ).

thf(5914,plain,
    ! [SV41: $i,SV206: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV206 @ tc_HOL_Obool ) ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV206 @ tc_HOL_Obool ) ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV206 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5748]) ).

thf(5915,plain,
    ! [SV42: $i,SV207: $i] :
      ( ( ! [SY1124: $i,SY1125: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1125 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1125 ) @ SY1124 ) @ SV207 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1125 ) @ SY1124 ) @ SV42 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1125 ) @ SY1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1125 @ tc_HOL_Obool ) ) @ SV207 ) @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5749]) ).

thf(5916,plain,
    ! [SV43: $i,SV208: $i] :
      ( ( ! [SY1126: $i,SY1127: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1127 @ tc_HOL_Obool ) ) @ SY1126 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1127 ) @ SV208 ) @ SV43 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1127 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1127 @ tc_HOL_Obool ) ) @ SY1126 ) @ SV43 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1127 ) @ SV208 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1127 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5750]) ).

thf(5917,plain,
    ! [SV44: $i,SV209: $i] :
      ( ( ! [SY1128: $i,SY1129: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1129 @ tc_HOL_Obool ) ) @ SY1128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1129 ) @ SV209 ) @ SV44 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1129 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1129 @ tc_HOL_Obool ) ) @ SY1128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1129 ) @ SV209 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1129 @ tc_HOL_Obool ) ) ) ) ) @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5751]) ).

thf(5918,plain,
    ! [SV45: $i,SV210: $i] :
      ( ( ! [SY1130: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1130 ) @ SV210 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1130 @ tc_HOL_Obool ) ) @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1130 ) @ SV210 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1130 @ tc_HOL_Obool ) ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1130 ) @ SV210 ) @ SV45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5752]) ).

thf(5919,plain,
    ! [SV46: $i,SV211: $i] :
      ( ( ! [SY1131: $i,SY1132: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1132 @ SY1131 ) @ SV211 ) @ SV46 ) @ ( hAPP @ SV211 @ SV46 ) )
            = SV211 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5753]) ).

thf(5920,plain,
    ! [SV47: $i,SV212: $i] :
      ( ( ! [SY1133: $i,SY1134: $i,SY1135: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1135 @ SY1134 ) @ SY1133 ) @ SV212 ) @ SV47 ) @ SV212 )
            = SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5754]) ).

thf(5921,plain,
    ! [SV48: $i,SV213: $i] :
      ( ( ! [SY1136: $i,SY1137: $i,SY1138: $i,SY1139: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1139 @ SY1138 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1139 @ SY1138 ) @ SY1137 ) @ SY1136 ) @ SV213 ) ) @ SY1136 ) @ SV48 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1139 @ SY1138 ) @ SY1137 ) @ SY1136 ) @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5755]) ).

thf(5922,plain,
    ! [SV49: $i,SV214: $i] :
      ( ( ! [SY1140: $i,SY1141: $i] : ( c_Nitpick_Ofold__graph_H @ SY1141 @ SY1140 @ SV214 @ SV49 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1141 @ tc_HOL_Obool ) ) @ SV49 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5756]) ).

thf(5923,plain,
    ! [SV50: $i,SV215: $i] :
      ( ( ! [SY1142: $i,SY1143: $i] : ( c_Nitpick_Ofold__graph_H @ SY1143 @ SY1142 @ SV215 @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1143 @ tc_HOL_Obool ) ) @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5757]) ).

thf(5924,plain,
    ! [SV51: $i,SV216: $i] :
      ( ( ! [SY1144: $i] : ( c_Fun_Oinj__on @ SY1144 @ SV216 @ SV51 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1144 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5758]) ).

thf(5925,plain,
    ! [SV53: $i,SV217: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV217 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV217 @ tc_HOL_Obool ) ) ) @ SV53 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV217 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5760]) ).

thf(5926,plain,
    ! [SV54: $i,SV218: $i] :
      ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV218 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV218 @ tc_HOL_Obool ) ) @ SV54 ) )
        = SV54 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5761]) ).

thf(5927,plain,
    ! [SV55: $i,SV219: $i] :
      ( ( ! [SY1145: $i] :
            ( ( hAPP @ ( c_Relation_OImage @ SY1145 @ SV219 @ SV55 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1145 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV219 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5762]) ).

thf(5928,plain,
    ! [SV56: $i,SV220: $i] :
      ( ( ! [SY1146: $i,SY1147: $i] :
            ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1147 @ ( tc_fun @ SY1146 @ tc_HOL_Obool ) ) ) @ SV220 ) @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5763]) ).

thf(5929,plain,
    ! [SV57: $i,SV221: $i] :
      ( ( ! [SY1148: $i,SY1149: $i,SY1150: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY1150 @ SY1149 @ SY1148 ) @ SV221 ) @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1149 @ tc_HOL_Obool ) ) )
            = SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5764]) ).

thf(5930,plain,
    ! [SV58: $i,SV222: $i] :
      ( ( ! [SY1151: $i] :
            ( ( hAPP @ ( c_Set_Ovimage @ SY1151 @ SV222 @ SV58 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV222 @ tc_HOL_Obool ) ) )
            = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1151 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5765]) ).

thf(5931,plain,
    ! [SV59: $i,SV223: $i] :
      ( ( ! [SY1152: $i,SY1153: $i,SY1154: $i,SY1155: $i,SY1156: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1156 @ SY1155 @ SY1154 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1156 @ SY1153 @ SY1155 ) @ SY1152 ) @ SV223 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1156 @ SY1153 @ SY1154 ) @ SY1152 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1153 @ SY1155 @ SY1154 ) @ SV223 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5766]) ).

thf(5932,plain,
    ! [SV60: $i,SV224: $i] :
      ( ( ( hAPP @ ( c_Fun_Oid @ SV224 ) @ SV60 )
        = SV60 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5767]) ).

thf(5933,plain,
    ! [SV61: $i,SV225: $i] :
      ( ( ( hAPP @ ( c_Fun_Oid @ SV225 ) @ SV61 )
        = SV61 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5768]) ).

thf(5934,plain,
    ! [SV62: $i,SV226: $i] :
      ( ( ! [SY1157: $i] :
            ( ( hAPP @ ( c_Finite__Set_Ofold1 @ SY1157 @ SV226 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1157 ) @ SV62 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1157 @ tc_HOL_Obool ) ) ) )
            = SV62 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5769]) ).

thf(5935,plain,
    ! [SV63: $i,SV227: $i] :
      ( ( ! [SY1158: $i,SY1159: $i,SY1160: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1160 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1160 @ SY1159 ) @ SY1158 ) @ SV227 ) ) @ SY1158 ) @ SV63 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1160 @ SY1159 ) @ SY1158 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5770]) ).

thf(5936,plain,
    ! [SV65: $i,SV228: $i] :
      ( ( ! [SY1161: $i,SY1162: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1162 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1162 ) @ SY1161 ) @ SV228 ) ) @ SV65 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1162 ) @ SY1161 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1162 ) @ SV228 ) @ SV65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5772]) ).

thf(5937,plain,
    ! [SV66: $i,SV229: $i] :
      ( ( ( hAPP @ ( c_List_Orev @ SV229 ) @ ( hAPP @ ( c_List_Orev @ SV229 ) @ SV66 ) )
        = SV66 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5773]) ).

thf(5938,plain,
    ! [SV67: $i,SV230: $i] :
      ( ( ! [SY1163: $i] :
            ( ( hAPP @ ( c_Relation_Oconverse @ SY1163 @ SV230 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV230 @ SY1163 ) @ SV67 ) )
            = SV67 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5774]) ).

thf(5939,plain,
    ! [SV68: $i,SV231: $i] :
      ( ( c_Relation_Ototal__on @ SV231 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV231 @ tc_HOL_Obool ) ) @ SV68 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5775]) ).

thf(5940,plain,
    ! [SV69: $i,SV232: $i] :
      ( ( ! [SY1164: $i,SY1165: $i] :
            ( ( hAPP @ SY1165 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1164 @ SY1164 ) @ SV232 ) @ SY1165 ) @ SV69 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1164 @ SY1164 ) @ SV232 ) @ SY1165 ) @ ( hAPP @ SY1165 @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5776]) ).

thf(5941,plain,
    ! [SV70: $i,SV233: $i] :
      ( ( ! [SY1166: $i,SY1167: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY1167 @ SY1166 @ SV233 ) @ SV70 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1167 @ tc_HOL_Obool ) ) )
            = SV70 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5777]) ).

thf(5942,plain,
    ! [SV73: $i,SV234: $i] :
      ( ( ( hAPP @ ( c_COMBI @ SV234 ) @ SV73 )
        = SV73 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5780]) ).

thf(5943,plain,
    ! [SV74: $i,SV235: $i] :
      ( ( ! [SY1168: $i,SY1169: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1169 @ SY1168 ) @ SV235 ) @ SV74 )
            = SV235 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5781]) ).

thf(5944,plain,
    ! [SV75: $i,SV236: $i] :
      ( ( ! [SY1170: $i,SY1171: $i,SY1172: $i,SY1173: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1173 @ SY1172 @ SY1171 ) @ SY1170 ) @ SV236 ) @ SV75 )
            = ( hAPP @ SY1170 @ ( hAPP @ SV236 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5782]) ).

thf(5945,plain,
    ! [SV76: $i,SV237: $i] :
      ( ( ! [SY1174: $i,SY1175: $i,SY1176: $i,SY1177: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1177 @ SY1176 @ SY1175 ) @ SY1174 ) @ SV237 ) @ SV76 )
            = ( hAPP @ ( hAPP @ SY1174 @ SV76 ) @ SV237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5783]) ).

thf(5946,plain,
    ! [SV77: $i,SV238: $i] :
      ( ( ! [SY1178: $i,SY1179: $i,SY1180: $i,SY1181: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1181 @ SY1180 @ SY1179 ) @ SY1178 ) @ SV238 ) @ SV77 )
            = ( hAPP @ ( hAPP @ SY1178 @ SV77 ) @ ( hAPP @ SV238 @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5784]) ).

thf(5947,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
                | ( SV239 = SV78 ) )
            | ~ ( ( SV239 != SV78 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5786]) ).

thf(5948,plain,
    ! [SV79: $i,SV240: $i] :
      ( ( ! [SY1182: $i,SY1183: $i,SY1184: $i,SY1185: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1185 @ SY1184 ) @ SY1183 ) @ SY1182 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1185 @ SY1184 ) @ SV240 ) @ SV79 ) )
                  | ~ ( ( SY1183 != SV240 )
                      | ( SY1182 != SV79 ) ) )
              | ~ ( ~ ~ ( ( SY1183 != SV240 )
                        | ( SY1182 != SV79 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1185 @ SY1184 ) @ SY1183 ) @ SY1182 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1185 @ SY1184 ) @ SV240 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5787]) ).

thf(5949,plain,
    ! [SV80: $i,SV241: $i] :
      ( ( ! [SY1186: $i,SY1187: $i,SY1188: $i,SY1189: $i,SY1190: $i,SY1191: $i,SY1192: $i,SY1193: $i,SY1194: $i] :
            ( ( ( hAPP @ SY1194 @ ( hAPP @ SY1193 @ SY1192 ) )
             != ( hAPP @ SY1191 @ ( hAPP @ SY1190 @ SY1189 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1188 @ SY1187 @ SY1186 @ SY1194 ) @ SY1193 ) @ SY1192 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SY1187 @ SV80 @ SY1191 ) @ SY1190 ) @ SY1189 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5788]) ).

thf(5950,plain,
    ! [SV81: $i,SV242: $i] :
      ( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i] :
            ( ~ ( ( SY1198 != SY1197 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1196 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1196 @ SY1195 ) @ SY1198 ) @ SV242 ) ) @ SY1197 ) @ SV81 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1196 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1196 @ SY1195 ) @ SY1197 ) @ SV81 ) ) @ SY1198 ) @ SV242 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5789]) ).

thf(5951,plain,
    ! [SV82: $i,SV243: $i] :
      ( ( ! [SY1199: $i,SY1200: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1200 ) @ SY1199 ) @ SV243 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1200 ) @ SY1199 ) @ SV82 ) )
                  | ( SV243 = SV82 ) )
              | ~ ( ( SV243 != SV82 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1200 ) @ SY1199 ) @ SV243 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1200 ) @ SY1199 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5790]) ).

thf(5952,plain,
    ! [SV83: $i,SV244: $i] :
      ( ( ! [SY1201: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1201 @ tc_HOL_Obool ) ) @ SV244 )
                   != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1201 @ tc_HOL_Obool ) ) @ SV83 ) )
                  | ( SV244 = SV83 ) )
              | ~ ( ( SV244 != SV83 )
                  | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1201 @ tc_HOL_Obool ) ) @ SV244 )
                    = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1201 @ tc_HOL_Obool ) ) @ SV83 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5791]) ).

thf(5953,plain,
    ! [SV84: $i,SV245: $i] :
      ( ( ! [SY1202: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1202 ) @ SV245 ) @ SV84 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1202 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
                  | ( SV245
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1202 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV245
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1202 @ tc_HOL_Obool ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1202 ) @ SV245 ) @ SV84 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1202 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5792]) ).

thf(5954,plain,
    ! [SV85: $i,SV246: $i] :
      ( ( ! [SY1203: $i,SY1204: $i,SY1205: $i,SY1206: $i,SY1207: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1207 @ SY1206 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1207 @ SY1205 @ SY1204 @ SY1203 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1207 @ SY1206 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1207 @ SY1203 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1207 @ SY1206 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1207 @ SY1205 @ ( c_Com_Ocom_OSemi @ SY1204 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1207 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5793]) ).

thf(5955,plain,
    ! [SV86: $i,SV247: $i] :
      ( ( ! [SY1208: $i,SY1209: $i,SY1210: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SY1209 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SY1208 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1210 @ tc_HOL_Obool ) ) ) )
                   != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1210 @ tc_HOL_Obool ) ) ) ) )
                  | ~ ( ( SY1209 != SV247 )
                      | ( SY1208 != SV86 ) )
                  | ~ ( ( SY1209 != SV86 )
                      | ( SY1208 != SV247 ) ) )
              | ~ ( ~ ( ~ ( ( SY1209 != SV247 )
                          | ( SY1208 != SV86 ) )
                      | ~ ( ( SY1209 != SV86 )
                          | ( SY1208 != SV247 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SY1209 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SY1208 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1210 @ tc_HOL_Obool ) ) ) )
                    = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1210 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1210 @ tc_HOL_Obool ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5794]) ).

thf(5956,plain,
    ! [SV87: $i,SV248: $i] :
      ( ( ! [SY1211: $i,SY1212: $i,SY1213: $i,SY1214: $i,SY1215: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1215 @ SY1214 @ SY1213 @ SY1212 ) @ SY1211 )
             != SV248 )
            | ( ( hAPP @ SY1212 @ ( hAPP @ SY1211 @ SV87 ) )
              = ( hAPP @ SV248 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5795]) ).

thf(5957,plain,
    ! [SV88: $i,SV249: $i] :
      ( ( ~ ( class_Lattices_Obounded__lattice @ SV249 )
        | ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV88 @ SV249 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5796]) ).

thf(5958,plain,
    ! [SV89: $i,SV250: $i] :
      ( ( ! [SY1216: $i,SY1217: $i,SY1218: $i,SY1219: $i,SY1220: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1220 @ SY1219 @ SY1218 @ SY1217 @ SY1216 )
            | ~ ( ~ ( ( ( hAPP @ SY1218 @ SV250 )
                     != ( hAPP @ SY1218 @ SV89 ) )
                    | ( SV250 = SV89 ) )
                | ~ ( ( SV250 != SV89 )
                    | ( ( hAPP @ SY1218 @ SV250 )
                      = ( hAPP @ SY1218 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5797]) ).

thf(5959,plain,
    ! [SV90: $i,SV251: $i] :
      ( ( ! [SY1221: $i] :
            ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1221 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                   != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1221 ) @ SV251 ) @ SV90 ) )
                  | ( SV251
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1221 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV251
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1221 @ tc_HOL_Obool ) ) )
                  | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1221 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                    = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1221 ) @ SV251 ) @ SV90 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5798]) ).

thf(5960,plain,
    ! [SV91: $i,SV252: $i] :
      ( ( c_Com_Ocom_OSKIP
       != ( c_Com_Ocom_OAss @ SV252 @ SV91 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5799]) ).

thf(5961,plain,
    ! [SV92: $i,SV253: $i] :
      ( ( c_Com_Ocom_OSKIP
       != ( c_Com_Ocom_OSemi @ SV253 @ SV92 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5800]) ).

thf(5962,plain,
    ! [SV93: $i,SV254: $i] :
      ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV254 )
        | ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV93 @ SV254 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5801]) ).

thf(5963,plain,
    ! [SV94: $i,SV255: $i] :
      ( ( ! [SY1222: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1222 ) @ SV255 ) @ SV94 )
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1222 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5802]) ).

thf(5964,plain,
    ! [SV95: $i] :
      ( ( SV95
        = ( hAPP @ c_Nat_OSuc @ SV95 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5803]) ).

thf(5965,plain,
    ! [SV96: $i,SV256: $i] :
      ( ( ! [SY1223: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1223 ) @ SV256 )
                   != SV96 )
                  | ( SV256
                    = ( hAPP @ ( c_List_Orev @ SY1223 ) @ SV96 ) ) )
              | ~ ( ( SV256
                   != ( hAPP @ ( c_List_Orev @ SY1223 ) @ SV96 ) )
                  | ( ( hAPP @ ( c_List_Orev @ SY1223 ) @ SV256 )
                    = SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5804]) ).

thf(5966,plain,
    ! [SV97: $i,SV257: $i] :
      ( ( ! [SY1224: $i] :
            ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY1224 @ SV257 @ SV97 )
            | ( SV97 = SY1224 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5805]) ).

thf(5967,plain,
    ! [SV98: $i,SV258: $i] :
      ( ( ~ ( class_Lattices_Oboolean__algebra @ SV258 )
        | ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV98 @ SV258 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5806]) ).

thf(5968,plain,
    ! [SV99: $i,SV259: $i] :
      ( ( ! [SY1225: $i,SY1226: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1226 ) @ SY1225 ) @ SV259 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1226 ) @ SV99 ) @ SV259 ) )
                  | ( SY1225 = SV99 ) )
              | ~ ( ( SY1225 != SV99 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1226 ) @ SY1225 ) @ SV259 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1226 ) @ SV99 ) @ SV259 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5807]) ).

thf(5969,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
                 != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
                | ( SV260 = SV100 ) )
            | ~ ( ( SV260 != SV100 )
                | ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
                  = ( hAPP @ c_Int_ORep__Integ @ SV100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5808]) ).

thf(5970,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
                 != ( hAPP @ c_Nat_OSuc @ SV101 ) )
                | ( SV261 = SV101 ) )
            | ~ ( ( SV261 != SV101 )
                | ( ( hAPP @ c_Nat_OSuc @ SV261 )
                  = ( hAPP @ c_Nat_OSuc @ SV101 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5809]) ).

thf(5971,plain,
    ! [SV102: $i,SV262: $i] :
      ( ( ! [SY1227: $i,SY1228: $i,SY1229: $i,SY1230: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm @ SY1230 @ SY1229 @ SY1228 )
            | ( ( hAPP @ ( hAPP @ SY1228 @ SY1227 ) @ ( hAPP @ ( hAPP @ SY1228 @ SV262 ) @ SV102 ) )
              = ( hAPP @ ( hAPP @ SY1228 @ SV262 ) @ ( hAPP @ ( hAPP @ SY1228 @ SY1227 ) @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5810]) ).

thf(5972,plain,
    ! [SV103: $i,SV263: $i] :
      ( ( ! [SY1231: $i,SY1232: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY1232 @ SY1231 @ SV263 ) @ SV103 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1231 @ tc_HOL_Obool ) ) )
                  | ( SV103
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1232 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV103
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1232 @ tc_HOL_Obool ) ) )
                  | ( ( hAPP @ ( c_Set_Oimage @ SY1232 @ SY1231 @ SV263 ) @ SV103 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1231 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5811]) ).

thf(5973,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
                 != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
                | ( SV264 = SV104 ) )
            | ~ ( ( SV264 != SV104 )
                | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
                  = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5812]) ).

thf(5974,plain,
    ! [SV105: $i,SV265: $i] :
      ( ( ! [SY1233: $i,SY1234: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1234 @ SY1233 @ SV265 )
            | ( ( hAPP @ ( hAPP @ SY1233 @ SV105 ) @ SV105 )
              = SV105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5813]) ).

thf(5975,plain,
    ! [SV106: $i,SV266: $i] :
      ( ( ! [SY1235: $i,SY1236: $i] :
            ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1236 @ tc_HOL_Obool ) )
                   != ( hAPP @ ( c_Set_Oimage @ SY1235 @ SY1236 @ SV266 ) @ SV106 ) )
                  | ( SV106
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1235 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV106
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1235 @ tc_HOL_Obool ) ) )
                  | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1236 @ tc_HOL_Obool ) )
                    = ( hAPP @ ( c_Set_Oimage @ SY1235 @ SY1236 @ SV266 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5814]) ).

thf(5976,plain,
    ! [SV107: $i] :
      ( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV107 @ tc_HOL_Obool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV107 @ tc_HOL_Obool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5815]) ).

thf(5977,plain,
    ! [SV108: $i,SV267: $i] :
      ( ( ! [SY1237: $i,SY1238: $i,SY1239: $i,SY1240: $i,SY1241: $i,SY1242: $i,SY1243: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1243 @ SY1242 @ SY1241 @ SY1240 ) @ SY1239 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1238 @ SY1242 @ SY1241 @ SY1237 ) @ SV267 ) )
            | ( ( hAPP @ SY1240 @ ( hAPP @ SY1239 @ SV108 ) )
              = ( hAPP @ SY1237 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5816]) ).

thf(5978,plain,
    ! [SV109: $i,SV268: $i] :
      ( ( ! [SY1244: $i,SY1245: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1245 @ SY1244 @ SV268 )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1245 @ SV109 @ SY1244 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1245 @ SV109 @ SV268 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5817]) ).

thf(5979,plain,
    ! [SV110: $i,SV269: $i] :
      ( ( ( c_Com_Ocom_OWhile @ SV269 @ SV110 )
       != c_Com_Ocom_OSKIP )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5818]) ).

thf(5980,plain,
    ! [SV111: $i,SV270: $i] :
      ( ( ! [SY1246: $i] :
            ( ~ ( class_Orderings_Obot @ SY1246 )
            | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV270 @ SY1246 ) ) @ SV111 )
              = ( c_Orderings_Obot__class_Obot @ SY1246 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5819]) ).

thf(5981,plain,
    ! [SV112: $i,SV271: $i] :
      ( ( ~ ( class_Orderings_Opreorder @ SV271 )
        | ( class_Orderings_Opreorder @ ( tc_fun @ SV112 @ SV271 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5820]) ).

thf(5982,plain,
    ! [SV113: $i,SV272: $i] :
      ( ( ! [SY1247: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1247 ) @ SV272 ) @ SV113 )
           != SV113 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5821]) ).

thf(5983,plain,
    ! [SV114: $i,SV273: $i] :
      ( ( ~ ! [SY1248: $i] :
              ( ( hAPP @ SV273 @ SY1248 )
              = ( hAPP @ SV114 @ SY1248 ) )
        | ( SV273 = SV114 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5822]) ).

thf(5984,plain,
    ! [SV115: $i,SV274: $i] :
      ( ( ! [SY1249: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1249 ) @ SV274 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1249 @ tc_HOL_Obool ) ) )
             != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1249 ) @ SV115 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1249 @ tc_HOL_Obool ) ) ) )
            | ( SV274 = SV115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5823]) ).

thf(5985,plain,
    ! [SV116: $i,SV275: $i] :
      ( ( ~ ( class_Orderings_Obot @ SV275 )
        | ( class_Orderings_Obot @ ( tc_fun @ SV116 @ SV275 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5824]) ).

thf(5986,plain,
    ! [SV117: $i] :
      ( ( ( hAPP @ c_Nat_OSuc @ SV117 )
        = SV117 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5825]) ).

thf(5987,plain,
    ! [SV118: $i,SV276: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV276 )
        | ( class_Orderings_Oord @ ( tc_fun @ SV118 @ SV276 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5826]) ).

thf(5988,plain,
    ! [SV119: $i,SV277: $i] :
      ( ( ! [SY1250: $i,SY1251: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one @ SY1251 @ SY1250 @ SV277 )
            | ( ( hAPP @ SV277 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1251 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1251 @ tc_HOL_Obool ) ) ) )
              = SV119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5827]) ).

thf(5989,plain,
    ! [SV120: $i,SV278: $i] :
      ( ( ! [SY1252: $i] :
            ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1252 @ tc_HOL_Obool ) )
           != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1252 ) @ SV278 ) @ SV120 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5828]) ).

thf(5990,plain,
    ! [SV121: $i,SV279: $i] :
      ( ( c_Com_Ocom_OSKIP
       != ( c_Com_Ocom_OWhile @ SV279 @ SV121 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5829]) ).

thf(5991,plain,
    ! [SV122: $i,SV280: $i] :
      ( ( ! [SY1253: $i,SY1254: $i,SY1255: $i] :
            ( ( ( hAPP @ SY1255 @ SY1254 )
             != SY1253 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SY1255 ) @ SY1254 ) @ SY1253 )
              = SY1255 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5830]) ).

thf(5992,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
                 != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
                | ( SV281 = SV123 ) )
            | ~ ( ( SV281 != SV123 )
                | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
                  = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5831]) ).

thf(5993,plain,
    ! [SV124: $i,SV282: $i] :
      ( ( ! [SY1256: $i] :
            ( SY1256
           != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV282 ) @ SV124 ) @ SY1256 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5832]) ).

thf(5994,plain,
    ! [SV125: $i,SV283: $i] :
      ( ( ( c_Com_Ocom_OAss @ SV283 @ SV125 )
       != c_Com_Ocom_OSKIP )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5833]) ).

thf(5995,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV284 )
              | ~ ( class_Finite__Set_Ofinite @ SV126 ) )
        | ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5834]) ).

thf(5996,plain,
    ! [SV127: $i,SV285: $i] :
      ( ( ( hAPP @ ( c_Set_OPow @ SV285 ) @ SV127 )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV285 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5835]) ).

thf(5997,plain,
    ! [SV128: $i,SV286: $i] :
      ( ( ! [SY1257: $i,SY1258: $i,SY1259: $i,SY1260: $i,SY1261: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1261 @ SY1260 @ SY1259 @ SY1258 @ SY1257 @ SV286 )
            | ( ( hAPP @ ( hAPP @ SY1259 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5836]) ).

thf(5998,plain,
    ! [SV129: $i,SV287: $i] :
      ( ( ! [SY1262: $i,SY1263: $i,SY1264: $i,SY1265: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple @ SY1265 @ SY1264 @ SY1263 @ SY1262 @ SV287 @ SV129 )
            | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1264 @ tc_HOL_Obool ) ) )
              = SY1262 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5837]) ).

thf(5999,plain,
    ! [SV130: $i,SV288: $i] :
      ( ( ! [SY1266: $i,SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i] :
            ( ~ ( ( SY1270 != SY1269 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1268 @ SY1267 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1268 @ SY1267 ) @ SY1266 ) @ SY1270 ) @ SV288 ) ) @ SY1269 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1268 @ SY1267 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1268 @ SY1267 ) @ SY1266 ) @ SY1269 ) @ SV130 ) ) @ SY1270 ) @ SV288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5838]) ).

thf(6000,plain,
    ! [SV131: $i,SV289: $i] :
      ( ( ( c_Com_Ocom_OSemi @ SV289 @ SV131 )
       != c_Com_Ocom_OSKIP )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5839]) ).

thf(6001,plain,
    ! [SV132: $i,SV290: $i] :
      ( ( ! [SY1271: $i,SY1272: $i,SY1273: $i,SY1274: $i] :
            ~ ( ~ ( ( SY1274 != SY1273 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1272 @ SY1271 ) @ SV290 ) @ SY1273 ) @ SV132 ) @ SY1274 )
                    = SV132 ) )
              | ~ ( ~ ( ( SY1274 != SY1273 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1272 @ SY1271 ) @ SV290 ) @ SY1273 ) @ SV132 ) @ SY1274 )
                    = ( hAPP @ SV290 @ SY1274 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5840]) ).

thf(6002,plain,
    ! [SV133: $i,SV291: $i] :
      ( ( ! [SY1275: $i,SY1276: $i,SY1277: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1276 ) @ SY1275 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SV291 ) @ SV133 ) )
                  | ~ ! [SY1278: $i] :
                        ~ ( ~ ( ( SY1276
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SV291 ) @ SY1278 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1278 ) @ SY1275 )
                               != SV133 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1276 ) @ SY1278 )
                               != SV291 )
                              | ( SY1275
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1278 ) @ SV133 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1279: $i] :
                          ~ ( ~ ( ( SY1276
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SV291 ) @ SY1279 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1279 ) @ SY1275 )
                                 != SV133 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1276 ) @ SY1279 )
                                 != SV291 )
                                | ( SY1275
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1279 ) @ SV133 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SY1276 ) @ SY1275 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1277 ) @ SV291 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5841]) ).

thf(6003,plain,
    ! [SV134: $i,SV292: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV292 )
        | ( class_Orderings_Oorder @ ( tc_fun @ SV134 @ SV292 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5842]) ).

thf(6004,plain,
    ! [SV135: $i,SV293: $i] :
      ( ( ! [SY1280: $i,SY1281: $i,SY1282: $i,SY1283: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1283 @ SY1282 ) @ SY1281 ) @ SY1280 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1283 @ SY1282 ) @ SV293 ) @ SV135 ) )
            | ~ ( ( SY1281 != SV293 )
                | ( SY1280 != SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5843]) ).

thf(6005,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV294 )
              | ~ ( class_Enum_Oenum @ SV136 ) )
        | ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5844]) ).

thf(6006,plain,
    ! [SV137: $i,SV295: $i] :
      ( ( ! [SY1284: $i,SY1285: $i,SY1286: $i,SY1287: $i] :
            ( ~ ( ( SY1287 != SY1286 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1285 @ SY1284 ) @ SV295 ) @ SY1286 ) @ SV137 ) @ SY1287 )
              = ( hAPP @ SV295 @ SY1287 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5845]) ).

thf(6007,plain,
    ! [SV138: $i,SV296: $i] :
      ( ( ! [SY1288: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) )
                  | ~ ( ( SV296
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) )
                      | ( SV138
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) ) ) )
              | ~ ( ~ ~ ( ( SV296
                         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) )
                        | ( SV138
                         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1288 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5846]) ).

thf(6008,plain,
    ! [SV139: $i,SV297: $i] :
      ( ( ! [SY1289: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OCond @ SY1289 @ SV297 @ SV139 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5847]) ).

thf(6009,plain,
    ! [SV140: $i,SV298: $i] :
      ( ( ! [SY1290: $i,SY1291: $i,SY1292: $i,SY1293: $i,SY1294: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1294 @ SY1293 @ SY1292 @ SY1291 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1294 @ SY1290 @ SV298 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SY1293 != SY1290 )
                            | ( SY1292 != SV298 ) )
                      | ( SY1291 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1293 != SY1290 )
                              | ( SY1292 != SV298 ) )
                        | ( SY1291 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1294 @ SY1293 @ SY1292 @ SY1291 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1294 @ SY1290 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5848]) ).

thf(6010,plain,
    ! [SV141: $i,SV299: $i] :
      ( ( ~ ( class_Orderings_Otop @ SV299 )
        | ( class_Orderings_Otop @ ( tc_fun @ SV141 @ SV299 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5849]) ).

thf(6011,plain,
    ! [SV142: $i,SV300: $i] :
      ( ( ! [SY1295: $i,SY1296: $i,SY1297: $i,SY1298: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1298 @ SY1297 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1298 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1298 @ SY1296 @ SY1295 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1298 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY982: $i,SY983: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY982 ) @ SY983 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SY1296 @ SY982 ) @ SY983 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1298 @ SY1297 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1298 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1298 @ SV142 @ SY1295 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1298 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5850]) ).

thf(6012,plain,
    ! [SV143: $i,SV301: $i] :
      ( ( ~ ( class_Lattices_Odistrib__lattice @ SV301 )
        | ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV143 @ SV301 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5851]) ).

thf(6013,plain,
    ! [SV144: $i,SV302: $i] :
      ( ( ~ ( class_Groups_Ominus @ SV302 )
        | ( class_Groups_Ominus @ ( tc_fun @ SV144 @ SV302 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5852]) ).

thf(6014,plain,
    ! [SV145: $i,SV303: $i] :
      ( ( ~ ( class_Lattices_Olattice @ SV303 )
        | ( class_Lattices_Olattice @ ( tc_fun @ SV145 @ SV303 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5853]) ).

thf(6015,plain,
    ! [SV146: $i,SV304: $i] :
      ( ( ! [SY1301: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1301 ) @ SV304 )
                   != ( hAPP @ ( c_Option_Ooption_OSome @ SY1301 ) @ SV146 ) )
                  | ( SV304 = SV146 ) )
              | ~ ( ( SV304 != SV146 )
                  | ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1301 ) @ SV304 )
                    = ( hAPP @ ( c_Option_Ooption_OSome @ SY1301 ) @ SV146 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5854]) ).

thf(6016,plain,
    ! [SV147: $i,SV305: $i] :
      ( ( ! [SY1302: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1302 ) @ SV305 )
                   != ( hAPP @ ( c_List_Orev @ SY1302 ) @ SV147 ) )
                  | ( SV305 = SV147 ) )
              | ~ ( ( SV305 != SV147 )
                  | ( ( hAPP @ ( c_List_Orev @ SY1302 ) @ SV305 )
                    = ( hAPP @ ( c_List_Orev @ SY1302 ) @ SV147 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5855]) ).

thf(6017,plain,
    ! [SV148: $i,SV306: $i] :
      ( ( ! [SY1303: $i,SY1304: $i,SY1305: $i,SY1306: $i,SY1307: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1307 @ SY1306 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1307 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1307 @ SY1305 @ SY1304 @ SY1303 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1307 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1308: $i,SY1309: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1308 ) @ SY1309 ) )
                  | ! [SY999: $i] :
                      ( ~ ! [SX10: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1305 @ SX10 ) @ SY1309 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SY1303 @ SX10 ) @ SY999 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1308 ) @ SY999 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1307 @ SY1306 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1307 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1307 @ SV306 @ SY1304 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1307 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5856]) ).

thf(6018,plain,
    ! [SV149: $i,SV307: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV307 )
         != ( hAPP @ c_Nat_OSuc @ SV149 ) )
        | ( SV307 = SV149 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5857]) ).

thf(6019,plain,
    ! [SV150: $i,SV308: $i] :
      ( ( ! [SY1312: $i,SY1313: $i,SY1314: $i,SY1315: $i,SY1316: $i,SY1317: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1317 @ SY1316 @ SY1315 @ SY1314 ) @ SY1313 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1312 @ SY1316 @ SY1315 @ SV308 ) @ SV150 ) )
            | ! [SY1318: $i] :
                ( ( hAPP @ SY1314 @ ( hAPP @ SY1313 @ SY1318 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5858]) ).

thf(6020,plain,
    ! [SV151: $i,SV309: $i] :
      ( ( ! [SY1319: $i,SY1320: $i,SY1321: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1321 @ SY1320 @ SY1319 )
            | ( ( hAPP @ ( hAPP @ SY1319 @ SV309 ) @ ( hAPP @ ( hAPP @ SY1319 @ SV309 ) @ SV151 ) )
              = ( hAPP @ ( hAPP @ SY1319 @ SV309 ) @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5859]) ).

thf(6021,plain,
    ! [SV152: $i,SV310: $i] :
      ( ( ! [SY1322: $i,SY1323: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1323 @ SY1322 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1323 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1323 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1323 @ SY1322 @ SV152 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1323 @ SY1322 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1323 ) ) @ SV310 ) @ SV152 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5860]) ).

thf(6022,plain,
    ! [SV153: $i,SV311: $i] :
      ( ( ! [SY1324: $i,SY1325: $i,SY1326: $i,SY1327: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1327 ) @ SY1326 ) @ SY1325 )
             != SY1324 )
            | ( SV311
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1327 ) @ SY1325 ) @ SV153 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1327 ) @ SY1326 ) @ SV311 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1327 ) @ SY1324 ) @ SV153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5861]) ).

thf(6023,plain,
    ! [SV154: $i,SV312: $i] :
      ( ( ! [SY1328: $i,SY1329: $i,SY1330: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1330 ) @ SY1329 ) @ SY1328 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1330 ) @ SV312 ) @ SV154 ) )
                  | ~ ( ( SY1329 != SV312 )
                      | ( SY1328 != SV154 ) ) )
              | ~ ( ~ ~ ( ( SY1329 != SV312 )
                        | ( SY1328 != SV154 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1330 ) @ SY1329 ) @ SY1328 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1330 ) @ SV312 ) @ SV154 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5862]) ).

thf(6024,plain,
    ! [SV155: $i,SV313: $i] :
      ( ( ~ ( class_Groups_Ouminus @ SV313 )
        | ( class_Groups_Ouminus @ ( tc_fun @ SV155 @ SV313 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5863]) ).

thf(6025,plain,
    ! [SV156: $i,SV314: $i] :
      ( ( ! [SY1331: $i,SY1332: $i,SY1333: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ SY1331 ) @ SV314 ) @ SV156 )
                   != SY1331 )
                  | ( ( hAPP @ SY1331 @ SV314 )
                    = SV156 ) )
              | ~ ( ( ( hAPP @ SY1331 @ SV314 )
                   != SV156 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1333 @ SY1332 ) @ SY1331 ) @ SV314 ) @ SV156 )
                    = SY1331 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5864]) ).

thf(6026,plain,
    ! [SV157: $i,SV315: $i] :
      ( ( ! [SY1334: $i] :
            ( ~ ( class_Orderings_Obot @ SY1334 )
            | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ SY1334 ) ) @ SV157 )
              = ( c_Orderings_Obot__class_Obot @ SY1334 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5865]) ).

thf(6027,plain,
    ! [SV158: $i,SV316: $i] :
      ( ( ! [SY1335: $i] :
            ( ( c_Com_Ocom_OCond @ SY1335 @ SV316 @ SV158 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5866]) ).

thf(6028,plain,
    ! [SV159: $i,SV317: $i] :
      ( ( ! [SY1336: $i] :
            ( ( c_Com_Ocom_OLocal @ SY1336 @ SV317 @ SV159 )
           != c_Com_Ocom_OSKIP ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5867]) ).

thf(6029,plain,
    ! [SV160: $i,SV318: $i] :
      ( ( ! [SY1337: $i,SY1338: $i,SY1339: $i,SY1340: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1340 @ SY1339 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1340 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1340 @ SY1338 @ SY1337 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1340 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1341: $i,SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1340 @ SY1339 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1340 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1340 @ SY1338 @ SY1337 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1340 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5868]) ).

thf(6030,plain,
    ! [SV161: $i,SV319: $i] :
      ( ( ! [SY1343: $i] :
            ( c_Com_Ocom_OSKIP
           != ( c_Com_Ocom_OLocal @ SY1343 @ SV319 @ SV161 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5869]) ).

thf(6031,plain,
    ! [SV162: $i,SV320: $i] :
      ( ( ! [SY1344: $i,SY1345: $i,SY1346: $i,SY1347: $i] :
            ~ ( ~ ( ( SY1347 != SY1346 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1345 @ SY1344 ) @ SV320 ) @ SY1346 ) @ SV162 ) @ SY1347 )
                    = SV162 ) )
              | ~ ( ~ ( ( SY1347 != SY1346 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1345 @ SY1344 ) @ SV320 ) @ SY1346 ) @ SV162 ) @ SY1347 )
                    = ( hAPP @ SV320 @ SY1347 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5870]) ).

thf(6032,plain,
    ! [SV163: $i,SV321: $i] :
      ( ( ! [SY1348: $i,SY1349: $i] :
            ( ( SY1349
             != ( c_Finite__Set_Ofold1 @ SY1348 @ SV321 ) )
            | ( ( hAPP @ SY1349 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1348 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1348 @ tc_HOL_Obool ) ) ) )
              = SV163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5871]) ).

thf(6033,plain,
    ! [SV164: $i,SV322: $i] :
      ( ( ! [SY1350: $i,SY1351: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1351 ) @ SY1350 ) @ SV322 ) @ SV164 ) )
                  | ( SY1350 = SV164 )
                  | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
              | ~ ( ~ ( ( SY1350 = SV164 )
                      | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1351 ) @ SY1350 ) @ SV322 ) @ SV164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5872]) ).

thf(6034,plain,
    ! [SV165: $i,SV323: $i] :
      ( ( ! [SY1352: $i,SY1353: $i,SY1354: $i,SY1355: $i] :
            ( ( SY1355 != SY1354 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1353 @ SY1352 @ SV323 ) @ SV165 ) @ SY1355 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1353 @ SY1352 @ SV323 ) @ SV165 ) @ SY1354 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5873]) ).

thf(6035,plain,
    ! [SV166: $i,SV324: $i] :
      ( ( ! [SY1356: $i,SY1357: $i,SY1358: $i,SY1359: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1359 @ SY1358 @ SY1357 @ SY1356 @ SV324 )
            | ( ( hAPP @ SY1356 @ ( hAPP @ SY1357 @ SV166 ) )
              = SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5874]) ).

thf(6036,plain,
    ! [SV2: $i,SV168: $i,SV325: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ SV168 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV325 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV325 @ SV2 @ c_Com_Ocom_OSKIP @ SV2 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV325 ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5876]) ).

thf(6037,plain,
    ! [SV4: $i,SV170: $i,SV326: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ SV170 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV326 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV326 @ SV4 @ c_Com_Ocom_OSKIP @ SV4 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV326 ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5878]) ).

thf(6038,plain,
    ! [SV5: $i,SV171: $i,SV327: $i] :
      ( ( ! [SY1360: $i,SY1361: $i,SY1362: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SY1362 @ SY1361 @ SY1360 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1362 @ SV327 @ SV171 @ SV5 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY1360 @ SV327 ) @ SV171 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5879]) ).

thf(6039,plain,
    ! [SV6: $i,SV172: $i,SV328: $i] :
      ( ( ! [SY1363: $i,SY1364: $i,SY1365: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY1365 @ SY1364 @ SY1363 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1365 @ SV328 @ SV172 @ SV6 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SY1363 @ SV328 ) @ SV172 ) @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5880]) ).

thf(6040,plain,
    ! [SV7: $i,SV173: $i,SV329: $i] :
      ( ( ! [SY1366: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1366 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1366 ) @ SV173 ) @ SV7 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1366 ) @ SV173 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1366 ) @ SV329 ) @ SV7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5881]) ).

thf(6041,plain,
    ! [SV8: $i,SV174: $i,SV330: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV330 ) @ SV174 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV330 ) @ SV174 ) @ SV8 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV330 ) @ SV174 ) @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5882]) ).

thf(6042,plain,
    ! [SV10: $i,SV176: $i,SV331: $i] :
      ( ( ! [SY1367: $i,SY1368: $i,SY1369: $i,SY1370: $i,SY1371: $i,SY1372: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SY1368 @ SY1367 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1371 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5884]) ).

thf(6043,plain,
    ! [SV11: $i,SV177: $i,SV332: $i] :
      ( ( ! [SY1373: $i,SY1374: $i,SY1375: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1375 @ SY1374 @ SY1373 @ SV332 ) @ SV177 ) @ SV11 )
            = ( hAPP @ SV332 @ ( hAPP @ SV177 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5885]) ).

thf(6044,plain,
    ! [SV14: $i,SV180: $i,SV333: $i] :
      ( ( ! [SY1376: $i,SY1377: $i,SY1378: $i,SY1379: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1379 @ SY1378 @ SY1377 @ SY1376 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1379 @ SY1377 @ SV180 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1378 @ SY1377 @ ( hAPP @ ( c_Fun_Ocomp @ SY1379 @ SY1378 @ SV333 @ SY1376 ) @ SV180 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5888]) ).

thf(6045,plain,
    ! [SV15: $i,SV181: $i,SV334: $i] :
      ( ( ! [SY1380: $i,SY1381: $i,SY1382: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1382 @ SY1381 @ SY1380 @ SV334 ) @ SV181 ) @ SV15 )
            = ( hAPP @ SV334 @ ( hAPP @ SV181 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5889]) ).

thf(6046,plain,
    ! [SV16: $i,SV182: $i,SV335: $i] :
      ( ( ! [SY1383: $i] :
            ( ( c_Fun_Ooverride__on @ SY1383 @ SV335 @ SV182 @ SV16 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1383 @ tc_HOL_Obool ) ) )
            = SV182 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5890]) ).

thf(6047,plain,
    ! [SV20: $i,SV185: $i,SV336: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV336 @ tc_HOL_Obool ) ) @ SV185 ) @ SV20 )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV336 @ tc_HOL_Obool ) ) @ SV20 ) @ SV185 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5893]) ).

thf(6048,plain,
    ! [SV21: $i,SV186: $i,SV337: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV337 @ tc_HOL_Obool ) ) @ SV186 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV337 @ tc_HOL_Obool ) ) @ SV186 ) @ SV21 ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV337 @ tc_HOL_Obool ) ) @ SV186 ) @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5894]) ).

thf(6049,plain,
    ! [SV22: $i,SV187: $i,SV338: $i] :
      ( ( ! [SY1384: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SV338 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SV187 ) @ SV22 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SV187 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SV338 ) @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5895]) ).

thf(6050,plain,
    ! [SV23: $i,SV188: $i,SV339: $i] :
      ( ( ! [SY1385: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SV339 ) @ SV188 ) ) @ SV23 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SV339 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) @ SV188 ) @ SV23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5896]) ).

thf(6051,plain,
    ! [SV24: $i,SV189: $i,SV340: $i] :
      ( ( ( hAPP @ ( c_Set_Oimage @ SV340 @ SV189 @ SV24 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV340 @ tc_HOL_Obool ) ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5897]) ).

thf(6052,plain,
    ! [SV25: $i,SV190: $i,SV341: $i] :
      ( ( ! [SY1386: $i,SY1387: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY1387 @ SY1386 @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1387 ) @ SV190 ) @ SV25 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1386 ) @ ( hAPP @ SV341 @ SV190 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1387 @ SY1386 @ SV341 ) @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5898]) ).

thf(6053,plain,
    ! [SV28: $i,SV193: $i,SV342: $i] :
      ( ( ! [SY1388: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1388 @ tc_HOL_Obool ) ) @ SV342 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1388 ) @ SV193 ) @ SV28 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1388 ) @ SV193 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1388 @ tc_HOL_Obool ) ) @ SV342 ) @ SV28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5901]) ).

thf(6054,plain,
    ! [SV29: $i,SV194: $i,SV343: $i] :
      ( ( ! [SY1389: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1389 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1389 ) @ SV343 ) @ SV194 ) ) @ SV29 )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1389 ) @ SV343 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1389 @ tc_HOL_Obool ) ) @ SV194 ) @ SV29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5902]) ).

thf(6055,plain,
    ! [SV30: $i,SV195: $i,SV344: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV344 ) @ SV195 ) @ SV30 )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV344 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV344 ) @ SV195 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV344 @ tc_HOL_Obool ) ) ) ) @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5903]) ).

thf(6056,plain,
    ! [SV32: $i,SV197: $i,SV345: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) @ SV197 ) @ SV32 )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) @ SV32 ) @ SV197 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5905]) ).

thf(6057,plain,
    ! [SV33: $i,SV198: $i,SV346: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV346 @ tc_HOL_Obool ) ) @ SV198 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV346 @ tc_HOL_Obool ) ) @ SV198 ) @ SV33 ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV346 @ tc_HOL_Obool ) ) @ SV198 ) @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5906]) ).

thf(6058,plain,
    ! [SV34: $i,SV199: $i,SV347: $i] :
      ( ( ! [SY1390: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1390 @ tc_HOL_Obool ) ) @ SV347 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1390 @ tc_HOL_Obool ) ) @ SV199 ) @ SV34 ) )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1390 @ tc_HOL_Obool ) ) @ SV199 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1390 @ tc_HOL_Obool ) ) @ SV347 ) @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5907]) ).

thf(6059,plain,
    ! [SV35: $i,SV200: $i,SV348: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV348 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV348 @ tc_HOL_Obool ) ) @ SV200 ) @ SV35 ) ) @ SV35 )
        = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV348 @ tc_HOL_Obool ) ) @ SV200 ) @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5908]) ).

thf(6060,plain,
    ! [SV36: $i,SV201: $i,SV349: $i] :
      ( ( ! [SY1391: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) ) @ SV349 ) @ SV201 ) ) @ SV36 )
            = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) ) @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) ) @ SV201 ) @ SV36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5909]) ).

thf(6061,plain,
    ! [SV42: $i,SV207: $i,SV350: $i] :
      ( ( ! [SY1392: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1392 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1392 ) @ SV350 ) @ SV207 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1392 ) @ SV350 ) @ SV42 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1392 ) @ SV350 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1392 @ tc_HOL_Obool ) ) @ SV207 ) @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5915]) ).

thf(6062,plain,
    ! [SV43: $i,SV208: $i,SV351: $i] :
      ( ( ! [SY1393: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1393 @ tc_HOL_Obool ) ) @ SV351 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1393 ) @ SV208 ) @ SV43 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1393 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1393 @ tc_HOL_Obool ) ) @ SV351 ) @ SV43 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1393 ) @ SV208 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1393 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5916]) ).

thf(6063,plain,
    ! [SV44: $i,SV209: $i,SV352: $i] :
      ( ( ! [SY1394: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1394 @ tc_HOL_Obool ) ) @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1394 ) @ SV209 ) @ SV44 ) )
            = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1394 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1394 @ tc_HOL_Obool ) ) @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1394 ) @ SV209 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1394 @ tc_HOL_Obool ) ) ) ) ) @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5917]) ).

thf(6064,plain,
    ! [SV45: $i,SV210: $i,SV353: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV353 ) @ SV210 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV353 @ tc_HOL_Obool ) ) @ SV45 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV353 ) @ SV210 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV353 @ tc_HOL_Obool ) ) ) ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV353 ) @ SV210 ) @ SV45 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5918]) ).

thf(6065,plain,
    ! [SV46: $i,SV211: $i,SV354: $i] :
      ( ( ! [SY1395: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1395 @ SV354 ) @ SV211 ) @ SV46 ) @ ( hAPP @ SV211 @ SV46 ) )
            = SV211 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5919]) ).

thf(6066,plain,
    ! [SV47: $i,SV212: $i,SV355: $i] :
      ( ( ! [SY1396: $i,SY1397: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1397 @ SY1396 ) @ SV355 ) @ SV212 ) @ SV47 ) @ SV212 )
            = SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5920]) ).

thf(6067,plain,
    ! [SV48: $i,SV213: $i,SV356: $i] :
      ( ( ! [SY1398: $i,SY1399: $i,SY1400: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1400 @ SY1399 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1400 @ SY1399 ) @ SY1398 ) @ SV356 ) @ SV213 ) ) @ SV356 ) @ SV48 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1400 @ SY1399 ) @ SY1398 ) @ SV356 ) @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5921]) ).

thf(6068,plain,
    ! [SV49: $i,SV214: $i,SV357: $i] :
      ( ( ! [SY1401: $i] : ( c_Nitpick_Ofold__graph_H @ SY1401 @ SV357 @ SV214 @ SV49 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1401 @ tc_HOL_Obool ) ) @ SV49 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5922]) ).

thf(6069,plain,
    ! [SV50: $i,SV215: $i,SV358: $i] :
      ( ( ! [SY1402: $i] : ( c_Nitpick_Ofold__graph_H @ SY1402 @ SV358 @ SV215 @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1402 @ tc_HOL_Obool ) ) @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5923]) ).

thf(6070,plain,
    ! [SV51: $i,SV216: $i,SV359: $i] :
      ( ( c_Fun_Oinj__on @ SV359 @ SV216 @ SV51 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV359 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5924]) ).

thf(6071,plain,
    ! [SV55: $i,SV219: $i,SV360: $i] :
      ( ( ( hAPP @ ( c_Relation_OImage @ SV360 @ SV219 @ SV55 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV360 @ tc_HOL_Obool ) ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV219 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5927]) ).

thf(6072,plain,
    ! [SV56: $i,SV220: $i,SV361: $i] :
      ( ( ! [SY1403: $i] :
            ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1403 @ ( tc_fun @ SV361 @ tc_HOL_Obool ) ) ) @ SV220 ) @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5928]) ).

thf(6073,plain,
    ! [SV57: $i,SV221: $i,SV362: $i] :
      ( ( ! [SY1404: $i,SY1405: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY1405 @ SY1404 @ SV362 ) @ SV221 ) @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1404 @ tc_HOL_Obool ) ) )
            = SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5929]) ).

thf(6074,plain,
    ! [SV58: $i,SV222: $i,SV363: $i] :
      ( ( ( hAPP @ ( c_Set_Ovimage @ SV363 @ SV222 @ SV58 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV222 @ tc_HOL_Obool ) ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV363 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5930]) ).

thf(6075,plain,
    ! [SV59: $i,SV223: $i,SV364: $i] :
      ( ( ! [SY1406: $i,SY1407: $i,SY1408: $i,SY1409: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1409 @ SY1408 @ SY1407 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1409 @ SY1406 @ SY1408 ) @ SV364 ) @ SV223 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1409 @ SY1406 @ SY1407 ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1406 @ SY1408 @ SY1407 ) @ SV223 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5931]) ).

thf(6076,plain,
    ! [SV62: $i,SV226: $i,SV365: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ SV365 @ SV226 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV365 ) @ SV62 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV365 @ tc_HOL_Obool ) ) ) )
        = SV62 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5934]) ).

thf(6077,plain,
    ! [SV63: $i,SV227: $i,SV366: $i] :
      ( ( ! [SY1410: $i,SY1411: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1411 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1411 @ SY1410 ) @ SV366 ) @ SV227 ) ) @ SV366 ) @ SV63 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1411 @ SY1410 ) @ SV366 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5935]) ).

thf(6078,plain,
    ! [SV65: $i,SV228: $i,SV367: $i] :
      ( ( ! [SY1412: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1412 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1412 ) @ SV367 ) @ SV228 ) ) @ SV65 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1412 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1412 ) @ SV228 ) @ SV65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5936]) ).

thf(6079,plain,
    ! [SV67: $i,SV230: $i,SV368: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ SV368 @ SV230 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV230 @ SV368 ) @ SV67 ) )
        = SV67 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5938]) ).

thf(6080,plain,
    ! [SV69: $i,SV232: $i,SV369: $i] :
      ( ( ! [SY1413: $i] :
            ( ( hAPP @ SY1413 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV369 @ SV369 ) @ SV232 ) @ SY1413 ) @ SV69 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV369 @ SV369 ) @ SV232 ) @ SY1413 ) @ ( hAPP @ SY1413 @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5940]) ).

thf(6081,plain,
    ! [SV70: $i,SV233: $i,SV370: $i] :
      ( ( ! [SY1414: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY1414 @ SV370 @ SV233 ) @ SV70 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1414 @ tc_HOL_Obool ) ) )
            = SV70 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5941]) ).

thf(6082,plain,
    ! [SV74: $i,SV235: $i,SV371: $i] :
      ( ( ! [SY1415: $i] :
            ( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1415 @ SV371 ) @ SV235 ) @ SV74 )
            = SV235 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5943]) ).

thf(6083,plain,
    ! [SV75: $i,SV236: $i,SV372: $i] :
      ( ( ! [SY1416: $i,SY1417: $i,SY1418: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1418 @ SY1417 @ SY1416 ) @ SV372 ) @ SV236 ) @ SV75 )
            = ( hAPP @ SV372 @ ( hAPP @ SV236 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5944]) ).

thf(6084,plain,
    ! [SV76: $i,SV237: $i,SV373: $i] :
      ( ( ! [SY1419: $i,SY1420: $i,SY1421: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1421 @ SY1420 @ SY1419 ) @ SV373 ) @ SV237 ) @ SV76 )
            = ( hAPP @ ( hAPP @ SV373 @ SV76 ) @ SV237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5945]) ).

thf(6085,plain,
    ! [SV77: $i,SV238: $i,SV374: $i] :
      ( ( ! [SY1422: $i,SY1423: $i,SY1424: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1424 @ SY1423 @ SY1422 ) @ SV374 ) @ SV238 ) @ SV77 )
            = ( hAPP @ ( hAPP @ SV374 @ SV77 ) @ ( hAPP @ SV238 @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5946]) ).

thf(6086,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
            | ( SV239 = SV78 ) )
        | ~ ( ( SV239 != SV78 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5947]) ).

thf(6087,plain,
    ! [SV79: $i,SV240: $i,SV375: $i] :
      ( ( ! [SY1425: $i,SY1426: $i,SY1427: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1427 @ SY1426 ) @ SY1425 ) @ SV375 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1427 @ SY1426 ) @ SV240 ) @ SV79 ) )
                  | ~ ( ( SY1425 != SV240 )
                      | ( SV375 != SV79 ) ) )
              | ~ ( ~ ~ ( ( SY1425 != SV240 )
                        | ( SV375 != SV79 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1427 @ SY1426 ) @ SY1425 ) @ SV375 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1427 @ SY1426 ) @ SV240 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5948]) ).

thf(6088,plain,
    ! [SV80: $i,SV241: $i,SV376: $i] :
      ( ( ! [SY1428: $i,SY1429: $i,SY1430: $i,SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i,SY1435: $i] :
            ( ( ( hAPP @ SY1435 @ ( hAPP @ SY1434 @ SY1433 ) )
             != ( hAPP @ SY1432 @ ( hAPP @ SY1431 @ SY1430 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1429 @ SY1428 @ SV376 @ SY1435 ) @ SY1434 ) @ SY1433 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SY1428 @ SV80 @ SY1432 ) @ SY1431 ) @ SY1430 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5949]) ).

thf(6089,plain,
    ! [SV81: $i,SV242: $i,SV377: $i] :
      ( ( ! [SY1436: $i,SY1437: $i,SY1438: $i] :
            ( ~ ( ( SY1438 != SY1437 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1436 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1436 @ SV377 ) @ SY1438 ) @ SV242 ) ) @ SY1437 ) @ SV81 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1436 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1436 @ SV377 ) @ SY1437 ) @ SV81 ) ) @ SY1438 ) @ SV242 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5950]) ).

thf(6090,plain,
    ! [SV82: $i,SV243: $i,SV378: $i] :
      ( ( ! [SY1439: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1439 ) @ SV378 ) @ SV243 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1439 ) @ SV378 ) @ SV82 ) )
                  | ( SV243 = SV82 ) )
              | ~ ( ( SV243 != SV82 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1439 ) @ SV378 ) @ SV243 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1439 ) @ SV378 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5951]) ).

thf(6091,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
                 != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
                | ( SV244 = SV83 ) )
            | ~ ( ( SV244 != SV83 )
                | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
                  = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5952]) ).

thf(6092,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
                | ( SV245
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SV245
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5953]) ).

thf(6093,plain,
    ! [SV85: $i,SV246: $i,SV381: $i] :
      ( ( ! [SY1440: $i,SY1441: $i,SY1442: $i,SY1443: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1443 @ SY1442 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1443 @ SY1441 @ SY1440 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1443 @ SY1442 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1443 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1443 @ SY1442 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1443 @ SY1441 @ ( c_Com_Ocom_OSemi @ SY1440 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1443 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5954]) ).

thf(6094,plain,
    ! [SV86: $i,SV247: $i,SV382: $i] :
      ( ( ! [SY1444: $i,SY1445: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SY1444 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) ) )
                   != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) ) ) )
                  | ~ ( ( SY1444 != SV247 )
                      | ( SV382 != SV86 ) )
                  | ~ ( ( SY1444 != SV86 )
                      | ( SV382 != SV247 ) ) )
              | ~ ( ~ ( ~ ( ( SY1444 != SV247 )
                          | ( SV382 != SV86 ) )
                      | ~ ( ( SY1444 != SV86 )
                          | ( SV382 != SV247 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SY1444 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) ) )
                    = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1445 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1445 @ tc_HOL_Obool ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5955]) ).

thf(6095,plain,
    ! [SV87: $i,SV248: $i,SV383: $i] :
      ( ( ! [SY1446: $i,SY1447: $i,SY1448: $i,SY1449: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1449 @ SY1448 @ SY1447 @ SY1446 ) @ SV383 )
             != SV248 )
            | ( ( hAPP @ SY1446 @ ( hAPP @ SV383 @ SV87 ) )
              = ( hAPP @ SV248 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5956]) ).

thf(6096,plain,
    ! [SV88: $i,SV249: $i] :
      ( ( ( ~ ( class_Lattices_Obounded__lattice @ SV249 ) )
        = $true )
      | ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV88 @ SV249 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5957]) ).

thf(6097,plain,
    ! [SV89: $i,SV250: $i,SV384: $i] :
      ( ( ! [SY1450: $i,SY1451: $i,SY1452: $i,SY1453: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1453 @ SY1452 @ SY1451 @ SY1450 @ SV384 )
            | ~ ( ~ ( ( ( hAPP @ SY1451 @ SV250 )
                     != ( hAPP @ SY1451 @ SV89 ) )
                    | ( SV250 = SV89 ) )
                | ~ ( ( SV250 != SV89 )
                    | ( ( hAPP @ SY1451 @ SV250 )
                      = ( hAPP @ SY1451 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5958]) ).

thf(6098,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                 != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
                | ( SV251
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SV251
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
                | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
                  = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5959]) ).

thf(6099,plain,
    ! [SV91: $i,SV252: $i] :
      ( ( c_Com_Ocom_OSKIP
        = ( c_Com_Ocom_OAss @ SV252 @ SV91 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5960]) ).

thf(6100,plain,
    ! [SV92: $i,SV253: $i] :
      ( ( c_Com_Ocom_OSKIP
        = ( c_Com_Ocom_OSemi @ SV253 @ SV92 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5961]) ).

thf(6101,plain,
    ! [SV93: $i,SV254: $i] :
      ( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV254 ) )
        = $true )
      | ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV93 @ SV254 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5962]) ).

thf(6102,plain,
    ! [SV94: $i,SV255: $i,SV386: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV386 ) @ SV255 ) @ SV94 )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV386 @ tc_HOL_Obool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5963]) ).

thf(6103,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
                 != SV96 )
                | ( SV256
                  = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) ) )
            | ~ ( ( SV256
                 != ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
                | ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
                  = SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5965]) ).

thf(6104,plain,
    ! [SV97: $i,SV257: $i,SV388: $i] :
      ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV388 @ SV257 @ SV97 )
        | ( SV97 = SV388 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5966]) ).

thf(6105,plain,
    ! [SV98: $i,SV258: $i] :
      ( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV258 ) )
        = $true )
      | ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV98 @ SV258 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5967]) ).

thf(6106,plain,
    ! [SV99: $i,SV259: $i,SV389: $i] :
      ( ( ! [SY1454: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1454 ) @ SV389 ) @ SV259 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1454 ) @ SV99 ) @ SV259 ) )
                  | ( SV389 = SV99 ) )
              | ~ ( ( SV389 != SV99 )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1454 ) @ SV389 ) @ SV259 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1454 ) @ SV99 ) @ SV259 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5968]) ).

thf(6107,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
             != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
            | ( SV260 = SV100 ) )
        | ~ ( ( SV260 != SV100 )
            | ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
              = ( hAPP @ c_Int_ORep__Integ @ SV100 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5969]) ).

thf(6108,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
             != ( hAPP @ c_Nat_OSuc @ SV101 ) )
            | ( SV261 = SV101 ) )
        | ~ ( ( SV261 != SV101 )
            | ( ( hAPP @ c_Nat_OSuc @ SV261 )
              = ( hAPP @ c_Nat_OSuc @ SV101 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5970]) ).

thf(6109,plain,
    ! [SV102: $i,SV262: $i,SV390: $i] :
      ( ( ! [SY1455: $i,SY1456: $i,SY1457: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm @ SY1457 @ SY1456 @ SY1455 )
            | ( ( hAPP @ ( hAPP @ SY1455 @ SV390 ) @ ( hAPP @ ( hAPP @ SY1455 @ SV262 ) @ SV102 ) )
              = ( hAPP @ ( hAPP @ SY1455 @ SV262 ) @ ( hAPP @ ( hAPP @ SY1455 @ SV390 ) @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5971]) ).

thf(6110,plain,
    ! [SV103: $i,SV263: $i,SV391: $i] :
      ( ( ! [SY1458: $i] :
            ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY1458 @ SV391 @ SV263 ) @ SV103 )
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
                  | ( SV103
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1458 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV103
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1458 @ tc_HOL_Obool ) ) )
                  | ( ( hAPP @ ( c_Set_Oimage @ SY1458 @ SV391 @ SV263 ) @ SV103 )
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5972]) ).

thf(6111,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
            | ( SV264 = SV104 ) )
        | ~ ( ( SV264 != SV104 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5973]) ).

thf(6112,plain,
    ! [SV105: $i,SV265: $i,SV392: $i] :
      ( ( ! [SY1459: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1459 @ SV392 @ SV265 )
            | ( ( hAPP @ ( hAPP @ SV392 @ SV105 ) @ SV105 )
              = SV105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5974]) ).

thf(6113,plain,
    ! [SV106: $i,SV266: $i,SV393: $i] :
      ( ( ! [SY1460: $i] :
            ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) )
                   != ( hAPP @ ( c_Set_Oimage @ SV393 @ SY1460 @ SV266 ) @ SV106 ) )
                  | ( SV106
                    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) ) )
              | ~ ( ( SV106
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
                  | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) )
                    = ( hAPP @ ( c_Set_Oimage @ SV393 @ SY1460 @ SV266 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5975]) ).

thf(6114,plain,
    ! [SV108: $i,SV267: $i,SV394: $i] :
      ( ( ! [SY1461: $i,SY1462: $i,SY1463: $i,SY1464: $i,SY1465: $i,SY1466: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1466 @ SY1465 @ SY1464 @ SY1463 ) @ SY1462 )
             != ( hAPP @ ( c_Fun_Ocomp @ SY1461 @ SY1465 @ SY1464 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SY1463 @ ( hAPP @ SY1462 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5977]) ).

thf(6115,plain,
    ! [SV109: $i,SV268: $i,SV395: $i] :
      ( ( ! [SY1467: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1467 @ SV395 @ SV268 )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1467 @ SV109 @ SV395 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1467 @ SV109 @ SV268 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5978]) ).

thf(6116,plain,
    ! [SV110: $i,SV269: $i] :
      ( ( ( c_Com_Ocom_OWhile @ SV269 @ SV110 )
        = c_Com_Ocom_OSKIP )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5979]) ).

thf(6117,plain,
    ! [SV111: $i,SV270: $i,SV396: $i] :
      ( ( ~ ( class_Orderings_Obot @ SV396 )
        | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV270 @ SV396 ) ) @ SV111 )
          = ( c_Orderings_Obot__class_Obot @ SV396 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5980]) ).

thf(6118,plain,
    ! [SV112: $i,SV271: $i] :
      ( ( ( ~ ( class_Orderings_Opreorder @ SV271 ) )
        = $true )
      | ( ( class_Orderings_Opreorder @ ( tc_fun @ SV112 @ SV271 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5981]) ).

thf(6119,plain,
    ! [SV113: $i,SV272: $i,SV397: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV397 ) @ SV272 ) @ SV113 )
       != SV113 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5982]) ).

thf(6120,plain,
    ! [SV114: $i,SV273: $i] :
      ( ( ( ~ ! [SY1248: $i] :
                ( ( hAPP @ SV273 @ SY1248 )
                = ( hAPP @ SV114 @ SY1248 ) ) )
        = $true )
      | ( ( SV273 = SV114 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5983]) ).

thf(6121,plain,
    ! [SV115: $i,SV274: $i,SV398: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV274 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV115 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) ) )
        | ( SV274 = SV115 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5984]) ).

thf(6122,plain,
    ! [SV116: $i,SV275: $i] :
      ( ( ( ~ ( class_Orderings_Obot @ SV275 ) )
        = $true )
      | ( ( class_Orderings_Obot @ ( tc_fun @ SV116 @ SV275 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5985]) ).

thf(6123,plain,
    ! [SV118: $i,SV276: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV276 ) )
        = $true )
      | ( ( class_Orderings_Oord @ ( tc_fun @ SV118 @ SV276 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5987]) ).

thf(6124,plain,
    ! [SV119: $i,SV277: $i,SV399: $i] :
      ( ( ! [SY1468: $i] :
            ( ~ ( c_Finite__Set_Ofolding__one @ SY1468 @ SV399 @ SV277 )
            | ( ( hAPP @ SV277 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1468 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1468 @ tc_HOL_Obool ) ) ) )
              = SV119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5988]) ).

thf(6125,plain,
    ! [SV120: $i,SV278: $i,SV400: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV400 @ tc_HOL_Obool ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV400 ) @ SV278 ) @ SV120 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5989]) ).

thf(6126,plain,
    ! [SV121: $i,SV279: $i] :
      ( ( c_Com_Ocom_OSKIP
        = ( c_Com_Ocom_OWhile @ SV279 @ SV121 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5990]) ).

thf(6127,plain,
    ! [SV122: $i,SV280: $i,SV401: $i] :
      ( ( ! [SY1469: $i,SY1470: $i] :
            ( ( ( hAPP @ SY1470 @ SY1469 )
             != SV401 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SY1470 ) @ SY1469 ) @ SV401 )
              = SY1470 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5991]) ).

thf(6128,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
             != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
            | ( SV281 = SV123 ) )
        | ~ ( ( SV281 != SV123 )
            | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
              = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5992]) ).

thf(6129,plain,
    ! [SV124: $i,SV282: $i,SV402: $i] :
      ( ( SV402
       != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV282 ) @ SV124 ) @ SV402 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5993]) ).

thf(6130,plain,
    ! [SV125: $i,SV283: $i] :
      ( ( ( c_Com_Ocom_OAss @ SV283 @ SV125 )
        = c_Com_Ocom_OSKIP )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5994]) ).

thf(6131,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV284 )
                | ~ ( class_Finite__Set_Ofinite @ SV126 ) ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5995]) ).

thf(6132,plain,
    ! [SV127: $i,SV285: $i] :
      ( ( ( hAPP @ ( c_Set_OPow @ SV285 ) @ SV127 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV285 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5996]) ).

thf(6133,plain,
    ! [SV128: $i,SV286: $i,SV403: $i] :
      ( ( ! [SY1471: $i,SY1472: $i,SY1473: $i,SY1474: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1474 @ SY1473 @ SY1472 @ SY1471 @ SV403 @ SV286 )
            | ( ( hAPP @ ( hAPP @ SY1472 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5997]) ).

thf(6134,plain,
    ! [SV129: $i,SV287: $i,SV404: $i] :
      ( ( ! [SY1475: $i,SY1476: $i,SY1477: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple @ SY1477 @ SY1476 @ SY1475 @ SV404 @ SV287 @ SV129 )
            | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1476 @ tc_HOL_Obool ) ) )
              = SV404 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5998]) ).

thf(6135,plain,
    ! [SV130: $i,SV288: $i,SV405: $i] :
      ( ( ! [SY1478: $i,SY1479: $i,SY1480: $i,SY1481: $i] :
            ( ~ ( ( SY1481 != SY1480 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1479 @ SY1478 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1479 @ SY1478 ) @ SV405 ) @ SY1481 ) @ SV288 ) ) @ SY1480 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1479 @ SY1478 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1479 @ SY1478 ) @ SV405 ) @ SY1480 ) @ SV130 ) ) @ SY1481 ) @ SV288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5999]) ).

thf(6136,plain,
    ! [SV131: $i,SV289: $i] :
      ( ( ( c_Com_Ocom_OSemi @ SV289 @ SV131 )
        = c_Com_Ocom_OSKIP )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6000]) ).

thf(6137,plain,
    ! [SV132: $i,SV290: $i,SV406: $i] :
      ( ( ! [SY1482: $i,SY1483: $i,SY1484: $i] :
            ~ ( ~ ( ( SY1484 != SY1483 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1482 @ SV406 ) @ SV290 ) @ SY1483 ) @ SV132 ) @ SY1484 )
                    = SV132 ) )
              | ~ ( ~ ( ( SY1484 != SY1483 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1482 @ SV406 ) @ SV290 ) @ SY1483 ) @ SV132 ) @ SY1484 )
                    = ( hAPP @ SV290 @ SY1484 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6001]) ).

thf(6138,plain,
    ! [SV133: $i,SV291: $i,SV407: $i] :
      ( ( ! [SY1485: $i,SY1486: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1485 ) @ SV407 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SV291 ) @ SV133 ) )
                  | ~ ! [SY1487: $i] :
                        ~ ( ~ ( ( SY1485
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SV291 ) @ SY1487 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1487 ) @ SV407 )
                               != SV133 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1485 ) @ SY1487 )
                               != SV291 )
                              | ( SV407
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1487 ) @ SV133 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1488: $i] :
                          ~ ( ~ ( ( SY1485
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SV291 ) @ SY1488 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1488 ) @ SV407 )
                                 != SV133 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1485 ) @ SY1488 )
                                 != SV291 )
                                | ( SV407
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1488 ) @ SV133 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SY1485 ) @ SV407 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1486 ) @ SV291 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6002]) ).

thf(6139,plain,
    ! [SV134: $i,SV292: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV292 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ ( tc_fun @ SV134 @ SV292 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6003]) ).

thf(6140,plain,
    ! [SV135: $i,SV293: $i,SV408: $i] :
      ( ( ! [SY1489: $i,SY1490: $i,SY1491: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1491 @ SY1490 ) @ SY1489 ) @ SV408 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1491 @ SY1490 ) @ SV293 ) @ SV135 ) )
            | ~ ( ( SY1489 != SV293 )
                | ( SV408 != SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6004]) ).

thf(6141,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV294 )
                | ~ ( class_Enum_Oenum @ SV136 ) ) )
        = $true )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6005]) ).

thf(6142,plain,
    ! [SV137: $i,SV295: $i,SV409: $i] :
      ( ( ! [SY1492: $i,SY1493: $i,SY1494: $i] :
            ( ~ ( ( SY1494 != SY1493 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1492 @ SV409 ) @ SV295 ) @ SY1493 ) @ SV137 ) @ SY1494 )
              = ( hAPP @ SV295 @ SY1494 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6006]) ).

thf(6143,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                | ~ ( ( SV296
                     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                    | ( SV138
                     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
            | ~ ( ~ ~ ( ( SV296
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                      | ( SV138
                       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6007]) ).

thf(6144,plain,
    ! [SV139: $i,SV297: $i,SV411: $i] :
      ( ( c_Com_Ocom_OSKIP
       != ( c_Com_Ocom_OCond @ SV411 @ SV297 @ SV139 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6008]) ).

thf(6145,plain,
    ! [SV140: $i,SV298: $i,SV412: $i] :
      ( ( ! [SY1495: $i,SY1496: $i,SY1497: $i,SY1498: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1498 @ SY1497 @ SY1496 @ SY1495 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1498 @ SV412 @ SV298 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SY1497 != SV412 )
                            | ( SY1496 != SV298 ) )
                      | ( SY1495 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1497 != SV412 )
                              | ( SY1496 != SV298 ) )
                        | ( SY1495 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1498 @ SY1497 @ SY1496 @ SY1495 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1498 @ SV412 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6009]) ).

thf(6146,plain,
    ! [SV141: $i,SV299: $i] :
      ( ( ( ~ ( class_Orderings_Otop @ SV299 ) )
        = $true )
      | ( ( class_Orderings_Otop @ ( tc_fun @ SV141 @ SV299 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6010]) ).

thf(6147,plain,
    ! [SV142: $i,SV300: $i,SV413: $i] :
      ( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1501 @ SY1500 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1501 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1501 @ SY1499 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1501 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY982: $i,SY983: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY982 ) @ SY983 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SY1499 @ SY982 ) @ SY983 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1501 @ SY1500 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1501 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1501 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1501 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6011]) ).

thf(6148,plain,
    ! [SV143: $i,SV301: $i] :
      ( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV301 ) )
        = $true )
      | ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV143 @ SV301 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6012]) ).

thf(6149,plain,
    ! [SV144: $i,SV302: $i] :
      ( ( ( ~ ( class_Groups_Ominus @ SV302 ) )
        = $true )
      | ( ( class_Groups_Ominus @ ( tc_fun @ SV144 @ SV302 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6013]) ).

thf(6150,plain,
    ! [SV145: $i,SV303: $i] :
      ( ( ( ~ ( class_Lattices_Olattice @ SV303 ) )
        = $true )
      | ( ( class_Lattices_Olattice @ ( tc_fun @ SV145 @ SV303 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6014]) ).

thf(6151,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
                 != ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
                | ( SV304 = SV146 ) )
            | ~ ( ( SV304 != SV146 )
                | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
                  = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6015]) ).

thf(6152,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
                 != ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
                | ( SV305 = SV147 ) )
            | ~ ( ( SV305 != SV147 )
                | ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
                  = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6016]) ).

thf(6153,plain,
    ! [SV148: $i,SV306: $i,SV416: $i] :
      ( ( ! [SY1504: $i,SY1505: $i,SY1506: $i,SY1507: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1507 @ SY1506 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1507 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1507 @ SY1505 @ SY1504 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1507 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1508: $i,SY1509: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1508 ) @ SY1509 ) )
                  | ! [SY1510: $i] :
                      ( ~ ! [SY1511: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1505 @ SY1511 ) @ SY1509 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1511 ) @ SY1510 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1508 ) @ SY1510 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1507 @ SY1506 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1507 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1507 @ SV306 @ SY1504 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1507 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6017]) ).

thf(6154,plain,
    ! [SV149: $i,SV307: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV307 )
         != ( hAPP @ c_Nat_OSuc @ SV149 ) )
        = $true )
      | ( ( SV307 = SV149 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6018]) ).

thf(6155,plain,
    ! [SV150: $i,SV308: $i,SV417: $i] :
      ( ( ! [SY1512: $i,SY1513: $i,SY1514: $i,SY1515: $i,SY1516: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1516 @ SY1515 @ SY1514 @ SY1513 ) @ SY1512 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SY1515 @ SY1514 @ SV308 ) @ SV150 ) )
            | ! [SY1318: $i] :
                ( ( hAPP @ SY1513 @ ( hAPP @ SY1512 @ SY1318 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6019]) ).

thf(6156,plain,
    ! [SV151: $i,SV309: $i,SV418: $i] :
      ( ( ! [SY1518: $i,SY1519: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1519 @ SY1518 @ SV418 )
            | ( ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
              = ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6020]) ).

thf(6157,plain,
    ! [SV152: $i,SV310: $i,SV419: $i] :
      ( ( ! [SY1520: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1520 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1520 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1520 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1520 @ SV419 @ SV152 )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1520 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1520 ) ) @ SV310 ) @ SV152 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6021]) ).

thf(6158,plain,
    ! [SV153: $i,SV311: $i,SV420: $i] :
      ( ( ! [SY1521: $i,SY1522: $i,SY1523: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1523 ) @ SY1522 ) @ SY1521 )
             != SV420 )
            | ( SV311
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1523 ) @ SY1521 ) @ SV153 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1523 ) @ SY1522 ) @ SV311 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1523 ) @ SV420 ) @ SV153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6022]) ).

thf(6159,plain,
    ! [SV154: $i,SV312: $i,SV421: $i] :
      ( ( ! [SY1524: $i,SY1525: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1525 ) @ SY1524 ) @ SV421 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1525 ) @ SV312 ) @ SV154 ) )
                  | ~ ( ( SY1524 != SV312 )
                      | ( SV421 != SV154 ) ) )
              | ~ ( ~ ~ ( ( SY1524 != SV312 )
                        | ( SV421 != SV154 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1525 ) @ SY1524 ) @ SV421 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1525 ) @ SV312 ) @ SV154 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6023]) ).

thf(6160,plain,
    ! [SV155: $i,SV313: $i] :
      ( ( ( ~ ( class_Groups_Ouminus @ SV313 ) )
        = $true )
      | ( ( class_Groups_Ouminus @ ( tc_fun @ SV155 @ SV313 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6024]) ).

thf(6161,plain,
    ! [SV156: $i,SV314: $i,SV422: $i] :
      ( ( ! [SY1526: $i,SY1527: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1527 @ SY1526 ) @ SV422 ) @ SV314 ) @ SV156 )
                   != SV422 )
                  | ( ( hAPP @ SV422 @ SV314 )
                    = SV156 ) )
              | ~ ( ( ( hAPP @ SV422 @ SV314 )
                   != SV156 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1527 @ SY1526 ) @ SV422 ) @ SV314 ) @ SV156 )
                    = SV422 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6025]) ).

thf(6162,plain,
    ! [SV157: $i,SV315: $i,SV423: $i] :
      ( ( ~ ( class_Orderings_Obot @ SV423 )
        | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ SV423 ) ) @ SV157 )
          = ( c_Orderings_Obot__class_Obot @ SV423 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6026]) ).

thf(6163,plain,
    ! [SV158: $i,SV316: $i,SV424: $i] :
      ( ( ( c_Com_Ocom_OCond @ SV424 @ SV316 @ SV158 )
       != c_Com_Ocom_OSKIP )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6027]) ).

thf(6164,plain,
    ! [SV159: $i,SV317: $i,SV425: $i] :
      ( ( ( c_Com_Ocom_OLocal @ SV425 @ SV317 @ SV159 )
       != c_Com_Ocom_OSKIP )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6028]) ).

thf(6165,plain,
    ! [SV160: $i,SV318: $i,SV426: $i] :
      ( ( ! [SY1528: $i,SY1529: $i,SY1530: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1530 @ SY1529 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1530 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1530 @ SY1528 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1530 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1341: $i,SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1530 @ SY1529 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1530 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1530 @ SY1528 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1530 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6029]) ).

thf(6166,plain,
    ! [SV161: $i,SV319: $i,SV427: $i] :
      ( ( c_Com_Ocom_OSKIP
       != ( c_Com_Ocom_OLocal @ SV427 @ SV319 @ SV161 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6030]) ).

thf(6167,plain,
    ! [SV162: $i,SV320: $i,SV428: $i] :
      ( ( ! [SY1533: $i,SY1534: $i,SY1535: $i] :
            ~ ( ~ ( ( SY1535 != SY1534 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1533 @ SV428 ) @ SV320 ) @ SY1534 ) @ SV162 ) @ SY1535 )
                    = SV162 ) )
              | ~ ( ~ ( ( SY1535 != SY1534 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1533 @ SV428 ) @ SV320 ) @ SY1534 ) @ SV162 ) @ SY1535 )
                    = ( hAPP @ SV320 @ SY1535 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6031]) ).

thf(6168,plain,
    ! [SV163: $i,SV321: $i,SV429: $i] :
      ( ( ! [SY1536: $i] :
            ( ( SY1536
             != ( c_Finite__Set_Ofold1 @ SV429 @ SV321 ) )
            | ( ( hAPP @ SY1536 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV429 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV429 @ tc_HOL_Obool ) ) ) )
              = SV163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6032]) ).

thf(6169,plain,
    ! [SV164: $i,SV322: $i,SV430: $i] :
      ( ( ! [SY1537: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1537 ) @ SV430 ) @ SV322 ) @ SV164 ) )
                  | ( SV430 = SV164 )
                  | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
              | ~ ( ~ ( ( SV430 = SV164 )
                      | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1537 ) @ SV430 ) @ SV322 ) @ SV164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6033]) ).

thf(6170,plain,
    ! [SV165: $i,SV323: $i,SV431: $i] :
      ( ( ! [SY1538: $i,SY1539: $i,SY1540: $i] :
            ( ( SY1540 != SY1539 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1538 @ SV431 @ SV323 ) @ SV165 ) @ SY1540 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1538 @ SV431 @ SV323 ) @ SV165 ) @ SY1539 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6034]) ).

thf(6171,plain,
    ! [SV166: $i,SV324: $i,SV432: $i] :
      ( ( ! [SY1541: $i,SY1542: $i,SY1543: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1543 @ SY1542 @ SY1541 @ SV432 @ SV324 )
            | ( ( hAPP @ SV432 @ ( hAPP @ SY1541 @ SV166 ) )
              = SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6035]) ).

thf(6172,plain,
    ! [SV5: $i,SV171: $i,SV327: $i,SV433: $i] :
      ( ( ! [SY1544: $i,SY1545: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SY1545 @ SY1544 @ SV433 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1545 @ SV327 @ SV171 @ SV5 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SV433 @ SV327 ) @ SV171 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6038]) ).

thf(6173,plain,
    ! [SV6: $i,SV172: $i,SV328: $i,SV434: $i] :
      ( ( ! [SY1546: $i,SY1547: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY1547 @ SY1546 @ SV434 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1547 @ SV328 @ SV172 @ SV6 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SV434 @ SV328 ) @ SV172 ) @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6039]) ).

thf(6174,plain,
    ! [SV7: $i,SV173: $i,SV329: $i,SV435: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV435 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV435 ) @ SV173 ) @ SV7 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV435 ) @ SV173 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV435 ) @ SV329 ) @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6040]) ).

thf(6175,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i] :
      ( ( ! [SY1548: $i,SY1549: $i,SY1550: $i,SY1551: $i,SY1552: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1552 @ SY1551 @ SY1550 @ SY1549 @ SY1548 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1551 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6042]) ).

thf(6176,plain,
    ! [SV11: $i,SV177: $i,SV332: $i,SV437: $i] :
      ( ( ! [SY1553: $i,SY1554: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1554 @ SY1553 @ SV437 @ SV332 ) @ SV177 ) @ SV11 )
            = ( hAPP @ SV332 @ ( hAPP @ SV177 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6043]) ).

thf(6177,plain,
    ! [SV14: $i,SV180: $i,SV333: $i,SV438: $i] :
      ( ( ! [SY1555: $i,SY1556: $i,SY1557: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1557 @ SY1556 @ SY1555 @ SV438 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1557 @ SY1555 @ SV180 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1556 @ SY1555 @ ( hAPP @ ( c_Fun_Ocomp @ SY1557 @ SY1556 @ SV333 @ SV438 ) @ SV180 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6044]) ).

thf(6178,plain,
    ! [SV15: $i,SV181: $i,SV334: $i,SV439: $i] :
      ( ( ! [SY1558: $i,SY1559: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1559 @ SY1558 @ SV439 @ SV334 ) @ SV181 ) @ SV15 )
            = ( hAPP @ SV334 @ ( hAPP @ SV181 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6045]) ).

thf(6179,plain,
    ! [SV16: $i,SV182: $i,SV335: $i,SV440: $i] :
      ( ( ( c_Fun_Ooverride__on @ SV440 @ SV335 @ SV182 @ SV16 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV440 @ tc_HOL_Obool ) ) )
        = SV182 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6046]) ).

thf(6180,plain,
    ! [SV22: $i,SV187: $i,SV338: $i,SV441: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV441 @ tc_HOL_Obool ) ) @ SV338 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV441 @ tc_HOL_Obool ) ) @ SV187 ) @ SV22 ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV441 @ tc_HOL_Obool ) ) @ SV187 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV441 @ tc_HOL_Obool ) ) @ SV338 ) @ SV22 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6049]) ).

thf(6181,plain,
    ! [SV23: $i,SV188: $i,SV339: $i,SV442: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV442 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV442 @ tc_HOL_Obool ) ) @ SV339 ) @ SV188 ) ) @ SV23 )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV442 @ tc_HOL_Obool ) ) @ SV339 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV442 @ tc_HOL_Obool ) ) @ SV188 ) @ SV23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6050]) ).

thf(6182,plain,
    ! [SV25: $i,SV190: $i,SV341: $i,SV443: $i] :
      ( ( ! [SY1560: $i] :
            ( ( hAPP @ ( c_Set_Oimage @ SY1560 @ SV443 @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1560 ) @ SV190 ) @ SV25 ) )
            = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV443 ) @ ( hAPP @ SV341 @ SV190 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1560 @ SV443 @ SV341 ) @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6052]) ).

thf(6183,plain,
    ! [SV28: $i,SV193: $i,SV342: $i,SV444: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV444 @ tc_HOL_Obool ) ) @ SV342 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV444 ) @ SV193 ) @ SV28 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV444 ) @ SV193 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV444 @ tc_HOL_Obool ) ) @ SV342 ) @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6053]) ).

thf(6184,plain,
    ! [SV29: $i,SV194: $i,SV343: $i,SV445: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV445 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV445 ) @ SV343 ) @ SV194 ) ) @ SV29 )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV445 ) @ SV343 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV445 @ tc_HOL_Obool ) ) @ SV194 ) @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6054]) ).

thf(6185,plain,
    ! [SV34: $i,SV199: $i,SV347: $i,SV446: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) @ SV347 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) @ SV199 ) @ SV34 ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) @ SV199 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV446 @ tc_HOL_Obool ) ) @ SV347 ) @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6058]) ).

thf(6186,plain,
    ! [SV36: $i,SV201: $i,SV349: $i,SV447: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV447 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV447 @ tc_HOL_Obool ) ) @ SV349 ) @ SV201 ) ) @ SV36 )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV447 @ tc_HOL_Obool ) ) @ SV349 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV447 @ tc_HOL_Obool ) ) @ SV201 ) @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6060]) ).

thf(6187,plain,
    ! [SV42: $i,SV207: $i,SV350: $i,SV448: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV448 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV448 ) @ SV350 ) @ SV207 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV448 ) @ SV350 ) @ SV42 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV448 ) @ SV350 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV448 @ tc_HOL_Obool ) ) @ SV207 ) @ SV42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6061]) ).

thf(6188,plain,
    ! [SV43: $i,SV208: $i,SV351: $i,SV449: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV449 @ tc_HOL_Obool ) ) @ SV351 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV449 ) @ SV208 ) @ SV43 ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV449 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV449 @ tc_HOL_Obool ) ) @ SV351 ) @ SV43 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV449 ) @ SV208 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV449 @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6062]) ).

thf(6189,plain,
    ! [SV44: $i,SV209: $i,SV352: $i,SV450: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV450 @ tc_HOL_Obool ) ) @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV450 ) @ SV209 ) @ SV44 ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV450 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV450 @ tc_HOL_Obool ) ) @ SV352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV450 ) @ SV209 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_HOL_Obool ) ) ) ) ) @ SV44 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6063]) ).

thf(6190,plain,
    ! [SV46: $i,SV211: $i,SV354: $i,SV451: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV451 @ SV354 ) @ SV211 ) @ SV46 ) @ ( hAPP @ SV211 @ SV46 ) )
        = SV211 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6065]) ).

thf(6191,plain,
    ! [SV47: $i,SV212: $i,SV355: $i,SV452: $i] :
      ( ( ! [SY1561: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1561 @ SV452 ) @ SV355 ) @ SV212 ) @ SV47 ) @ SV212 )
            = SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6066]) ).

thf(6192,plain,
    ! [SV48: $i,SV213: $i,SV356: $i,SV453: $i] :
      ( ( ! [SY1562: $i,SY1563: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1563 @ SY1562 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1563 @ SY1562 ) @ SV453 ) @ SV356 ) @ SV213 ) ) @ SV356 ) @ SV48 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1563 @ SY1562 ) @ SV453 ) @ SV356 ) @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6067]) ).

thf(6193,plain,
    ! [SV49: $i,SV214: $i,SV357: $i,SV454: $i] :
      ( ( c_Nitpick_Ofold__graph_H @ SV454 @ SV357 @ SV214 @ SV49 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_HOL_Obool ) ) @ SV49 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6068]) ).

thf(6194,plain,
    ! [SV50: $i,SV215: $i,SV358: $i,SV455: $i] :
      ( ( c_Nitpick_Ofold__graph_H @ SV455 @ SV358 @ SV215 @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV455 @ tc_HOL_Obool ) ) @ SV50 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6069]) ).

thf(6195,plain,
    ! [SV56: $i,SV220: $i,SV361: $i,SV456: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ ( tc_fun @ SV361 @ tc_HOL_Obool ) ) ) @ SV220 ) @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6072]) ).

thf(6196,plain,
    ! [SV57: $i,SV221: $i,SV362: $i,SV457: $i] :
      ( ( ! [SY1564: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY1564 @ SV457 @ SV362 ) @ SV221 ) @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV457 @ tc_HOL_Obool ) ) )
            = SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6073]) ).

thf(6197,plain,
    ! [SV59: $i,SV223: $i,SV364: $i,SV458: $i] :
      ( ( ! [SY1565: $i,SY1566: $i,SY1567: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SY1566 @ SY1565 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SV458 @ SY1566 ) @ SV364 ) @ SV223 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SV458 @ SY1565 ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV458 @ SY1566 @ SY1565 ) @ SV223 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6075]) ).

thf(6198,plain,
    ! [SV63: $i,SV227: $i,SV366: $i,SV459: $i] :
      ( ( ! [SY1568: $i] :
            ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1568 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1568 @ SV459 ) @ SV366 ) @ SV227 ) ) @ SV366 ) @ SV63 )
            = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1568 @ SV459 ) @ SV366 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6077]) ).

thf(6199,plain,
    ! [SV65: $i,SV228: $i,SV367: $i,SV460: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV367 ) @ SV228 ) ) @ SV65 )
        = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV228 ) @ SV65 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6078]) ).

thf(6200,plain,
    ! [SV69: $i,SV232: $i,SV369: $i,SV461: $i] :
      ( ( ( hAPP @ SV461 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV369 @ SV369 ) @ SV232 ) @ SV461 ) @ SV69 ) )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV369 @ SV369 ) @ SV232 ) @ SV461 ) @ ( hAPP @ SV461 @ SV69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6080]) ).

thf(6201,plain,
    ! [SV70: $i,SV233: $i,SV370: $i,SV462: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SV462 @ SV370 @ SV233 ) @ SV70 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV462 @ tc_HOL_Obool ) ) )
        = SV70 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6081]) ).

thf(6202,plain,
    ! [SV74: $i,SV235: $i,SV371: $i,SV463: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV463 @ SV371 ) @ SV235 ) @ SV74 )
        = SV235 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6082]) ).

thf(6203,plain,
    ! [SV75: $i,SV236: $i,SV372: $i,SV464: $i] :
      ( ( ! [SY1569: $i,SY1570: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1570 @ SY1569 @ SV464 ) @ SV372 ) @ SV236 ) @ SV75 )
            = ( hAPP @ SV372 @ ( hAPP @ SV236 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6083]) ).

thf(6204,plain,
    ! [SV76: $i,SV237: $i,SV373: $i,SV465: $i] :
      ( ( ! [SY1571: $i,SY1572: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1572 @ SY1571 @ SV465 ) @ SV373 ) @ SV237 ) @ SV76 )
            = ( hAPP @ ( hAPP @ SV373 @ SV76 ) @ SV237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6084]) ).

thf(6205,plain,
    ! [SV77: $i,SV238: $i,SV374: $i,SV466: $i] :
      ( ( ! [SY1573: $i,SY1574: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1574 @ SY1573 @ SV466 ) @ SV374 ) @ SV238 ) @ SV77 )
            = ( hAPP @ ( hAPP @ SV374 @ SV77 ) @ ( hAPP @ SV238 @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6085]) ).

thf(6206,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
            | ( SV239 = SV78 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6086]) ).

thf(6207,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ~ ( ( SV239 != SV78 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6086]) ).

thf(6208,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i] :
      ( ( ! [SY1575: $i,SY1576: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1576 @ SY1575 ) @ SV467 ) @ SV375 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1576 @ SY1575 ) @ SV240 ) @ SV79 ) )
                  | ~ ( ( SV467 != SV240 )
                      | ( SV375 != SV79 ) ) )
              | ~ ( ~ ~ ( ( SV467 != SV240 )
                        | ( SV375 != SV79 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1576 @ SY1575 ) @ SV467 ) @ SV375 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1576 @ SY1575 ) @ SV240 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6087]) ).

thf(6209,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i] :
      ( ( ! [SY1577: $i,SY1578: $i,SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i,SY1583: $i] :
            ( ( ( hAPP @ SY1583 @ ( hAPP @ SY1582 @ SY1581 ) )
             != ( hAPP @ SY1580 @ ( hAPP @ SY1579 @ SY1578 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1577 @ SV468 @ SV376 @ SY1583 ) @ SY1582 ) @ SY1581 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SY1580 ) @ SY1579 ) @ SY1578 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6088]) ).

thf(6210,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i] :
      ( ( ! [SY1584: $i,SY1585: $i] :
            ( ~ ( ( SY1585 != SY1584 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SY1585 ) @ SV242 ) ) @ SY1584 ) @ SV81 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SY1584 ) @ SV81 ) ) @ SY1585 ) @ SV242 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6089]) ).

thf(6211,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
                | ( SV243 = SV82 ) )
            | ~ ( ( SV243 != SV82 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6090]) ).

thf(6212,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
             != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
            | ( SV244 = SV83 ) )
        | ~ ( ( SV244 != SV83 )
            | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
              = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6091]) ).

thf(6213,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
            | ( SV245
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) ) )
        | ~ ( ( SV245
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6092]) ).

thf(6214,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i] :
      ( ( ! [SY1586: $i,SY1587: $i,SY1588: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1588 @ SY1587 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1588 @ SY1586 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1588 @ SY1587 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1588 @ SY1587 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1588 @ SY1586 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1588 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6093]) ).

thf(6215,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i] :
      ( ( ! [SY1589: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1589 @ tc_HOL_Obool ) ) ) )
                   != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1589 @ tc_HOL_Obool ) ) ) ) )
                  | ~ ( ( SV472 != SV247 )
                      | ( SV382 != SV86 ) )
                  | ~ ( ( SV472 != SV86 )
                      | ( SV382 != SV247 ) ) )
              | ~ ( ~ ( ~ ( ( SV472 != SV247 )
                          | ( SV382 != SV86 ) )
                      | ~ ( ( SV472 != SV86 )
                          | ( SV382 != SV247 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1589 @ tc_HOL_Obool ) ) ) )
                    = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1589 @ tc_HOL_Obool ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6094]) ).

thf(6216,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i] :
      ( ( ! [SY1590: $i,SY1591: $i,SY1592: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1592 @ SY1591 @ SY1590 @ SV473 ) @ SV383 )
             != SV248 )
            | ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
              = ( hAPP @ SV248 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6095]) ).

thf(6217,plain,
    ! [SV88: $i,SV249: $i] :
      ( ( ( class_Lattices_Obounded__lattice @ SV249 )
        = $false )
      | ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV88 @ SV249 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6096]) ).

thf(6218,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i] :
      ( ( ! [SY1593: $i,SY1594: $i,SY1595: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1595 @ SY1594 @ SY1593 @ SV474 @ SV384 )
            | ~ ( ~ ( ( ( hAPP @ SY1593 @ SV250 )
                     != ( hAPP @ SY1593 @ SV89 ) )
                    | ( SV250 = SV89 ) )
                | ~ ( ( SV250 != SV89 )
                    | ( ( hAPP @ SY1593 @ SV250 )
                      = ( hAPP @ SY1593 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6097]) ).

thf(6219,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
             != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
            | ( SV251
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) ) )
        | ~ ( ( SV251
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
            | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
              = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6098]) ).

thf(6220,plain,
    ! [SV93: $i,SV254: $i] :
      ( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV254 )
        = $false )
      | ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV93 @ SV254 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6101]) ).

thf(6221,plain,
    ! [SV94: $i,SV255: $i,SV386: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV386 ) @ SV255 ) @ SV94 )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV386 @ tc_HOL_Obool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6102]) ).

thf(6222,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
             != SV96 )
            | ( SV256
              = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) ) )
        | ~ ( ( SV256
             != ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
            | ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
              = SV96 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6103]) ).

thf(6223,plain,
    ! [SV97: $i,SV257: $i,SV388: $i] :
      ( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV388 @ SV257 @ SV97 ) )
        = $true )
      | ( ( SV97 = SV388 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6104]) ).

thf(6224,plain,
    ! [SV98: $i,SV258: $i] :
      ( ( ( class_Lattices_Oboolean__algebra @ SV258 )
        = $false )
      | ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV98 @ SV258 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6105]) ).

thf(6225,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
                | ( SV389 = SV99 ) )
            | ~ ( ( SV389 != SV99 )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6106]) ).

thf(6226,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
             != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
            | ( SV260 = SV100 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6107]) ).

thf(6227,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ~ ( ( SV260 != SV100 )
            | ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
              = ( hAPP @ c_Int_ORep__Integ @ SV100 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6107]) ).

thf(6228,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
             != ( hAPP @ c_Nat_OSuc @ SV101 ) )
            | ( SV261 = SV101 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6108]) ).

thf(6229,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ~ ( ( SV261 != SV101 )
            | ( ( hAPP @ c_Nat_OSuc @ SV261 )
              = ( hAPP @ c_Nat_OSuc @ SV101 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6108]) ).

thf(6230,plain,
    ! [SV102: $i,SV262: $i,SV390: $i,SV476: $i] :
      ( ( ! [SY1596: $i,SY1597: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm @ SY1597 @ SY1596 @ SV476 )
            | ( ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ SV102 ) )
              = ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6109]) ).

thf(6231,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
                | ( SV103
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SV103
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
                | ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6110]) ).

thf(6232,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
             != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
            | ( SV264 = SV104 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6111]) ).

thf(6233,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ~ ( ( SV264 != SV104 )
            | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
              = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6111]) ).

thf(6234,plain,
    ! [SV105: $i,SV265: $i,SV392: $i,SV478: $i] :
      ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV478 @ SV392 @ SV265 )
        | ( ( hAPP @ ( hAPP @ SV392 @ SV105 ) @ SV105 )
          = SV105 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6112]) ).

thf(6235,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
                 != ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
                | ( SV106
                  = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) ) )
            | ~ ( ( SV106
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
                | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
                  = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6113]) ).

thf(6236,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i] :
      ( ( ! [SY1598: $i,SY1599: $i,SY1600: $i,SY1601: $i,SY1602: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1602 @ SY1601 @ SY1600 @ SY1599 ) @ SY1598 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SY1601 @ SY1600 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SY1599 @ ( hAPP @ SY1598 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6114]) ).

thf(6237,plain,
    ! [SV109: $i,SV268: $i,SV395: $i,SV481: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV395 @ SV268 )
        | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV395 )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV268 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6115]) ).

thf(6238,plain,
    ! [SV111: $i,SV270: $i,SV396: $i] :
      ( ( ( ~ ( class_Orderings_Obot @ SV396 ) )
        = $true )
      | ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV270 @ SV396 ) ) @ SV111 )
          = ( c_Orderings_Obot__class_Obot @ SV396 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6117]) ).

thf(6239,plain,
    ! [SV112: $i,SV271: $i] :
      ( ( ( class_Orderings_Opreorder @ SV271 )
        = $false )
      | ( ( class_Orderings_Opreorder @ ( tc_fun @ SV112 @ SV271 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6118]) ).

thf(6240,plain,
    ! [SV113: $i,SV272: $i,SV397: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV397 ) @ SV272 ) @ SV113 )
        = SV113 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6119]) ).

thf(6241,plain,
    ! [SV114: $i,SV273: $i] :
      ( ( ( ! [SY1248: $i] :
              ( ( hAPP @ SV273 @ SY1248 )
              = ( hAPP @ SV114 @ SY1248 ) ) )
        = $false )
      | ( ( SV273 = SV114 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6120]) ).

thf(6242,plain,
    ! [SV115: $i,SV274: $i,SV398: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV274 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV115 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( SV274 = SV115 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6121]) ).

thf(6243,plain,
    ! [SV116: $i,SV275: $i] :
      ( ( ( class_Orderings_Obot @ SV275 )
        = $false )
      | ( ( class_Orderings_Obot @ ( tc_fun @ SV116 @ SV275 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6122]) ).

thf(6244,plain,
    ! [SV118: $i,SV276: $i] :
      ( ( ( class_Orderings_Oord @ SV276 )
        = $false )
      | ( ( class_Orderings_Oord @ ( tc_fun @ SV118 @ SV276 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6123]) ).

thf(6245,plain,
    ! [SV119: $i,SV277: $i,SV399: $i,SV482: $i] :
      ( ( ~ ( c_Finite__Set_Ofolding__one @ SV482 @ SV399 @ SV277 )
        | ( ( hAPP @ SV277 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV482 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_HOL_Obool ) ) ) )
          = SV119 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6124]) ).

thf(6246,plain,
    ! [SV120: $i,SV278: $i,SV400: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV400 @ tc_HOL_Obool ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV400 ) @ SV278 ) @ SV120 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6125]) ).

thf(6247,plain,
    ! [SV122: $i,SV280: $i,SV401: $i,SV483: $i] :
      ( ( ! [SY1603: $i] :
            ( ( ( hAPP @ SY1603 @ SV483 )
             != SV401 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SY1603 ) @ SV483 ) @ SV401 )
              = SY1603 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6127]) ).

thf(6248,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
             != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
            | ( SV281 = SV123 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6128]) ).

thf(6249,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ~ ( ( SV281 != SV123 )
            | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
              = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6128]) ).

thf(6250,plain,
    ! [SV124: $i,SV282: $i,SV402: $i] :
      ( ( SV402
        = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV282 ) @ SV124 ) @ SV402 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6129]) ).

thf(6251,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ( ~ ( ~ ( class_Finite__Set_Ofinite @ SV284 )
              | ~ ( class_Finite__Set_Ofinite @ SV126 ) ) )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6131]) ).

thf(6252,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i] :
      ( ( ! [SY1604: $i,SY1605: $i,SY1606: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1606 @ SY1605 @ SY1604 @ SV484 @ SV403 @ SV286 )
            | ( ( hAPP @ ( hAPP @ SY1604 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6133]) ).

thf(6253,plain,
    ! [SV129: $i,SV287: $i,SV404: $i,SV485: $i] :
      ( ( ! [SY1607: $i,SY1608: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple @ SY1608 @ SY1607 @ SV485 @ SV404 @ SV287 @ SV129 )
            | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1607 @ tc_HOL_Obool ) ) )
              = SV404 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6134]) ).

thf(6254,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i] :
      ( ( ! [SY1609: $i,SY1610: $i,SY1611: $i] :
            ( ~ ( ( SY1611 != SY1610 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1609 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1609 @ SV486 ) @ SV405 ) @ SY1611 ) @ SV288 ) ) @ SY1610 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1609 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1609 @ SV486 ) @ SV405 ) @ SY1610 ) @ SV130 ) ) @ SY1611 ) @ SV288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6135]) ).

thf(6255,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i] :
      ( ( ! [SY1612: $i,SY1613: $i] :
            ~ ( ~ ( ( SY1613 != SY1612 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SY1612 ) @ SV132 ) @ SY1613 )
                    = SV132 ) )
              | ~ ( ~ ( ( SY1613 != SY1612 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SY1612 ) @ SV132 ) @ SY1613 )
                    = ( hAPP @ SV290 @ SY1613 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6137]) ).

thf(6256,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i] :
      ( ( ! [SY1614: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV488 ) @ SV407 )
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV291 ) @ SV133 ) )
                  | ~ ! [SY1615: $i] :
                        ~ ( ~ ( ( SV488
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV291 ) @ SY1615 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SY1615 ) @ SV407 )
                               != SV133 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV488 ) @ SY1615 )
                               != SV291 )
                              | ( SV407
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SY1615 ) @ SV133 ) ) ) ) )
              | ~ ( ~ ~ ! [SY1616: $i] :
                          ~ ( ~ ( ( SV488
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV291 ) @ SY1616 ) )
                                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SY1616 ) @ SV407 )
                                 != SV133 ) )
                            | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV488 ) @ SY1616 )
                                 != SV291 )
                                | ( SV407
                                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SY1616 ) @ SV133 ) ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV488 ) @ SV407 )
                    = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1614 ) @ SV291 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6138]) ).

thf(6257,plain,
    ! [SV134: $i,SV292: $i] :
      ( ( ( class_Orderings_Oorder @ SV292 )
        = $false )
      | ( ( class_Orderings_Oorder @ ( tc_fun @ SV134 @ SV292 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6139]) ).

thf(6258,plain,
    ! [SV135: $i,SV293: $i,SV408: $i,SV489: $i] :
      ( ( ! [SY1617: $i,SY1618: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1618 @ SY1617 ) @ SV489 ) @ SV408 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1618 @ SY1617 ) @ SV293 ) @ SV135 ) )
            | ~ ( ( SV489 != SV293 )
                | ( SV408 != SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6140]) ).

thf(6259,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ( ~ ( ~ ( class_Enum_Oenum @ SV294 )
              | ~ ( class_Enum_Oenum @ SV136 ) ) )
        = $false )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6141]) ).

thf(6260,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i] :
      ( ( ! [SY1619: $i,SY1620: $i] :
            ( ~ ( ( SY1620 != SY1619 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SY1619 ) @ SV137 ) @ SY1620 )
              = ( hAPP @ SV295 @ SY1620 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6142]) ).

thf(6261,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
            | ~ ( ( SV296
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                | ( SV138
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
        | ~ ( ~ ~ ( ( SV296
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                  | ( SV138
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6143]) ).

thf(6262,plain,
    ! [SV139: $i,SV297: $i,SV411: $i] :
      ( ( c_Com_Ocom_OSKIP
        = ( c_Com_Ocom_OCond @ SV411 @ SV297 @ SV139 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6144]) ).

thf(6263,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i] :
      ( ( ! [SY1621: $i,SY1622: $i,SY1623: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1623 @ SY1622 @ SY1621 @ SV491 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1623 @ SV412 @ SV298 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SY1622 != SV412 )
                            | ( SY1621 != SV298 ) )
                      | ( SV491 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1622 != SV412 )
                              | ( SY1621 != SV298 ) )
                        | ( SV491 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1623 @ SY1622 @ SY1621 @ SV491 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1623 @ SV412 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6145]) ).

thf(6264,plain,
    ! [SV141: $i,SV299: $i] :
      ( ( ( class_Orderings_Otop @ SV299 )
        = $false )
      | ( ( class_Orderings_Otop @ ( tc_fun @ SV141 @ SV299 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6146]) ).

thf(6265,plain,
    ! [SV142: $i,SV300: $i,SV413: $i,SV492: $i] :
      ( ( ! [SY1624: $i,SY1625: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1625 @ SY1624 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1625 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1625 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1625 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1626: $i,SY1627: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1625 @ SY1624 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1625 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1625 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1625 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6147]) ).

thf(6266,plain,
    ! [SV143: $i,SV301: $i] :
      ( ( ( class_Lattices_Odistrib__lattice @ SV301 )
        = $false )
      | ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV143 @ SV301 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6148]) ).

thf(6267,plain,
    ! [SV144: $i,SV302: $i] :
      ( ( ( class_Groups_Ominus @ SV302 )
        = $false )
      | ( ( class_Groups_Ominus @ ( tc_fun @ SV144 @ SV302 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6149]) ).

thf(6268,plain,
    ! [SV145: $i,SV303: $i] :
      ( ( ( class_Lattices_Olattice @ SV303 )
        = $false )
      | ( ( class_Lattices_Olattice @ ( tc_fun @ SV145 @ SV303 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6150]) ).

thf(6269,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
             != ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
            | ( SV304 = SV146 ) )
        | ~ ( ( SV304 != SV146 )
            | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
              = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6151]) ).

thf(6270,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
             != ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
            | ( SV305 = SV147 ) )
        | ~ ( ( SV305 != SV147 )
            | ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
              = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6152]) ).

thf(6271,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i] :
      ( ( ! [SY1628: $i,SY1629: $i,SY1630: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1630 @ SY1629 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1630 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1630 @ SY1628 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1630 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1508: $i,SY1509: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1508 ) @ SY1509 ) )
                  | ! [SY1510: $i] :
                      ( ~ ! [SY1511: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1628 @ SY1511 ) @ SY1509 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1511 ) @ SY1510 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1508 ) @ SY1510 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1630 @ SY1629 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1630 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1630 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1630 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6153]) ).

thf(6272,plain,
    ! [SV149: $i,SV307: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV307 )
          = ( hAPP @ c_Nat_OSuc @ SV149 ) )
        = $false )
      | ( ( SV307 = SV149 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6154]) ).

thf(6273,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i] :
      ( ( ! [SY1635: $i,SY1636: $i,SY1637: $i,SY1638: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1638 @ SY1637 @ SY1636 @ SY1635 ) @ SV494 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SY1637 @ SY1636 @ SV308 ) @ SV150 ) )
            | ! [SY1639: $i] :
                ( ( hAPP @ SY1635 @ ( hAPP @ SV494 @ SY1639 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1639 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6155]) ).

thf(6274,plain,
    ! [SV151: $i,SV309: $i,SV418: $i,SV495: $i] :
      ( ( ! [SY1640: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1640 @ SV495 @ SV418 )
            | ( ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
              = ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6156]) ).

thf(6275,plain,
    ! [SV152: $i,SV310: $i,SV419: $i,SV496: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) @ tc_HOL_Obool ) ) ) )
        | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ SV152 )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ SV152 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6157]) ).

thf(6276,plain,
    ! [SV153: $i,SV311: $i,SV420: $i,SV497: $i] :
      ( ( ! [SY1641: $i,SY1642: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1642 ) @ SY1641 ) @ SV497 )
             != SV420 )
            | ( SV311
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1642 ) @ SV497 ) @ SV153 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1642 ) @ SY1641 ) @ SV311 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1642 ) @ SV420 ) @ SV153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6158]) ).

thf(6277,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i] :
      ( ( ! [SY1643: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1643 ) @ SV498 ) @ SV421 )
                   != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1643 ) @ SV312 ) @ SV154 ) )
                  | ~ ( ( SV498 != SV312 )
                      | ( SV421 != SV154 ) ) )
              | ~ ( ~ ~ ( ( SV498 != SV312 )
                        | ( SV421 != SV154 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1643 ) @ SV498 ) @ SV421 )
                    = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1643 ) @ SV312 ) @ SV154 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6159]) ).

thf(6278,plain,
    ! [SV155: $i,SV313: $i] :
      ( ( ( class_Groups_Ouminus @ SV313 )
        = $false )
      | ( ( class_Groups_Ouminus @ ( tc_fun @ SV155 @ SV313 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6160]) ).

thf(6279,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i] :
      ( ( ! [SY1644: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1644 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
                   != SV422 )
                  | ( ( hAPP @ SV422 @ SV314 )
                    = SV156 ) )
              | ~ ( ( ( hAPP @ SV422 @ SV314 )
                   != SV156 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1644 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
                    = SV422 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6161]) ).

thf(6280,plain,
    ! [SV157: $i,SV315: $i,SV423: $i] :
      ( ( ( ~ ( class_Orderings_Obot @ SV423 ) )
        = $true )
      | ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ SV423 ) ) @ SV157 )
          = ( c_Orderings_Obot__class_Obot @ SV423 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6162]) ).

thf(6281,plain,
    ! [SV158: $i,SV316: $i,SV424: $i] :
      ( ( ( c_Com_Ocom_OCond @ SV424 @ SV316 @ SV158 )
        = c_Com_Ocom_OSKIP )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6163]) ).

thf(6282,plain,
    ! [SV159: $i,SV317: $i,SV425: $i] :
      ( ( ( c_Com_Ocom_OLocal @ SV425 @ SV317 @ SV159 )
        = c_Com_Ocom_OSKIP )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6164]) ).

thf(6283,plain,
    ! [SV160: $i,SV318: $i,SV426: $i,SV500: $i] :
      ( ( ! [SY1645: $i,SY1646: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1646 @ SY1645 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1646 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1646 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1646 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1341: $i,SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1646 @ SY1645 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1646 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1646 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1646 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6165]) ).

thf(6284,plain,
    ! [SV161: $i,SV319: $i,SV427: $i] :
      ( ( c_Com_Ocom_OSKIP
        = ( c_Com_Ocom_OLocal @ SV427 @ SV319 @ SV161 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6166]) ).

thf(6285,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i] :
      ( ( ! [SY1649: $i,SY1650: $i] :
            ~ ( ~ ( ( SY1650 != SY1649 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SY1649 ) @ SV162 ) @ SY1650 )
                    = SV162 ) )
              | ~ ( ~ ( ( SY1650 != SY1649 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SY1649 ) @ SV162 ) @ SY1650 )
                    = ( hAPP @ SV320 @ SY1650 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6167]) ).

thf(6286,plain,
    ! [SV163: $i,SV321: $i,SV429: $i,SV502: $i] :
      ( ( ( SV502
         != ( c_Finite__Set_Ofold1 @ SV429 @ SV321 ) )
        | ( ( hAPP @ SV502 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV429 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV429 @ tc_HOL_Obool ) ) ) )
          = SV163 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6168]) ).

thf(6287,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
                | ( SV430 = SV164 )
                | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
            | ~ ( ~ ( ( SV430 = SV164 )
                    | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6169]) ).

thf(6288,plain,
    ! [SV165: $i,SV323: $i,SV431: $i,SV504: $i] :
      ( ( ! [SY1651: $i,SY1652: $i] :
            ( ( SY1652 != SY1651 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SY1652 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SY1651 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6170]) ).

thf(6289,plain,
    ! [SV166: $i,SV324: $i,SV432: $i,SV505: $i] :
      ( ( ! [SY1653: $i,SY1654: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1654 @ SY1653 @ SV505 @ SV432 @ SV324 )
            | ( ( hAPP @ SV432 @ ( hAPP @ SV505 @ SV166 ) )
              = SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6171]) ).

thf(6290,plain,
    ! [SV5: $i,SV171: $i,SV327: $i,SV433: $i,SV506: $i] :
      ( ( ! [SY1655: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SY1655 @ SV506 @ SV433 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1655 @ SV327 @ SV171 @ SV5 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SV433 @ SV327 ) @ SV171 ) @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6172]) ).

thf(6291,plain,
    ! [SV6: $i,SV172: $i,SV328: $i,SV434: $i,SV507: $i] :
      ( ( ! [SY1656: $i] :
            ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY1656 @ SV507 @ SV434 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1656 @ SV328 @ SV172 @ SV6 ) )
            = ( hAPP @ ( hAPP @ ( hAPP @ SV434 @ SV328 ) @ SV172 ) @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6173]) ).

thf(6292,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i,SV508: $i] :
      ( ( ! [SY1657: $i,SY1658: $i,SY1659: $i,SY1660: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1660 @ SY1659 @ SY1658 @ SY1657 @ SV508 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1659 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6175]) ).

thf(6293,plain,
    ! [SV11: $i,SV177: $i,SV332: $i,SV437: $i,SV509: $i] :
      ( ( ! [SY1661: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1661 @ SV509 @ SV437 @ SV332 ) @ SV177 ) @ SV11 )
            = ( hAPP @ SV332 @ ( hAPP @ SV177 @ SV11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6176]) ).

thf(6294,plain,
    ! [SV14: $i,SV180: $i,SV333: $i,SV438: $i,SV510: $i] :
      ( ( ! [SY1662: $i,SY1663: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1663 @ SY1662 @ SV510 @ SV438 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1663 @ SV510 @ SV180 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1662 @ SV510 @ ( hAPP @ ( c_Fun_Ocomp @ SY1663 @ SY1662 @ SV333 @ SV438 ) @ SV180 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6177]) ).

thf(6295,plain,
    ! [SV15: $i,SV181: $i,SV334: $i,SV439: $i,SV511: $i] :
      ( ( ! [SY1664: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1664 @ SV511 @ SV439 @ SV334 ) @ SV181 ) @ SV15 )
            = ( hAPP @ SV334 @ ( hAPP @ SV181 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6178]) ).

thf(6296,plain,
    ! [SV25: $i,SV190: $i,SV341: $i,SV443: $i,SV512: $i] :
      ( ( ( hAPP @ ( c_Set_Oimage @ SV512 @ SV443 @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV512 ) @ SV190 ) @ SV25 ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV443 ) @ ( hAPP @ SV341 @ SV190 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV512 @ SV443 @ SV341 ) @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6182]) ).

thf(6297,plain,
    ! [SV47: $i,SV212: $i,SV355: $i,SV452: $i,SV513: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV513 @ SV452 ) @ SV355 ) @ SV212 ) @ SV47 ) @ SV212 )
        = SV47 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6191]) ).

thf(6298,plain,
    ! [SV48: $i,SV213: $i,SV356: $i,SV453: $i,SV514: $i] :
      ( ( ! [SY1665: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1665 @ SV514 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1665 @ SV514 ) @ SV453 ) @ SV356 ) @ SV213 ) ) @ SV356 ) @ SV48 )
            = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1665 @ SV514 ) @ SV453 ) @ SV356 ) @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6192]) ).

thf(6299,plain,
    ! [SV56: $i,SV220: $i,SV361: $i,SV456: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ ( tc_fun @ SV361 @ tc_HOL_Obool ) ) ) @ SV220 ) @ SV56 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6195]) ).

thf(6300,plain,
    ! [SV57: $i,SV221: $i,SV362: $i,SV457: $i,SV515: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SV515 @ SV457 @ SV362 ) @ SV221 ) @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV457 @ tc_HOL_Obool ) ) )
        = SV57 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6196]) ).

thf(6301,plain,
    ! [SV59: $i,SV223: $i,SV364: $i,SV458: $i,SV516: $i] :
      ( ( ! [SY1666: $i,SY1667: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1667 @ SY1666 @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1667 @ SV458 @ SY1666 ) @ SV364 ) @ SV223 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1667 @ SV458 @ SV516 ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV458 @ SY1666 @ SV516 ) @ SV223 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6197]) ).

thf(6302,plain,
    ! [SV63: $i,SV227: $i,SV366: $i,SV459: $i,SV517: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV517 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV517 @ SV459 ) @ SV366 ) @ SV227 ) ) @ SV366 ) @ SV63 )
        = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV517 @ SV459 ) @ SV366 ) @ SV63 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6198]) ).

thf(6303,plain,
    ! [SV75: $i,SV236: $i,SV372: $i,SV464: $i,SV518: $i] :
      ( ( ! [SY1668: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1668 @ SV518 @ SV464 ) @ SV372 ) @ SV236 ) @ SV75 )
            = ( hAPP @ SV372 @ ( hAPP @ SV236 @ SV75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6203]) ).

thf(6304,plain,
    ! [SV76: $i,SV237: $i,SV373: $i,SV465: $i,SV519: $i] :
      ( ( ! [SY1669: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1669 @ SV519 @ SV465 ) @ SV373 ) @ SV237 ) @ SV76 )
            = ( hAPP @ ( hAPP @ SV373 @ SV76 ) @ SV237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6204]) ).

thf(6305,plain,
    ! [SV77: $i,SV238: $i,SV374: $i,SV466: $i,SV520: $i] :
      ( ( ! [SY1670: $i] :
            ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1670 @ SV520 @ SV466 ) @ SV374 ) @ SV238 ) @ SV77 )
            = ( hAPP @ ( hAPP @ SV374 @ SV77 ) @ ( hAPP @ SV238 @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6205]) ).

thf(6306,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
        | ( SV239 = SV78 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6206]) ).

thf(6307,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( SV239 != SV78 )
        | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6207]) ).

thf(6308,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i] :
      ( ( ! [SY1671: $i] :
            ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1671 @ SV521 ) @ SV467 ) @ SV375 )
                   != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1671 @ SV521 ) @ SV240 ) @ SV79 ) )
                  | ~ ( ( SV467 != SV240 )
                      | ( SV375 != SV79 ) ) )
              | ~ ( ~ ~ ( ( SV467 != SV240 )
                        | ( SV375 != SV79 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1671 @ SV521 ) @ SV467 ) @ SV375 )
                    = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1671 @ SV521 ) @ SV240 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6208]) ).

thf(6309,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i] :
      ( ( ! [SY1672: $i,SY1673: $i,SY1674: $i,SY1675: $i,SY1676: $i,SY1677: $i] :
            ( ( ( hAPP @ SY1677 @ ( hAPP @ SY1676 @ SY1675 ) )
             != ( hAPP @ SY1674 @ ( hAPP @ SY1673 @ SY1672 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1677 ) @ SY1676 ) @ SY1675 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SY1674 ) @ SY1673 ) @ SY1672 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6209]) ).

thf(6310,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i,SV523: $i] :
      ( ( ! [SY1678: $i] :
            ( ~ ( ( SY1678 != SV523 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SY1678 ) @ SV242 ) ) @ SV523 ) @ SV81 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV523 ) @ SV81 ) ) @ SY1678 ) @ SV242 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6210]) ).

thf(6311,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
            | ( SV243 = SV82 ) )
        | ~ ( ( SV243 != SV82 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6211]) ).

thf(6312,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
             != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
            | ( SV244 = SV83 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6212]) ).

thf(6313,plain,
    ! [SV379: $i,SV83: $i,SV244: $i] :
      ( ( ~ ( ( SV244 != SV83 )
            | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
              = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6212]) ).

thf(6314,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
            | ( SV245
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6213]) ).

thf(6315,plain,
    ! [SV84: $i,SV380: $i,SV245: $i] :
      ( ( ~ ( ( SV245
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6213]) ).

thf(6316,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i,SV524: $i] :
      ( ( ! [SY1679: $i,SY1680: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1680 @ SY1679 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1680 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1680 @ SY1679 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1680 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1680 @ SY1679 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1680 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1680 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6214]) ).

thf(6317,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
                 != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
                | ~ ( ( SV472 != SV247 )
                    | ( SV382 != SV86 ) )
                | ~ ( ( SV472 != SV86 )
                    | ( SV382 != SV247 ) ) )
            | ~ ( ~ ( ~ ( ( SV472 != SV247 )
                        | ( SV382 != SV86 ) )
                    | ~ ( ( SV472 != SV86 )
                        | ( SV382 != SV247 ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
                  = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6215]) ).

thf(6318,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i,SV526: $i] :
      ( ( ! [SY1681: $i,SY1682: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1682 @ SY1681 @ SV526 @ SV473 ) @ SV383 )
             != SV248 )
            | ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
              = ( hAPP @ SV248 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6216]) ).

thf(6319,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i,SV527: $i] :
      ( ( ! [SY1683: $i,SY1684: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1684 @ SY1683 @ SV527 @ SV474 @ SV384 )
            | ~ ( ~ ( ( ( hAPP @ SV527 @ SV250 )
                     != ( hAPP @ SV527 @ SV89 ) )
                    | ( SV250 = SV89 ) )
                | ~ ( ( SV250 != SV89 )
                    | ( ( hAPP @ SV527 @ SV250 )
                      = ( hAPP @ SV527 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6218]) ).

thf(6320,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
             != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
            | ( SV251
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6219]) ).

thf(6321,plain,
    ! [SV90: $i,SV385: $i,SV251: $i] :
      ( ( ~ ( ( SV251
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
            | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
              = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6219]) ).

thf(6322,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
             != SV96 )
            | ( SV256
              = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6222]) ).

thf(6323,plain,
    ! [SV96: $i,SV387: $i,SV256: $i] :
      ( ( ~ ( ( SV256
             != ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
            | ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
              = SV96 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6222]) ).

thf(6324,plain,
    ! [SV97: $i,SV257: $i,SV388: $i] :
      ( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV388 @ SV257 @ SV97 )
        = $false )
      | ( ( SV97 = SV388 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6223]) ).

thf(6325,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
            | ( SV389 = SV99 ) )
        | ~ ( ( SV389 != SV99 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6225]) ).

thf(6326,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
         != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
        | ( SV260 = SV100 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6226]) ).

thf(6327,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( SV260 != SV100 )
        | ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
          = ( hAPP @ c_Int_ORep__Integ @ SV100 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6227]) ).

thf(6328,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
         != ( hAPP @ c_Nat_OSuc @ SV101 ) )
        | ( SV261 = SV101 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6228]) ).

thf(6329,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( SV261 != SV101 )
        | ( ( hAPP @ c_Nat_OSuc @ SV261 )
          = ( hAPP @ c_Nat_OSuc @ SV101 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6229]) ).

thf(6330,plain,
    ! [SV102: $i,SV262: $i,SV390: $i,SV476: $i,SV528: $i] :
      ( ( ! [SY1685: $i] :
            ( ~ ( c_Finite__Set_Ofun__left__comm @ SY1685 @ SV528 @ SV476 )
            | ( ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ SV102 ) )
              = ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ SV102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6230]) ).

thf(6331,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
            | ( SV103
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) ) )
        | ~ ( ( SV103
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
            | ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6231]) ).

thf(6332,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
        | ( SV264 = SV104 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6232]) ).

thf(6333,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( SV264 != SV104 )
        | ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6233]) ).

thf(6334,plain,
    ! [SV105: $i,SV265: $i,SV392: $i,SV478: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV478 @ SV392 @ SV265 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV392 @ SV105 ) @ SV105 )
          = SV105 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6234]) ).

thf(6335,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
             != ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
            | ( SV106
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) ) )
        | ~ ( ( SV106
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
            | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
              = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6235]) ).

thf(6336,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i] :
      ( ( ! [SY1686: $i,SY1687: $i,SY1688: $i,SY1689: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1689 @ SY1688 @ SY1687 @ SY1686 ) @ SV529 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SY1688 @ SY1687 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SY1686 @ ( hAPP @ SV529 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6236]) ).

thf(6337,plain,
    ! [SV109: $i,SV268: $i,SV395: $i,SV481: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV395 @ SV268 ) )
        = $true )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV395 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV268 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6237]) ).

thf(6338,plain,
    ! [SV111: $i,SV270: $i,SV396: $i] :
      ( ( ( class_Orderings_Obot @ SV396 )
        = $false )
      | ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV270 @ SV396 ) ) @ SV111 )
          = ( c_Orderings_Obot__class_Obot @ SV396 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6238]) ).

thf(6339,plain,
    ! [SV114: $i,SV273: $i] :
      ( ( ( ( hAPP @ SV273 @ ( sK1_SY1248 @ SV114 @ SV273 ) )
          = ( hAPP @ SV114 @ ( sK1_SY1248 @ SV114 @ SV273 ) ) )
        = $false )
      | ( ( SV273 = SV114 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[6241]) ).

thf(6340,plain,
    ! [SV115: $i,SV274: $i,SV398: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV274 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV115 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( SV274 = SV115 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6242]) ).

thf(6341,plain,
    ! [SV119: $i,SV277: $i,SV399: $i,SV482: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofolding__one @ SV482 @ SV399 @ SV277 ) )
        = $true )
      | ( ( ( hAPP @ SV277 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV482 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_HOL_Obool ) ) ) )
          = SV119 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6245]) ).

thf(6342,plain,
    ! [SV122: $i,SV280: $i,SV401: $i,SV483: $i,SV530: $i] :
      ( ( ( ( hAPP @ SV530 @ SV483 )
         != SV401 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SV530 ) @ SV483 ) @ SV401 )
          = SV530 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6247]) ).

thf(6343,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
         != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
        | ( SV281 = SV123 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6248]) ).

thf(6344,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( SV281 != SV123 )
        | ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6249]) ).

thf(6345,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ( ~ ( class_Finite__Set_Ofinite @ SV284 )
          | ~ ( class_Finite__Set_Ofinite @ SV126 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6251]) ).

thf(6346,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i,SV531: $i] :
      ( ( ! [SY1690: $i,SY1691: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1691 @ SY1690 @ SV531 @ SV484 @ SV403 @ SV286 )
            | ( ( hAPP @ ( hAPP @ SV531 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6252]) ).

thf(6347,plain,
    ! [SV129: $i,SV287: $i,SV404: $i,SV485: $i,SV532: $i] :
      ( ( ! [SY1692: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple @ SY1692 @ SV532 @ SV485 @ SV404 @ SV287 @ SV129 )
            | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV532 @ tc_HOL_Obool ) ) )
              = SV404 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6253]) ).

thf(6348,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i] :
      ( ( ! [SY1693: $i,SY1694: $i] :
            ( ~ ( ( SY1694 != SY1693 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SY1694 ) @ SV288 ) ) @ SY1693 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SY1693 ) @ SV130 ) ) @ SY1694 ) @ SV288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6254]) ).

thf(6349,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i] :
      ( ( ! [SY1695: $i] :
            ~ ( ~ ( ( SY1695 != SV534 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SY1695 )
                    = SV132 ) )
              | ~ ( ~ ( ( SY1695 != SV534 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SY1695 )
                    = ( hAPP @ SV290 @ SY1695 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6255]) ).

thf(6350,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
                 != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
                | ~ ! [SY1696: $i] :
                      ~ ( ~ ( ( SV488
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                             != SV133 ) )
                        | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                             != SV291 )
                            | ( SV407
                             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
            | ~ ( ~ ~ ! [SY1697: $i] :
                        ~ ( ~ ( ( SV488
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                               != SV133 ) )
                          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                               != SV291 )
                              | ( SV407
                               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
                  = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6256]) ).

thf(6351,plain,
    ! [SV135: $i,SV293: $i,SV408: $i,SV489: $i,SV536: $i] :
      ( ( ! [SY1698: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1698 @ SV536 ) @ SV489 ) @ SV408 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1698 @ SV536 ) @ SV293 ) @ SV135 ) )
            | ~ ( ( SV489 != SV293 )
                | ( SV408 != SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6258]) ).

thf(6352,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ( ~ ( class_Enum_Oenum @ SV294 )
          | ~ ( class_Enum_Oenum @ SV136 ) )
        = $true )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6259]) ).

thf(6353,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i,SV537: $i] :
      ( ( ! [SY1699: $i] :
            ( ~ ( ( SY1699 != SV537 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SV537 ) @ SV137 ) @ SY1699 )
              = ( hAPP @ SV295 @ SY1699 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6260]) ).

thf(6354,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
            | ~ ( ( SV296
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                | ( SV138
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6261]) ).

thf(6355,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ~ ( ~ ~ ( ( SV296
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                  | ( SV138
                   != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6261]) ).

thf(6356,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i] :
      ( ( ! [SY1700: $i,SY1701: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1701 @ SY1700 @ SV538 @ SV491 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1701 @ SV412 @ SV298 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SY1700 != SV412 )
                            | ( SV538 != SV298 ) )
                      | ( SV491 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SY1700 != SV412 )
                              | ( SV538 != SV298 ) )
                        | ( SV491 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1701 @ SY1700 @ SV538 @ SV491 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1701 @ SV412 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6263]) ).

thf(6357,plain,
    ! [SV142: $i,SV300: $i,SV413: $i,SV492: $i,SV539: $i] :
      ( ( ! [SY1702: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1702 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1702 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1702 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1702 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1626: $i,SY1627: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1702 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1702 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1702 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1702 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6265]) ).

thf(6358,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
             != ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
            | ( SV304 = SV146 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6269]) ).

thf(6359,plain,
    ! [SV414: $i,SV146: $i,SV304: $i] :
      ( ( ~ ( ( SV304 != SV146 )
            | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
              = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6269]) ).

thf(6360,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
             != ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
            | ( SV305 = SV147 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6270]) ).

thf(6361,plain,
    ! [SV415: $i,SV147: $i,SV305: $i] :
      ( ( ~ ( ( SV305 != SV147 )
            | ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
              = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6270]) ).

thf(6362,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i,SV540: $i] :
      ( ( ! [SY1705: $i,SY1706: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1706 @ SY1705 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1706 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1706 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1706 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1707: $i,SY1708: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
                  | ! [SY1709: $i] :
                      ( ~ ! [SY1710: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1706 @ SY1705 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1706 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1706 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1706 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6271]) ).

thf(6363,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i] :
      ( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1713 @ SY1712 @ SY1711 @ SV541 ) @ SV494 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SY1712 @ SY1711 @ SV308 ) @ SV150 ) )
            | ! [SY1714: $i] :
                ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6273]) ).

thf(6364,plain,
    ! [SV151: $i,SV309: $i,SV418: $i,SV495: $i,SV542: $i] :
      ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV542 @ SV495 @ SV418 )
        | ( ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
          = ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6274]) ).

thf(6365,plain,
    ! [SV152: $i,SV310: $i,SV419: $i,SV496: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ SV152 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ SV152 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6275]) ).

thf(6366,plain,
    ! [SV153: $i,SV311: $i,SV420: $i,SV497: $i,SV543: $i] :
      ( ( ! [SY1715: $i] :
            ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1715 ) @ SV543 ) @ SV497 )
             != SV420 )
            | ( SV311
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1715 ) @ SV497 ) @ SV153 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1715 ) @ SV543 ) @ SV311 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1715 ) @ SV420 ) @ SV153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6276]) ).

thf(6367,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
                 != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
                | ~ ( ( SV498 != SV312 )
                    | ( SV421 != SV154 ) ) )
            | ~ ( ~ ~ ( ( SV498 != SV312 )
                      | ( SV421 != SV154 ) )
                | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
                  = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6277]) ).

thf(6368,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
                 != SV422 )
                | ( ( hAPP @ SV422 @ SV314 )
                  = SV156 ) )
            | ~ ( ( ( hAPP @ SV422 @ SV314 )
                 != SV156 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
                  = SV422 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6279]) ).

thf(6369,plain,
    ! [SV157: $i,SV315: $i,SV423: $i] :
      ( ( ( class_Orderings_Obot @ SV423 )
        = $false )
      | ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ SV423 ) ) @ SV157 )
          = ( c_Orderings_Obot__class_Obot @ SV423 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6280]) ).

thf(6370,plain,
    ! [SV160: $i,SV318: $i,SV426: $i,SV500: $i,SV546: $i] :
      ( ( ! [SY1716: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1716 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1716 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1716 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1716 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1341: $i,SY1342: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1716 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1716 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1716 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1716 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6283]) ).

thf(6371,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i] :
      ( ( ! [SY1719: $i] :
            ~ ( ~ ( ( SY1719 != SV547 )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SY1719 )
                    = SV162 ) )
              | ~ ( ~ ( ( SY1719 != SV547 ) )
                  | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SY1719 )
                    = ( hAPP @ SV320 @ SY1719 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6285]) ).

thf(6372,plain,
    ! [SV163: $i,SV321: $i,SV429: $i,SV502: $i] :
      ( ( ( SV502
         != ( c_Finite__Set_Ofold1 @ SV429 @ SV321 ) )
        = $true )
      | ( ( ( hAPP @ SV502 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV429 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV429 @ tc_HOL_Obool ) ) ) )
          = SV163 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6286]) ).

thf(6373,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
            | ( SV430 = SV164 )
            | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
        | ~ ( ~ ( ( SV430 = SV164 )
                | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6287]) ).

thf(6374,plain,
    ! [SV165: $i,SV323: $i,SV431: $i,SV504: $i,SV548: $i] :
      ( ( ! [SY1720: $i] :
            ( ( SY1720 != SV548 )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SY1720 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV548 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6288]) ).

thf(6375,plain,
    ! [SV166: $i,SV324: $i,SV432: $i,SV505: $i,SV549: $i] :
      ( ( ! [SY1721: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1721 @ SV549 @ SV505 @ SV432 @ SV324 )
            | ( ( hAPP @ SV432 @ ( hAPP @ SV505 @ SV166 ) )
              = SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6289]) ).

thf(6376,plain,
    ! [SV5: $i,SV171: $i,SV327: $i,SV433: $i,SV506: $i,SV550: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV550 @ SV506 @ SV433 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV550 @ SV327 @ SV171 @ SV5 ) )
        = ( hAPP @ ( hAPP @ ( hAPP @ SV433 @ SV327 ) @ SV171 ) @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6290]) ).

thf(6377,plain,
    ! [SV6: $i,SV172: $i,SV328: $i,SV434: $i,SV507: $i,SV551: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV551 @ SV507 @ SV434 @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV551 @ SV328 @ SV172 @ SV6 ) )
        = ( hAPP @ ( hAPP @ ( hAPP @ SV434 @ SV328 ) @ SV172 ) @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6291]) ).

thf(6378,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i,SV508: $i,SV552: $i] :
      ( ( ! [SY1722: $i,SY1723: $i,SY1724: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1724 @ SY1723 @ SY1722 @ SV552 @ SV508 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1723 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6292]) ).

thf(6379,plain,
    ! [SV11: $i,SV177: $i,SV332: $i,SV437: $i,SV509: $i,SV553: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV553 @ SV509 @ SV437 @ SV332 ) @ SV177 ) @ SV11 )
        = ( hAPP @ SV332 @ ( hAPP @ SV177 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6293]) ).

thf(6380,plain,
    ! [SV14: $i,SV180: $i,SV333: $i,SV438: $i,SV510: $i,SV554: $i] :
      ( ( ! [SY1725: $i] :
            ( ( hAPP @ ( c_Fun_Ocomp @ SY1725 @ SV554 @ SV510 @ SV438 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SY1725 @ SV510 @ SV180 ) @ SV14 ) )
            = ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SV554 @ SV510 @ ( hAPP @ ( c_Fun_Ocomp @ SY1725 @ SV554 @ SV333 @ SV438 ) @ SV180 ) ) @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6294]) ).

thf(6381,plain,
    ! [SV15: $i,SV181: $i,SV334: $i,SV439: $i,SV511: $i,SV555: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV555 @ SV511 @ SV439 @ SV334 ) @ SV181 ) @ SV15 )
        = ( hAPP @ SV334 @ ( hAPP @ SV181 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6295]) ).

thf(6382,plain,
    ! [SV48: $i,SV213: $i,SV356: $i,SV453: $i,SV514: $i,SV556: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV556 @ SV514 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV556 @ SV514 ) @ SV453 ) @ SV356 ) @ SV213 ) ) @ SV356 ) @ SV48 )
        = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV556 @ SV514 ) @ SV453 ) @ SV356 ) @ SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6298]) ).

thf(6383,plain,
    ! [SV59: $i,SV223: $i,SV364: $i,SV458: $i,SV516: $i,SV557: $i] :
      ( ( ! [SY1726: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1726 @ SV557 @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1726 @ SV458 @ SV557 ) @ SV364 ) @ SV223 ) ) @ SV59 )
            = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1726 @ SV458 @ SV516 ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV458 @ SV557 @ SV516 ) @ SV223 ) @ SV59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6301]) ).

thf(6384,plain,
    ! [SV75: $i,SV236: $i,SV372: $i,SV464: $i,SV518: $i,SV558: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV558 @ SV518 @ SV464 ) @ SV372 ) @ SV236 ) @ SV75 )
        = ( hAPP @ SV372 @ ( hAPP @ SV236 @ SV75 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6303]) ).

thf(6385,plain,
    ! [SV76: $i,SV237: $i,SV373: $i,SV465: $i,SV519: $i,SV559: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV559 @ SV519 @ SV465 ) @ SV373 ) @ SV237 ) @ SV76 )
        = ( hAPP @ ( hAPP @ SV373 @ SV76 ) @ SV237 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6304]) ).

thf(6386,plain,
    ! [SV77: $i,SV238: $i,SV374: $i,SV466: $i,SV520: $i,SV560: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV560 @ SV520 @ SV466 ) @ SV374 ) @ SV238 ) @ SV77 )
        = ( hAPP @ ( hAPP @ SV374 @ SV77 ) @ ( hAPP @ SV238 @ SV77 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6305]) ).

thf(6387,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
        = $true )
      | ( ( SV239 = SV78 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6306]) ).

thf(6388,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( SV239 != SV78 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6307]) ).

thf(6389,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
                 != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
                | ~ ( ( SV467 != SV240 )
                    | ( SV375 != SV79 ) ) )
            | ~ ( ~ ~ ( ( SV467 != SV240 )
                      | ( SV375 != SV79 ) )
                | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
                  = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6308]) ).

thf(6390,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i] :
      ( ( ! [SY1727: $i,SY1728: $i,SY1729: $i,SY1730: $i,SY1731: $i] :
            ( ( ( hAPP @ SY1731 @ ( hAPP @ SY1730 @ SY1729 ) )
             != ( hAPP @ SY1728 @ ( hAPP @ SY1727 @ SV562 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1731 ) @ SY1730 ) @ SY1729 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SY1728 ) @ SY1727 ) @ SV562 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6309]) ).

thf(6391,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i,SV523: $i,SV563: $i] :
      ( ( ~ ( ( SV563 != SV523 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV563 ) @ SV242 ) ) @ SV523 ) @ SV81 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV523 ) @ SV81 ) ) @ SV563 ) @ SV242 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6310]) ).

thf(6392,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
            | ( SV243 = SV82 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6311]) ).

thf(6393,plain,
    ! [SV378: $i,SV470: $i,SV82: $i,SV243: $i] :
      ( ( ~ ( ( SV243 != SV82 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6311]) ).

thf(6394,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
         != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
        | ( SV244 = SV83 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6312]) ).

thf(6395,plain,
    ! [SV379: $i,SV83: $i,SV244: $i] :
      ( ( ( SV244 != SV83 )
        | ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
          = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6313]) ).

thf(6396,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        | ( SV245
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6314]) ).

thf(6397,plain,
    ! [SV84: $i,SV380: $i,SV245: $i] :
      ( ( ( SV245
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6315]) ).

thf(6398,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i,SV524: $i,SV564: $i] :
      ( ( ! [SY1732: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1732 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1732 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) @ tc_HOL_Obool ) ) ) )
            | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1732 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1732 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) @ tc_HOL_Obool ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1732 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1732 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1732 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6316]) ).

thf(6399,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
             != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
            | ~ ( ( SV472 != SV247 )
                | ( SV382 != SV86 ) )
            | ~ ( ( SV472 != SV86 )
                | ( SV382 != SV247 ) ) )
        | ~ ( ~ ( ~ ( ( SV472 != SV247 )
                    | ( SV382 != SV86 ) )
                | ~ ( ( SV472 != SV86 )
                    | ( SV382 != SV247 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
              = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6317]) ).

thf(6400,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i,SV526: $i,SV565: $i] :
      ( ( ! [SY1733: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1733 @ SV565 @ SV526 @ SV473 ) @ SV383 )
             != SV248 )
            | ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
              = ( hAPP @ SV248 @ SV87 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6318]) ).

thf(6401,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i,SV527: $i,SV566: $i] :
      ( ( ! [SY1734: $i] :
            ( ~ ( c_Typedef_Otype__definition @ SY1734 @ SV566 @ SV527 @ SV474 @ SV384 )
            | ~ ( ~ ( ( ( hAPP @ SV527 @ SV250 )
                     != ( hAPP @ SV527 @ SV89 ) )
                    | ( SV250 = SV89 ) )
                | ~ ( ( SV250 != SV89 )
                    | ( ( hAPP @ SV527 @ SV250 )
                      = ( hAPP @ SV527 @ SV89 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6319]) ).

thf(6402,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
         != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
        | ( SV251
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6320]) ).

thf(6403,plain,
    ! [SV90: $i,SV385: $i,SV251: $i] :
      ( ( ( SV251
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
        | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
          = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6321]) ).

thf(6404,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
         != SV96 )
        | ( SV256
          = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6322]) ).

thf(6405,plain,
    ! [SV96: $i,SV387: $i,SV256: $i] :
      ( ( ( SV256
         != ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
        | ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
          = SV96 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6323]) ).

thf(6406,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
            | ( SV389 = SV99 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6325]) ).

thf(6407,plain,
    ! [SV259: $i,SV475: $i,SV99: $i,SV389: $i] :
      ( ( ~ ( ( SV389 != SV99 )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6325]) ).

thf(6408,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
         != ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
        = $true )
      | ( ( SV260 = SV100 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6326]) ).

thf(6409,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( SV260 != SV100 )
        = $true )
      | ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
          = ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6327]) ).

thf(6410,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
         != ( hAPP @ c_Nat_OSuc @ SV101 ) )
        = $true )
      | ( ( SV261 = SV101 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6328]) ).

thf(6411,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( SV261 != SV101 )
        = $true )
      | ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
          = ( hAPP @ c_Nat_OSuc @ SV101 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6329]) ).

thf(6412,plain,
    ! [SV102: $i,SV262: $i,SV390: $i,SV476: $i,SV528: $i,SV567: $i] :
      ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV567 @ SV528 @ SV476 )
        | ( ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ SV102 ) )
          = ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ SV102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6330]) ).

thf(6413,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
            | ( SV103
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6331]) ).

thf(6414,plain,
    ! [SV263: $i,SV391: $i,SV477: $i,SV103: $i] :
      ( ( ~ ( ( SV103
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
            | ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6331]) ).

thf(6415,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
         != ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
        = $true )
      | ( ( SV264 = SV104 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6332]) ).

thf(6416,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( SV264 != SV104 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6333]) ).

thf(6417,plain,
    ! [SV105: $i,SV265: $i,SV392: $i,SV478: $i] :
      ( ( ( c_Finite__Set_Ofolding__one__idem @ SV478 @ SV392 @ SV265 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV392 @ SV105 ) @ SV105 )
          = SV105 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6334]) ).

thf(6418,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
             != ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
            | ( SV106
              = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6335]) ).

thf(6419,plain,
    ! [SV266: $i,SV479: $i,SV393: $i,SV106: $i] :
      ( ( ~ ( ( SV106
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
            | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
              = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6335]) ).

thf(6420,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i] :
      ( ( ! [SY1735: $i,SY1736: $i,SY1737: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1737 @ SY1736 @ SY1735 @ SV568 ) @ SV529 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SY1736 @ SY1735 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6336]) ).

thf(6421,plain,
    ! [SV109: $i,SV268: $i,SV395: $i,SV481: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV395 @ SV268 )
        = $false )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV395 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV268 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6337]) ).

thf(6422,plain,
    ! [SV119: $i,SV277: $i,SV399: $i,SV482: $i] :
      ( ( ( c_Finite__Set_Ofolding__one @ SV482 @ SV399 @ SV277 )
        = $false )
      | ( ( ( hAPP @ SV277 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV482 ) @ SV119 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_HOL_Obool ) ) ) )
          = SV119 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6341]) ).

thf(6423,plain,
    ! [SV122: $i,SV280: $i,SV401: $i,SV483: $i,SV530: $i] :
      ( ( ( ( hAPP @ SV530 @ SV483 )
         != SV401 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SV530 ) @ SV483 ) @ SV401 )
          = SV530 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6342]) ).

thf(6424,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
         != ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
        = $true )
      | ( ( SV281 = SV123 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6343]) ).

thf(6425,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( SV281 != SV123 )
        = $true )
      | ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6344]) ).

thf(6426,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ( ~ ( class_Finite__Set_Ofinite @ SV284 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV126 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6345]) ).

thf(6427,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i,SV531: $i,SV569: $i] :
      ( ( ! [SY1738: $i] :
            ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1738 @ SV569 @ SV531 @ SV484 @ SV403 @ SV286 )
            | ( ( hAPP @ ( hAPP @ SV531 @ SV128 ) @ SV128 )
              = SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6346]) ).

thf(6428,plain,
    ! [SV129: $i,SV287: $i,SV404: $i,SV485: $i,SV532: $i,SV570: $i] :
      ( ( ~ ( c_Finite__Set_Ofolding__image__simple @ SV570 @ SV532 @ SV485 @ SV404 @ SV287 @ SV129 )
        | ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV532 @ tc_HOL_Obool ) ) )
          = SV404 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6347]) ).

thf(6429,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i,SV571: $i] :
      ( ( ! [SY1739: $i] :
            ( ~ ( ( SY1739 != SV571 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SY1739 ) @ SV288 ) ) @ SV571 ) @ SV130 )
              = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV571 ) @ SV130 ) ) @ SY1739 ) @ SV288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6348]) ).

thf(6430,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ~ ( ~ ( ( SV572 != SV534 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
                  = SV132 ) )
            | ~ ( ~ ( ( SV572 != SV534 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
                  = ( hAPP @ SV290 @ SV572 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6349]) ).

thf(6431,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
            | ~ ! [SY1696: $i] :
                  ~ ( ~ ( ( SV488
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                         != SV133 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                         != SV291 )
                        | ( SV407
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
        | ~ ( ~ ~ ! [SY1697: $i] :
                    ~ ( ~ ( ( SV488
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                           != SV133 ) )
                      | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                           != SV291 )
                          | ( SV407
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6350]) ).

thf(6432,plain,
    ! [SV135: $i,SV293: $i,SV408: $i,SV489: $i,SV536: $i,SV573: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        | ~ ( ( SV489 != SV293 )
            | ( SV408 != SV135 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6351]) ).

thf(6433,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ( ~ ( class_Enum_Oenum @ SV294 ) )
        = $true )
      | ( ( ~ ( class_Enum_Oenum @ SV136 ) )
        = $true )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6352]) ).

thf(6434,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i,SV537: $i,SV574: $i] :
      ( ( ~ ( ( SV574 != SV537 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SV537 ) @ SV137 ) @ SV574 )
          = ( hAPP @ SV295 @ SV574 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6353]) ).

thf(6435,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        | ~ ( ( SV296
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
            | ( SV138
             != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6354]) ).

thf(6436,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ~ ~ ( ( SV296
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
              | ( SV138
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6355]) ).

thf(6437,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i] :
      ( ( ! [SY1740: $i] :
            ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1740 @ SV575 @ SV538 @ SV491 )
                   != ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1740 @ SV412 @ SV298 @ SV140 ) )
                  | ~ ( ~ ~ ( ( SV575 != SV412 )
                            | ( SV538 != SV298 ) )
                      | ( SV491 != SV140 ) ) )
              | ~ ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                              | ( SV538 != SV298 ) )
                        | ( SV491 != SV140 ) )
                  | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1740 @ SV575 @ SV538 @ SV491 )
                    = ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1740 @ SV412 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6356]) ).

thf(6438,plain,
    ! [SV142: $i,SV300: $i,SV413: $i,SV492: $i,SV539: $i,SV576: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        | ~ ! [SY1626: $i,SY1627: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6357]) ).

thf(6439,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
         != ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
        | ( SV304 = SV146 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6358]) ).

thf(6440,plain,
    ! [SV414: $i,SV146: $i,SV304: $i] :
      ( ( ( SV304 != SV146 )
        | ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6359]) ).

thf(6441,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
         != ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
        | ( SV305 = SV147 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6360]) ).

thf(6442,plain,
    ! [SV415: $i,SV147: $i,SV305: $i] :
      ( ( ( SV305 != SV147 )
        | ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
          = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6361]) ).

thf(6443,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i,SV540: $i,SV577: $i] :
      ( ( ! [SY1743: $i] :
            ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1743 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1743 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1743 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1743 ) @ tc_HOL_Obool ) ) ) )
            | ~ ! [SY1707: $i,SY1708: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
                  | ! [SY1709: $i] :
                      ( ~ ! [SY1710: $i] :
                            ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                            | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                      | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) )
            | ( c_Hoare__Mirabelle_Ohoare__derivs @ SY1743 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SY1743 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1743 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY1743 ) @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6362]) ).

thf(6444,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i,SV578: $i] :
      ( ( ! [SY1748: $i,SY1749: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1749 @ SY1748 @ SV578 @ SV541 ) @ SV494 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SY1748 @ SV578 @ SV308 ) @ SV150 ) )
            | ! [SY1714: $i] :
                ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6363]) ).

thf(6445,plain,
    ! [SV151: $i,SV309: $i,SV418: $i,SV495: $i,SV542: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV542 @ SV495 @ SV418 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
          = ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6364]) ).

thf(6446,plain,
    ! [SV152: $i,SV310: $i,SV419: $i,SV496: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ SV152 )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ SV152 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6365]) ).

thf(6447,plain,
    ! [SV153: $i,SV311: $i,SV420: $i,SV497: $i,SV543: $i,SV579: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV497 )
         != SV420 )
        | ( SV311
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV497 ) @ SV153 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV311 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV420 ) @ SV153 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6366]) ).

thf(6448,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
             != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
            | ~ ( ( SV498 != SV312 )
                | ( SV421 != SV154 ) ) )
        | ~ ( ~ ~ ( ( SV498 != SV312 )
                  | ( SV421 != SV154 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6367]) ).

thf(6449,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
             != SV422 )
            | ( ( hAPP @ SV422 @ SV314 )
              = SV156 ) )
        | ~ ( ( ( hAPP @ SV422 @ SV314 )
             != SV156 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
              = SV422 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6368]) ).

thf(6450,plain,
    ! [SV160: $i,SV318: $i,SV426: $i,SV500: $i,SV546: $i,SV580: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        | ~ ! [SY1341: $i,SY1342: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6370]) ).

thf(6451,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ~ ( ~ ( ( SV581 != SV547 )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
                  = SV162 ) )
            | ~ ( ~ ( ( SV581 != SV547 ) )
                | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
                  = ( hAPP @ SV320 @ SV581 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6371]) ).

thf(6452,plain,
    ! [SV163: $i,SV321: $i,SV429: $i,SV502: $i] :
      ( ( ( SV502
          = ( c_Finite__Set_Ofold1 @ SV429 @ SV321 ) )
        = $false )
      | ( ( ( hAPP @ SV502 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV429 ) @ SV163 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV429 @ tc_HOL_Obool ) ) ) )
          = SV163 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6372]) ).

thf(6453,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
            | ( SV430 = SV164 )
            | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6373]) ).

thf(6454,plain,
    ! [SV503: $i,SV322: $i,SV164: $i,SV430: $i] :
      ( ( ~ ( ~ ( ( SV430 = SV164 )
                | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
            | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6373]) ).

thf(6455,plain,
    ! [SV165: $i,SV323: $i,SV431: $i,SV504: $i,SV548: $i,SV582: $i] :
      ( ( ( SV582 != SV548 )
        | ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV582 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV548 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6374]) ).

thf(6456,plain,
    ! [SV166: $i,SV324: $i,SV432: $i,SV505: $i,SV549: $i,SV583: $i] :
      ( ( ~ ( c_Typedef_Otype__definition @ SV583 @ SV549 @ SV505 @ SV432 @ SV324 )
        | ( ( hAPP @ SV432 @ ( hAPP @ SV505 @ SV166 ) )
          = SV166 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6375]) ).

thf(6457,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i,SV508: $i,SV552: $i,SV584: $i] :
      ( ( ! [SY1753: $i,SY1754: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1754 @ SY1753 @ SV584 @ SV552 @ SV508 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SY1753 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6378]) ).

thf(6458,plain,
    ! [SV14: $i,SV180: $i,SV333: $i,SV438: $i,SV510: $i,SV554: $i,SV585: $i] :
      ( ( ( hAPP @ ( c_Fun_Ocomp @ SV585 @ SV554 @ SV510 @ SV438 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SV585 @ SV510 @ SV180 ) @ SV14 ) )
        = ( hAPP @ ( c_Fun_Ocomp @ SV333 @ SV554 @ SV510 @ ( hAPP @ ( c_Fun_Ocomp @ SV585 @ SV554 @ SV333 @ SV438 ) @ SV180 ) ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6380]) ).

thf(6459,plain,
    ! [SV59: $i,SV223: $i,SV364: $i,SV458: $i,SV516: $i,SV557: $i,SV586: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV586 @ SV557 @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV586 @ SV458 @ SV557 ) @ SV364 ) @ SV223 ) ) @ SV59 )
        = ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV586 @ SV458 @ SV516 ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV458 @ SV557 @ SV516 ) @ SV223 ) @ SV59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6383]) ).

thf(6460,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
        = $false )
      | ( ( SV239 = SV78 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6387]) ).

thf(6461,plain,
    ! [SV78: $i,SV239: $i] :
      ( ( ( SV239 = SV78 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV239 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV78 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6388]) ).

thf(6462,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
            | ~ ( ( SV467 != SV240 )
                | ( SV375 != SV79 ) ) )
        | ~ ( ~ ~ ( ( SV467 != SV240 )
                  | ( SV375 != SV79 ) )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6389]) ).

thf(6463,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i] :
      ( ( ! [SY1755: $i,SY1756: $i,SY1757: $i,SY1758: $i] :
            ( ( ( hAPP @ SY1758 @ ( hAPP @ SY1757 @ SY1756 ) )
             != ( hAPP @ SY1755 @ ( hAPP @ SV587 @ SV562 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1758 ) @ SY1757 ) @ SY1756 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SY1755 ) @ SV587 ) @ SV562 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6390]) ).

thf(6464,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i,SV523: $i,SV563: $i] :
      ( ( ( ~ ( ( SV563 != SV523 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV563 ) @ SV242 ) ) @ SV523 ) @ SV81 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV523 ) @ SV81 ) ) @ SV563 ) @ SV242 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6391]) ).

thf(6465,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
        | ( SV243 = SV82 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6392]) ).

thf(6466,plain,
    ! [SV378: $i,SV470: $i,SV82: $i,SV243: $i] :
      ( ( ( SV243 != SV82 )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6393]) ).

thf(6467,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
         != ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
        = $true )
      | ( ( SV244 = SV83 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6394]) ).

thf(6468,plain,
    ! [SV379: $i,SV83: $i,SV244: $i] :
      ( ( ( SV244 != SV83 )
        = $true )
      | ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
          = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6395]) ).

thf(6469,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( SV245
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6396]) ).

thf(6470,plain,
    ! [SV84: $i,SV380: $i,SV245: $i] :
      ( ( ( SV245
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6397]) ).

thf(6471,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i,SV524: $i,SV564: $i,SV588: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6398]) ).

thf(6472,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
             != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
            | ~ ( ( SV472 != SV247 )
                | ( SV382 != SV86 ) )
            | ~ ( ( SV472 != SV86 )
                | ( SV382 != SV247 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6399]) ).

thf(6473,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ~ ( ~ ( ~ ( ( SV472 != SV247 )
                    | ( SV382 != SV86 ) )
                | ~ ( ( SV472 != SV86 )
                    | ( SV382 != SV247 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
              = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6399]) ).

thf(6474,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i,SV526: $i,SV565: $i,SV589: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV589 @ SV565 @ SV526 @ SV473 ) @ SV383 )
         != SV248 )
        | ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
          = ( hAPP @ SV248 @ SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6400]) ).

thf(6475,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i,SV527: $i,SV566: $i,SV590: $i] :
      ( ( ~ ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        | ~ ( ~ ( ( ( hAPP @ SV527 @ SV250 )
                 != ( hAPP @ SV527 @ SV89 ) )
                | ( SV250 = SV89 ) )
            | ~ ( ( SV250 != SV89 )
                | ( ( hAPP @ SV527 @ SV250 )
                  = ( hAPP @ SV527 @ SV89 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6401]) ).

thf(6476,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
         != ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
        = $true )
      | ( ( SV251
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6402]) ).

thf(6477,plain,
    ! [SV90: $i,SV385: $i,SV251: $i] :
      ( ( ( SV251
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
          = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6403]) ).

thf(6478,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
         != SV96 )
        = $true )
      | ( ( SV256
          = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6404]) ).

thf(6479,plain,
    ! [SV96: $i,SV387: $i,SV256: $i] :
      ( ( ( SV256
         != ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
        = $true )
      | ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
          = SV96 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6405]) ).

thf(6480,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
        | ( SV389 = SV99 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6406]) ).

thf(6481,plain,
    ! [SV259: $i,SV475: $i,SV99: $i,SV389: $i] :
      ( ( ( SV389 != SV99 )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6407]) ).

thf(6482,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
          = ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
        = $false )
      | ( ( SV260 = SV100 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6408]) ).

thf(6483,plain,
    ! [SV100: $i,SV260: $i] :
      ( ( ( SV260 = SV100 )
        = $false )
      | ( ( ( hAPP @ c_Int_ORep__Integ @ SV260 )
          = ( hAPP @ c_Int_ORep__Integ @ SV100 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6409]) ).

thf(6484,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
          = ( hAPP @ c_Nat_OSuc @ SV101 ) )
        = $false )
      | ( ( SV261 = SV101 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6410]) ).

thf(6485,plain,
    ! [SV101: $i,SV261: $i] :
      ( ( ( SV261 = SV101 )
        = $false )
      | ( ( ( hAPP @ c_Nat_OSuc @ SV261 )
          = ( hAPP @ c_Nat_OSuc @ SV101 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6411]) ).

thf(6486,plain,
    ! [SV102: $i,SV262: $i,SV390: $i,SV476: $i,SV528: $i,SV567: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV567 @ SV528 @ SV476 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ SV102 ) )
          = ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ SV102 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6412]) ).

thf(6487,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
        | ( SV103
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6413]) ).

thf(6488,plain,
    ! [SV263: $i,SV391: $i,SV477: $i,SV103: $i] :
      ( ( ( SV103
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
        | ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6414]) ).

thf(6489,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
        = $false )
      | ( ( SV264 = SV104 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6415]) ).

thf(6490,plain,
    ! [SV104: $i,SV264: $i] :
      ( ( ( SV264 = SV104 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV264 )
          = ( hAPP @ c_Code__Numeral_Onat__of @ SV104 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6416]) ).

thf(6491,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
         != ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
        | ( SV106
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6418]) ).

thf(6492,plain,
    ! [SV266: $i,SV479: $i,SV393: $i,SV106: $i] :
      ( ( ( SV106
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
        | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
          = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6419]) ).

thf(6493,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i,SV591: $i] :
      ( ( ! [SY1759: $i,SY1760: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1760 @ SY1759 @ SV591 @ SV568 ) @ SV529 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SY1759 @ SV591 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6420]) ).

thf(6494,plain,
    ! [SV268: $i,SV395: $i,SV109: $i,SV481: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV395 ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV268 )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV395 @ SV268 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6421]) ).

thf(6495,plain,
    ! [SV122: $i,SV280: $i,SV401: $i,SV483: $i,SV530: $i] :
      ( ( ( ( hAPP @ SV530 @ SV483 )
          = SV401 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV280 @ SV122 ) @ SV530 ) @ SV483 ) @ SV401 )
          = SV530 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6423]) ).

thf(6496,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
        = $false )
      | ( ( SV281 = SV123 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6424]) ).

thf(6497,plain,
    ! [SV123: $i,SV281: $i] :
      ( ( ( SV281 = SV123 )
        = $false )
      | ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV281 )
          = ( hAPP @ c_Code__Numeral_Oof__nat @ SV123 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6425]) ).

thf(6498,plain,
    ! [SV126: $i,SV284: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV284 )
        = $false )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV126 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6426]) ).

thf(6499,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i,SV531: $i,SV569: $i,SV592: $i] :
      ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV592 @ SV569 @ SV531 @ SV484 @ SV403 @ SV286 )
        | ( ( hAPP @ ( hAPP @ SV531 @ SV128 ) @ SV128 )
          = SV128 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6427]) ).

thf(6500,plain,
    ! [SV129: $i,SV287: $i,SV404: $i,SV485: $i,SV532: $i,SV570: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofolding__image__simple @ SV570 @ SV532 @ SV485 @ SV404 @ SV287 @ SV129 ) )
        = $true )
      | ( ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV532 @ tc_HOL_Obool ) ) )
          = SV404 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6428]) ).

thf(6501,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i,SV571: $i,SV593: $i] :
      ( ( ~ ( ( SV593 != SV571 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV593 ) @ SV288 ) ) @ SV571 ) @ SV130 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV571 ) @ SV130 ) ) @ SV593 ) @ SV288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6429]) ).

thf(6502,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ~ ( ( SV572 != SV534 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
              = SV132 ) )
        | ~ ( ~ ( ( SV572 != SV534 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
              = ( hAPP @ SV290 @ SV572 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6430]) ).

thf(6503,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
             != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
            | ~ ! [SY1696: $i] :
                  ~ ( ~ ( ( SV488
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                         != SV133 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                         != SV291 )
                        | ( SV407
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6431]) ).

thf(6504,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ~ ( ~ ~ ! [SY1697: $i] :
                    ~ ( ~ ( ( SV488
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                           != SV133 ) )
                      | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                           != SV291 )
                          | ( SV407
                           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
              = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6431]) ).

thf(6505,plain,
    ! [SV135: $i,SV293: $i,SV408: $i,SV489: $i,SV536: $i,SV573: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $true )
      | ( ( ~ ( ( SV489 != SV293 )
              | ( SV408 != SV135 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6432]) ).

thf(6506,plain,
    ! [SV136: $i,SV294: $i] :
      ( ( ( class_Enum_Oenum @ SV294 )
        = $false )
      | ( ( ~ ( class_Enum_Oenum @ SV136 ) )
        = $true )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6433]) ).

thf(6507,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i,SV537: $i,SV574: $i] :
      ( ( ( ~ ( ( SV574 != SV537 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SV537 ) @ SV137 ) @ SV574 )
          = ( hAPP @ SV295 @ SV574 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6434]) ).

thf(6508,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ~ ( ( SV296
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
              | ( SV138
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6435]) ).

thf(6509,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( ~ ~ ( ( SV296
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
                | ( SV138
                 != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6436]) ).

thf(6510,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ~ ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
                 != ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
                | ~ ( ~ ~ ( ( SV575 != SV412 )
                          | ( SV538 != SV298 ) )
                    | ( SV491 != SV140 ) ) )
            | ~ ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                            | ( SV538 != SV298 ) )
                      | ( SV491 != SV140 ) )
                | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
                  = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6437]) ).

thf(6511,plain,
    ! [SV142: $i,SV300: $i,SV413: $i,SV492: $i,SV539: $i,SV576: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ! [SY1626: $i,SY1627: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6438]) ).

thf(6512,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
         != ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
        = $true )
      | ( ( SV304 = SV146 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6439]) ).

thf(6513,plain,
    ! [SV414: $i,SV146: $i,SV304: $i] :
      ( ( ( SV304 != SV146 )
        = $true )
      | ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6440]) ).

thf(6514,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
         != ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
        = $true )
      | ( ( SV305 = SV147 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6441]) ).

thf(6515,plain,
    ! [SV415: $i,SV147: $i,SV305: $i] :
      ( ( ( SV305 != SV147 )
        = $true )
      | ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
          = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6442]) ).

thf(6516,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i,SV540: $i,SV577: $i,SV595: $i] :
      ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        | ~ ! [SY1707: $i,SY1708: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
              | ! [SY1709: $i] :
                  ( ~ ! [SY1710: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                        | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) )
        | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6443]) ).

thf(6517,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i,SV578: $i,SV596: $i] :
      ( ( ! [SY1765: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1765 @ SV596 @ SV578 @ SV541 ) @ SV494 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SV596 @ SV578 @ SV308 ) @ SV150 ) )
            | ! [SY1714: $i] :
                ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
                = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6444]) ).

thf(6518,plain,
    ! [SV151: $i,SV309: $i,SV418: $i,SV495: $i,SV542: $i] :
      ( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV542 @ SV495 @ SV418 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
          = ( hAPP @ ( hAPP @ SV418 @ SV309 ) @ SV151 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6445]) ).

thf(6519,plain,
    ! [SV310: $i,SV152: $i,SV419: $i,SV496: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ SV152 ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ SV152 ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6446]) ).

thf(6520,plain,
    ! [SV153: $i,SV311: $i,SV420: $i,SV497: $i,SV543: $i,SV579: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV497 )
         != SV420 )
        = $true )
      | ( ( ( SV311
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV497 ) @ SV153 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV311 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV420 ) @ SV153 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6447]) ).

thf(6521,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
             != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
            | ~ ( ( SV498 != SV312 )
                | ( SV421 != SV154 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6448]) ).

thf(6522,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ~ ( ~ ~ ( ( SV498 != SV312 )
                  | ( SV421 != SV154 ) )
            | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
              = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6448]) ).

thf(6523,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
             != SV422 )
            | ( ( hAPP @ SV422 @ SV314 )
              = SV156 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6449]) ).

thf(6524,plain,
    ! [SV499: $i,SV545: $i,SV156: $i,SV314: $i,SV422: $i] :
      ( ( ~ ( ( ( hAPP @ SV422 @ SV314 )
             != SV156 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
              = SV422 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6449]) ).

thf(6525,plain,
    ! [SV160: $i,SV318: $i,SV426: $i,SV500: $i,SV546: $i,SV580: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ! [SY1341: $i,SY1342: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6450]) ).

thf(6526,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ~ ( ( SV581 != SV547 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
              = SV162 ) )
        | ~ ( ~ ( ( SV581 != SV547 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
              = ( hAPP @ SV320 @ SV581 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6451]) ).

thf(6527,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        | ( SV430 = SV164 )
        | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6453]) ).

thf(6528,plain,
    ! [SV503: $i,SV322: $i,SV164: $i,SV430: $i] :
      ( ( ~ ( ( SV430 = SV164 )
            | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
        | ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6454]) ).

thf(6529,plain,
    ! [SV165: $i,SV323: $i,SV431: $i,SV504: $i,SV548: $i,SV582: $i] :
      ( ( ( SV582 != SV548 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV582 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV548 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6455]) ).

thf(6530,plain,
    ! [SV166: $i,SV324: $i,SV432: $i,SV505: $i,SV549: $i,SV583: $i] :
      ( ( ( ~ ( c_Typedef_Otype__definition @ SV583 @ SV549 @ SV505 @ SV432 @ SV324 ) )
        = $true )
      | ( ( ( hAPP @ SV432 @ ( hAPP @ SV505 @ SV166 ) )
          = SV166 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6456]) ).

thf(6531,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i,SV508: $i,SV552: $i,SV584: $i,SV597: $i] :
      ( ( ! [SY1767: $i] :
            ( ( c_Com_Ocom_Ocom__case @ SY1767 @ SV597 @ SV584 @ SV552 @ SV508 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
            = SV597 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6457]) ).

thf(6532,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
             != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
            | ~ ( ( SV467 != SV240 )
                | ( SV375 != SV79 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6462]) ).

thf(6533,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ~ ( ~ ~ ( ( SV467 != SV240 )
                  | ( SV375 != SV79 ) )
            | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
              = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6462]) ).

thf(6534,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i] :
      ( ( ! [SY1768: $i,SY1769: $i,SY1770: $i] :
            ( ( ( hAPP @ SY1770 @ ( hAPP @ SY1769 @ SY1768 ) )
             != ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1770 ) @ SY1769 ) @ SY1768 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6463]) ).

thf(6535,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i,SV523: $i,SV563: $i] :
      ( ( ( SV563 != SV523 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV563 ) @ SV242 ) ) @ SV523 ) @ SV81 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV523 ) @ SV81 ) ) @ SV563 ) @ SV242 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6464]) ).

thf(6536,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
        = $true )
      | ( ( SV243 = SV82 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6465]) ).

thf(6537,plain,
    ! [SV378: $i,SV470: $i,SV82: $i,SV243: $i] :
      ( ( ( SV243 != SV82 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6466]) ).

thf(6538,plain,
    ! [SV83: $i,SV244: $i,SV379: $i] :
      ( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
          = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
        = $false )
      | ( ( SV244 = SV83 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6467]) ).

thf(6539,plain,
    ! [SV379: $i,SV83: $i,SV244: $i] :
      ( ( ( SV244 = SV83 )
        = $false )
      | ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV244 )
          = ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV379 @ tc_HOL_Obool ) ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6468]) ).

thf(6540,plain,
    ! [SV84: $i,SV245: $i,SV380: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( SV245
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6469]) ).

thf(6541,plain,
    ! [SV84: $i,SV380: $i,SV245: $i] :
      ( ( ( SV245
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV380 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV380 ) @ SV245 ) @ SV84 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV380 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6470]) ).

thf(6542,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i,SV524: $i,SV564: $i,SV588: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6471]) ).

thf(6543,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        | ~ ( ( SV472 != SV247 )
            | ( SV382 != SV86 ) )
        | ~ ( ( SV472 != SV86 )
            | ( SV382 != SV247 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6472]) ).

thf(6544,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ~ ( ~ ( ( SV472 != SV247 )
                | ( SV382 != SV86 ) )
            | ~ ( ( SV472 != SV86 )
                | ( SV382 != SV247 ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6473]) ).

thf(6545,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i,SV526: $i,SV565: $i,SV589: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV589 @ SV565 @ SV526 @ SV473 ) @ SV383 )
         != SV248 )
        = $true )
      | ( ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
          = ( hAPP @ SV248 @ SV87 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6474]) ).

thf(6546,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i,SV527: $i,SV566: $i,SV590: $i] :
      ( ( ( ~ ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( hAPP @ SV527 @ SV250 )
                   != ( hAPP @ SV527 @ SV89 ) )
                  | ( SV250 = SV89 ) )
              | ~ ( ( SV250 != SV89 )
                  | ( ( hAPP @ SV527 @ SV250 )
                    = ( hAPP @ SV527 @ SV89 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6475]) ).

thf(6547,plain,
    ! [SV90: $i,SV251: $i,SV385: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
          = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
        = $false )
      | ( ( SV251
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6476]) ).

thf(6548,plain,
    ! [SV90: $i,SV385: $i,SV251: $i] :
      ( ( ( SV251
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV385 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
          = ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV385 ) @ SV251 ) @ SV90 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6477]) ).

thf(6549,plain,
    ! [SV96: $i,SV256: $i,SV387: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
          = SV96 )
        = $false )
      | ( ( SV256
          = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6478]) ).

thf(6550,plain,
    ! [SV96: $i,SV387: $i,SV256: $i] :
      ( ( ( SV256
          = ( hAPP @ ( c_List_Orev @ SV387 ) @ SV96 ) )
        = $false )
      | ( ( ( hAPP @ ( c_List_Orev @ SV387 ) @ SV256 )
          = SV96 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6479]) ).

thf(6551,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
        = $true )
      | ( ( SV389 = SV99 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6480]) ).

thf(6552,plain,
    ! [SV259: $i,SV475: $i,SV99: $i,SV389: $i] :
      ( ( ( SV389 != SV99 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6481]) ).

thf(6553,plain,
    ! [SV102: $i,SV262: $i,SV390: $i,SV476: $i,SV528: $i,SV567: $i] :
      ( ( ( c_Finite__Set_Ofun__left__comm @ SV567 @ SV528 @ SV476 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ SV102 ) )
          = ( hAPP @ ( hAPP @ SV476 @ SV262 ) @ ( hAPP @ ( hAPP @ SV476 @ SV390 ) @ SV102 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6486]) ).

thf(6554,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( SV103
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6487]) ).

thf(6555,plain,
    ! [SV263: $i,SV391: $i,SV477: $i,SV103: $i] :
      ( ( ( SV103
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6488]) ).

thf(6556,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
         != ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
        = $true )
      | ( ( SV106
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6491]) ).

thf(6557,plain,
    ! [SV266: $i,SV479: $i,SV393: $i,SV106: $i] :
      ( ( ( SV106
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
          = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6492]) ).

thf(6558,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i,SV591: $i,SV599: $i] :
      ( ( ! [SY1771: $i] :
            ( ( ( hAPP @ ( c_Fun_Ocomp @ SY1771 @ SV599 @ SV591 @ SV568 ) @ SV529 )
             != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SV599 @ SV591 @ SV394 ) @ SV267 ) )
            | ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
              = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6493]) ).

thf(6559,plain,
    ! [SV268: $i,SV395: $i,SV109: $i,SV481: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV395 )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV109 @ SV268 )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV481 @ SV395 @ SV268 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6494]) ).

thf(6560,plain,
    ! [SV284: $i,SV126: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV126 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ SV284 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV284 @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6498]) ).

thf(6561,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i,SV531: $i,SV569: $i,SV592: $i] :
      ( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV592 @ SV569 @ SV531 @ SV484 @ SV403 @ SV286 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ SV531 @ SV128 ) @ SV128 )
          = SV128 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6499]) ).

thf(6562,plain,
    ! [SV129: $i,SV287: $i,SV404: $i,SV485: $i,SV532: $i,SV570: $i] :
      ( ( ( c_Finite__Set_Ofolding__image__simple @ SV570 @ SV532 @ SV485 @ SV404 @ SV287 @ SV129 )
        = $false )
      | ( ( ( hAPP @ SV129 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV532 @ tc_HOL_Obool ) ) )
          = SV404 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6500]) ).

thf(6563,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i,SV571: $i,SV593: $i] :
      ( ( ( ~ ( ( SV593 != SV571 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV593 ) @ SV288 ) ) @ SV571 ) @ SV130 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV571 ) @ SV130 ) ) @ SV593 ) @ SV288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6501]) ).

thf(6564,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ~ ( ( SV572 != SV534 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
              = SV132 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6502]) ).

thf(6565,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ~ ( ~ ( ( SV572 != SV534 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
              = ( hAPP @ SV290 @ SV572 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6502]) ).

thf(6566,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        | ~ ! [SY1696: $i] :
              ~ ( ~ ( ( SV488
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                     != SV133 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                     != SV291 )
                    | ( SV407
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6503]) ).

thf(6567,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ~ ~ ! [SY1697: $i] :
                ~ ( ~ ( ( SV488
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                       != SV133 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                       != SV291 )
                      | ( SV407
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6504]) ).

thf(6568,plain,
    ! [SV135: $i,SV293: $i,SV408: $i,SV489: $i,SV536: $i,SV573: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false )
      | ( ( ~ ( ( SV489 != SV293 )
              | ( SV408 != SV135 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6505]) ).

thf(6569,plain,
    ! [SV294: $i,SV136: $i] :
      ( ( ( class_Enum_Oenum @ SV136 )
        = $false )
      | ( ( class_Enum_Oenum @ SV294 )
        = $false )
      | ( ( class_Enum_Oenum @ ( tc_fun @ SV294 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6506]) ).

thf(6570,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i,SV537: $i,SV574: $i] :
      ( ( ( SV574 != SV537 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SV537 ) @ SV137 ) @ SV574 )
          = ( hAPP @ SV295 @ SV574 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6507]) ).

thf(6571,plain,
    ! [SV138: $i,SV296: $i,SV410: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ~ ( ( SV296
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
              | ( SV138
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6508]) ).

thf(6572,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( ~ ( ( SV296
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
              | ( SV138
               != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6509]) ).

thf(6573,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
             != ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
            | ~ ( ~ ~ ( ( SV575 != SV412 )
                      | ( SV538 != SV298 ) )
                | ( SV491 != SV140 ) ) )
        | ~ ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                        | ( SV538 != SV298 ) )
                  | ( SV491 != SV140 ) )
            | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
              = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6510]) ).

thf(6574,plain,
    ! [SV142: $i,SV300: $i,SV413: $i,SV492: $i,SV539: $i,SV576: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ~ ! [SY1626: $i,SY1627: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6511]) ).

thf(6575,plain,
    ! [SV146: $i,SV304: $i,SV414: $i] :
      ( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
        = $false )
      | ( ( SV304 = SV146 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6512]) ).

thf(6576,plain,
    ! [SV414: $i,SV146: $i,SV304: $i] :
      ( ( ( SV304 = SV146 )
        = $false )
      | ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV304 )
          = ( hAPP @ ( c_Option_Ooption_OSome @ SV414 ) @ SV146 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6513]) ).

thf(6577,plain,
    ! [SV147: $i,SV305: $i,SV415: $i] :
      ( ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
          = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
        = $false )
      | ( ( SV305 = SV147 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6514]) ).

thf(6578,plain,
    ! [SV415: $i,SV147: $i,SV305: $i] :
      ( ( ( SV305 = SV147 )
        = $false )
      | ( ( ( hAPP @ ( c_List_Orev @ SV415 ) @ SV305 )
          = ( hAPP @ ( c_List_Orev @ SV415 ) @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6515]) ).

thf(6579,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i,SV540: $i,SV577: $i,SV595: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ! [SY1707: $i,SY1708: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
                | ! [SY1709: $i] :
                    ( ~ ! [SY1710: $i] :
                          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6516]) ).

thf(6580,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i,SV578: $i,SV596: $i,SV600: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV600 @ SV596 @ SV578 @ SV541 ) @ SV494 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SV596 @ SV578 @ SV308 ) @ SV150 ) )
        | ! [SY1714: $i] :
            ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
            = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6517]) ).

thf(6581,plain,
    ! [SV310: $i,SV152: $i,SV419: $i,SV496: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ SV152 )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ SV152 ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV496 @ SV419 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) ) @ SV310 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV496 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6519]) ).

thf(6582,plain,
    ! [SV153: $i,SV311: $i,SV420: $i,SV497: $i,SV543: $i,SV579: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV497 )
          = SV420 )
        = $false )
      | ( ( ( SV311
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV497 ) @ SV153 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV311 )
            = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV420 ) @ SV153 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6520]) ).

thf(6583,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        | ~ ( ( SV498 != SV312 )
            | ( SV421 != SV154 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6521]) ).

thf(6584,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ~ ~ ( ( SV498 != SV312 )
              | ( SV421 != SV154 ) )
        | ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6522]) ).

thf(6585,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
         != SV422 )
        | ( ( hAPP @ SV422 @ SV314 )
          = SV156 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6523]) ).

thf(6586,plain,
    ! [SV499: $i,SV545: $i,SV156: $i,SV314: $i,SV422: $i] :
      ( ( ( ( hAPP @ SV422 @ SV314 )
         != SV156 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
          = SV422 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6524]) ).

thf(6587,plain,
    ! [SV160: $i,SV318: $i,SV426: $i,SV500: $i,SV546: $i,SV580: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ~ ! [SY1341: $i,SY1342: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6525]) ).

thf(6588,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ~ ( ( SV581 != SV547 )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
              = SV162 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6526]) ).

thf(6589,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ~ ( ~ ( ( SV581 != SV547 ) )
            | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
              = ( hAPP @ SV320 @ SV581 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6526]) ).

thf(6590,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) ) )
        = $true )
      | ( ( ( SV430 = SV164 )
          | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6527]) ).

thf(6591,plain,
    ! [SV503: $i,SV322: $i,SV164: $i,SV430: $i] :
      ( ( ( ~ ( ( SV430 = SV164 )
              | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6528]) ).

thf(6592,plain,
    ! [SV165: $i,SV323: $i,SV431: $i,SV504: $i,SV548: $i,SV582: $i] :
      ( ( ( SV582 = SV548 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV582 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV504 @ SV431 @ SV323 ) @ SV165 ) @ SV548 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6529]) ).

thf(6593,plain,
    ! [SV166: $i,SV324: $i,SV432: $i,SV505: $i,SV549: $i,SV583: $i] :
      ( ( ( c_Typedef_Otype__definition @ SV583 @ SV549 @ SV505 @ SV432 @ SV324 )
        = $false )
      | ( ( ( hAPP @ SV432 @ ( hAPP @ SV505 @ SV166 ) )
          = SV166 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6530]) ).

thf(6594,plain,
    ! [SV10: $i,SV176: $i,SV331: $i,SV436: $i,SV508: $i,SV552: $i,SV584: $i,SV597: $i,SV601: $i] :
      ( ( ( c_Com_Ocom_Ocom__case @ SV601 @ SV597 @ SV584 @ SV552 @ SV508 @ SV436 @ SV331 @ SV176 @ SV10 @ c_Com_Ocom_OSKIP )
        = SV597 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6531]) ).

thf(6595,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        | ~ ( ( SV467 != SV240 )
            | ( SV375 != SV79 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6532]) ).

thf(6596,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ~ ~ ( ( SV467 != SV240 )
              | ( SV375 != SV79 ) )
        | ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6533]) ).

thf(6597,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i,SV602: $i] :
      ( ( ! [SY1773: $i,SY1774: $i] :
            ( ( ( hAPP @ SY1774 @ ( hAPP @ SY1773 @ SV602 ) )
             != ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1774 ) @ SY1773 ) @ SV602 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6534]) ).

thf(6598,plain,
    ! [SV81: $i,SV242: $i,SV377: $i,SV469: $i,SV523: $i,SV563: $i] :
      ( ( ( SV563 = SV523 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV563 ) @ SV242 ) ) @ SV523 ) @ SV81 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV469 @ SV377 ) @ SV523 ) @ SV81 ) ) @ SV563 ) @ SV242 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6535]) ).

thf(6599,plain,
    ! [SV82: $i,SV243: $i,SV378: $i,SV470: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
        = $false )
      | ( ( SV243 = SV82 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6536]) ).

thf(6600,plain,
    ! [SV378: $i,SV470: $i,SV82: $i,SV243: $i] :
      ( ( ( SV243 = SV82 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV243 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV470 ) @ SV378 ) @ SV82 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6537]) ).

thf(6601,plain,
    ! [SV85: $i,SV246: $i,SV381: $i,SV471: $i,SV524: $i,SV564: $i,SV588: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6542]) ).

thf(6602,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
         != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( ~ ( ( SV472 != SV247 )
              | ( SV382 != SV86 ) )
          | ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6543]) ).

thf(6603,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ~ ( ~ ( ( SV472 != SV247 )
                  | ( SV382 != SV86 ) )
              | ~ ( ( SV472 != SV86 )
                  | ( SV382 != SV247 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6544]) ).

thf(6604,plain,
    ! [SV87: $i,SV248: $i,SV383: $i,SV473: $i,SV526: $i,SV565: $i,SV589: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV589 @ SV565 @ SV526 @ SV473 ) @ SV383 )
          = SV248 )
        = $false )
      | ( ( ( hAPP @ SV473 @ ( hAPP @ SV383 @ SV87 ) )
          = ( hAPP @ SV248 @ SV87 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6545]) ).

thf(6605,plain,
    ! [SV89: $i,SV250: $i,SV384: $i,SV474: $i,SV527: $i,SV566: $i,SV590: $i] :
      ( ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false )
      | ( ( ~ ( ~ ( ( ( hAPP @ SV527 @ SV250 )
                   != ( hAPP @ SV527 @ SV89 ) )
                  | ( SV250 = SV89 ) )
              | ~ ( ( SV250 != SV89 )
                  | ( ( hAPP @ SV527 @ SV250 )
                    = ( hAPP @ SV527 @ SV89 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6546]) ).

thf(6606,plain,
    ! [SV99: $i,SV259: $i,SV389: $i,SV475: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
        = $false )
      | ( ( SV389 = SV99 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6551]) ).

thf(6607,plain,
    ! [SV259: $i,SV475: $i,SV99: $i,SV389: $i] :
      ( ( ( SV389 = SV99 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV389 ) @ SV259 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV475 ) @ SV99 ) @ SV259 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6552]) ).

thf(6608,plain,
    ! [SV103: $i,SV263: $i,SV391: $i,SV477: $i] :
      ( ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( SV103
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6554]) ).

thf(6609,plain,
    ! [SV263: $i,SV391: $i,SV477: $i,SV103: $i] :
      ( ( ( SV103
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV477 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( hAPP @ ( c_Set_Oimage @ SV477 @ SV391 @ SV263 ) @ SV103 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV391 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6555]) ).

thf(6610,plain,
    ! [SV106: $i,SV266: $i,SV393: $i,SV479: $i] :
      ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
          = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
        = $false )
      | ( ( SV106
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6556]) ).

thf(6611,plain,
    ! [SV266: $i,SV479: $i,SV393: $i,SV106: $i] :
      ( ( ( SV106
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV393 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_HOL_Obool ) )
          = ( hAPP @ ( c_Set_Oimage @ SV393 @ SV479 @ SV266 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6557]) ).

thf(6612,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i,SV591: $i,SV599: $i,SV603: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV603 @ SV599 @ SV591 @ SV568 ) @ SV529 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SV599 @ SV591 @ SV394 ) @ SV267 ) )
        | ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
          = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6558]) ).

thf(6613,plain,
    ! [SV128: $i,SV286: $i,SV403: $i,SV484: $i,SV531: $i,SV569: $i,SV592: $i] :
      ( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV592 @ SV569 @ SV531 @ SV484 @ SV403 @ SV286 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ SV531 @ SV128 ) @ SV128 )
          = SV128 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6561]) ).

thf(6614,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i,SV571: $i,SV593: $i] :
      ( ( ( SV593 != SV571 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV593 ) @ SV288 ) ) @ SV571 ) @ SV130 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV571 ) @ SV130 ) ) @ SV593 ) @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6563]) ).

thf(6615,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( SV572 != SV534 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = SV132 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6564]) ).

thf(6616,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ~ ( ( SV572 != SV534 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = ( hAPP @ SV290 @ SV572 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6565]) ).

thf(6617,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true )
      | ( ( ~ ! [SY1696: $i] :
                ~ ( ~ ( ( SV488
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                       != SV133 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                       != SV291 )
                      | ( SV407
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6566]) ).

thf(6618,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ~ ! [SY1697: $i] :
                  ~ ( ~ ( ( SV488
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                        | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                         != SV133 ) )
                    | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                         != SV291 )
                        | ( SV407
                         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6567]) ).

thf(6619,plain,
    ! [SV536: $i,SV573: $i,SV135: $i,SV408: $i,SV293: $i,SV489: $i] :
      ( ( ( ( SV489 != SV293 )
          | ( SV408 != SV135 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6568]) ).

thf(6620,plain,
    ! [SV137: $i,SV295: $i,SV409: $i,SV490: $i,SV537: $i,SV574: $i] :
      ( ( ( SV574 = SV537 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV490 @ SV409 ) @ SV295 ) @ SV537 ) @ SV137 ) @ SV574 )
          = ( hAPP @ SV295 @ SV574 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6570]) ).

thf(6621,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( ( SV296
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
          | ( SV138
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6571]) ).

thf(6622,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( ( SV296
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
          | ( SV138
           != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6572]) ).

thf(6623,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ~ ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
             != ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
            | ~ ( ~ ~ ( ( SV575 != SV412 )
                      | ( SV538 != SV298 ) )
                | ( SV491 != SV140 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6573]) ).

thf(6624,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ~ ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                        | ( SV538 != SV298 ) )
                  | ( SV491 != SV140 ) )
            | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
              = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[6573]) ).

thf(6625,plain,
    ! [SV300: $i,SV413: $i,SV539: $i,SV576: $i,SV492: $i,SV142: $i] :
      ( ( ( ~ ! [SY1626: $i,SY1627: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6574]) ).

thf(6626,plain,
    ! [SV148: $i,SV306: $i,SV416: $i,SV493: $i,SV540: $i,SV577: $i,SV595: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( ~ ! [SY1707: $i,SY1708: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
                | ! [SY1709: $i] :
                    ( ~ ! [SY1710: $i] :
                          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) )
          | ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6579]) ).

thf(6627,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i,SV578: $i,SV596: $i,SV600: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV600 @ SV596 @ SV578 @ SV541 ) @ SV494 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SV596 @ SV578 @ SV308 ) @ SV150 ) )
        = $true )
      | ( ( ! [SY1714: $i] :
              ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
              = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6580]) ).

thf(6628,plain,
    ! [SV420: $i,SV543: $i,SV153: $i,SV497: $i,SV579: $i,SV311: $i] :
      ( ( ( SV311
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV497 ) @ SV153 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV311 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV420 ) @ SV153 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV497 )
          = SV420 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6582]) ).

thf(6629,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
         != ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true )
      | ( ( ~ ( ( SV498 != SV312 )
              | ( SV421 != SV154 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6583]) ).

thf(6630,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( ~ ~ ( ( SV498 != SV312 )
                | ( SV421 != SV154 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6584]) ).

thf(6631,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
         != SV422 )
        = $true )
      | ( ( ( hAPP @ SV422 @ SV314 )
          = SV156 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6585]) ).

thf(6632,plain,
    ! [SV499: $i,SV545: $i,SV156: $i,SV314: $i,SV422: $i] :
      ( ( ( ( hAPP @ SV422 @ SV314 )
         != SV156 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
          = SV422 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6586]) ).

thf(6633,plain,
    ! [SV426: $i,SV500: $i,SV546: $i,SV580: $i,SV160: $i,SV318: $i] :
      ( ( ( ~ ! [SY1341: $i,SY1342: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6587]) ).

thf(6634,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( SV581 != SV547 )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = SV162 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6588]) ).

thf(6635,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ~ ( ( SV581 != SV547 ) )
        | ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = ( hAPP @ SV320 @ SV581 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6589]) ).

thf(6636,plain,
    ! [SV164: $i,SV322: $i,SV430: $i,SV503: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $false )
      | ( ( ( SV430 = SV164 )
          | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6590]) ).

thf(6637,plain,
    ! [SV503: $i,SV322: $i,SV164: $i,SV430: $i] :
      ( ( ( ( SV430 = SV164 )
          | ( hBOOL @ ( hAPP @ SV322 @ SV164 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6591]) ).

thf(6638,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
         != ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true )
      | ( ( ~ ( ( SV467 != SV240 )
              | ( SV375 != SV79 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6595]) ).

thf(6639,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( ~ ~ ( ( SV467 != SV240 )
                | ( SV375 != SV79 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6596]) ).

thf(6640,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i,SV602: $i,SV604: $i] :
      ( ( ! [SY1775: $i] :
            ( ( ( hAPP @ SY1775 @ ( hAPP @ SV604 @ SV602 ) )
             != ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
            | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SY1775 ) @ SV604 ) @ SV602 )
              = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6597]) ).

thf(6641,plain,
    ! [SV471: $i,SV524: $i,SV85: $i,SV246: $i,SV381: $i,SV564: $i,SV588: $i] :
      ( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6601]) ).

thf(6642,plain,
    ! [SV86: $i,SV247: $i,SV382: $i,SV472: $i,SV525: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false )
      | ( ( ~ ( ( SV472 != SV247 )
              | ( SV382 != SV86 ) )
          | ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6602]) ).

thf(6643,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ~ ( ( SV472 != SV247 )
              | ( SV382 != SV86 ) )
          | ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6603]) ).

thf(6644,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV89: $i,SV250: $i,SV527: $i] :
      ( ( ( ~ ( ( ( hAPP @ SV527 @ SV250 )
               != ( hAPP @ SV527 @ SV89 ) )
              | ( SV250 = SV89 ) )
          | ~ ( ( SV250 != SV89 )
              | ( ( hAPP @ SV527 @ SV250 )
                = ( hAPP @ SV527 @ SV89 ) ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6605]) ).

thf(6645,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i,SV591: $i,SV599: $i,SV603: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV603 @ SV599 @ SV591 @ SV568 ) @ SV529 )
         != ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SV599 @ SV591 @ SV394 ) @ SV267 ) )
        = $true )
      | ( ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
          = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6612]) ).

thf(6646,plain,
    ! [SV130: $i,SV288: $i,SV405: $i,SV486: $i,SV533: $i,SV571: $i,SV593: $i] :
      ( ( ( SV593 = SV571 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV593 ) @ SV288 ) ) @ SV571 ) @ SV130 )
          = ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV533 @ SV486 ) @ SV405 ) @ SV571 ) @ SV130 ) ) @ SV593 ) @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6614]) ).

thf(6647,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( SV572 != SV534 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = SV132 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6615]) ).

thf(6648,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( ~ ( ( SV572 != SV534 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = ( hAPP @ SV290 @ SV572 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6616]) ).

thf(6649,plain,
    ! [SV133: $i,SV291: $i,SV407: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false )
      | ( ( ~ ! [SY1696: $i] :
                ~ ( ~ ( ( SV488
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                       != SV133 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                       != SV291 )
                      | ( SV407
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6617]) ).

thf(6650,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ! [SY1697: $i] :
                ~ ( ~ ( ( SV488
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                      | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                       != SV133 ) )
                  | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                       != SV291 )
                      | ( SV407
                       != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6618]) ).

thf(6651,plain,
    ! [SV135: $i,SV408: $i,SV536: $i,SV573: $i,SV293: $i,SV489: $i] :
      ( ( ( SV489 != SV293 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6619]) ).

thf(6652,plain,
    ! [SV293: $i,SV489: $i,SV536: $i,SV573: $i,SV135: $i,SV408: $i] :
      ( ( ( SV408 != SV135 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6619]) ).

thf(6653,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( SV296
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6621]) ).

thf(6654,plain,
    ! [SV296: $i,SV410: $i,SV138: $i] :
      ( ( ( SV138
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6621]) ).

thf(6655,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( SV296
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( SV138
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6622]) ).

thf(6656,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
         != ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        | ~ ( ~ ~ ( ( SV575 != SV412 )
                  | ( SV538 != SV298 ) )
            | ( SV491 != SV140 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6623]) ).

thf(6657,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                    | ( SV538 != SV298 ) )
              | ( SV491 != SV140 ) )
        | ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[6624]) ).

thf(6658,plain,
    ! [SV300: $i,SV413: $i,SV539: $i,SV576: $i,SV492: $i,SV142: $i] :
      ( ( ( ! [SY1626: $i,SY1627: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1626 ) @ SY1627 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SY1626 ) @ SY1627 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6625]) ).

thf(6659,plain,
    ! [SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i,SV306: $i] :
      ( ( ( ~ ! [SY1707: $i,SY1708: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
                | ! [SY1709: $i] :
                    ( ~ ! [SY1710: $i] :
                          ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                          | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6626]) ).

thf(6660,plain,
    ! [SV150: $i,SV308: $i,SV417: $i,SV494: $i,SV541: $i,SV578: $i,SV596: $i,SV600: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV600 @ SV596 @ SV578 @ SV541 ) @ SV494 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SV596 @ SV578 @ SV308 ) @ SV150 ) )
        = $false )
      | ( ( ! [SY1714: $i] :
              ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SY1714 ) )
              = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SY1714 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6627]) ).

thf(6661,plain,
    ! [SV420: $i,SV543: $i,SV153: $i,SV497: $i,SV579: $i,SV311: $i] :
      ( ( ( SV311
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV497 ) @ SV153 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV311 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV420 ) @ SV153 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV579 ) @ SV543 ) @ SV497 )
          = SV420 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6628]) ).

thf(6662,plain,
    ! [SV154: $i,SV312: $i,SV421: $i,SV498: $i,SV544: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false )
      | ( ( ~ ( ( SV498 != SV312 )
              | ( SV421 != SV154 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6629]) ).

thf(6663,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( ~ ( ( SV498 != SV312 )
              | ( SV421 != SV154 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6630]) ).

thf(6664,plain,
    ! [SV156: $i,SV314: $i,SV422: $i,SV499: $i,SV545: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
          = SV422 )
        = $false )
      | ( ( ( hAPP @ SV422 @ SV314 )
          = SV156 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6631]) ).

thf(6665,plain,
    ! [SV499: $i,SV545: $i,SV156: $i,SV314: $i,SV422: $i] :
      ( ( ( ( hAPP @ SV422 @ SV314 )
          = SV156 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV545 @ SV499 ) @ SV422 ) @ SV314 ) @ SV156 )
          = SV422 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6632]) ).

thf(6666,plain,
    ! [SV426: $i,SV500: $i,SV546: $i,SV580: $i,SV160: $i,SV318: $i] :
      ( ( ( ! [SY1341: $i,SY1342: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ SY1341 ) @ SY1342 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ SY1341 ) @ SY1342 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6633]) ).

thf(6667,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( SV581 != SV547 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = SV162 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6634]) ).

thf(6668,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( ~ ( ( SV581 != SV547 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = ( hAPP @ SV320 @ SV581 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6635]) ).

thf(6669,plain,
    ! [SV503: $i,SV322: $i,SV164: $i,SV430: $i] :
      ( ( ( SV430 = SV164 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV322 @ SV164 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6636]) ).

thf(6670,plain,
    ! [SV322: $i,SV503: $i,SV164: $i,SV430: $i] :
      ( ( ( SV430 = SV164 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6637]) ).

thf(6671,plain,
    ! [SV430: $i,SV503: $i,SV164: $i,SV322: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV322 @ SV164 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV503 ) @ SV430 ) @ SV322 ) @ SV164 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6637]) ).

thf(6672,plain,
    ! [SV79: $i,SV240: $i,SV375: $i,SV467: $i,SV521: $i,SV561: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false )
      | ( ( ~ ( ( SV467 != SV240 )
              | ( SV375 != SV79 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6638]) ).

thf(6673,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( ~ ( ( SV467 != SV240 )
              | ( SV375 != SV79 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6639]) ).

thf(6674,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i,SV602: $i,SV604: $i,SV605: $i] :
      ( ( ( ( hAPP @ SV605 @ ( hAPP @ SV604 @ SV602 ) )
         != ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
        | ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SV605 ) @ SV604 ) @ SV602 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6640]) ).

thf(6675,plain,
    ! [SV471: $i,SV524: $i,SV85: $i,SV246: $i,SV381: $i,SV564: $i,SV588: $i] :
      ( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV381 @ SV246 @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ ( c_Com_Ocom_OSemi @ SV471 @ SV246 ) @ SV85 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV588 @ SV564 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV588 @ SV524 @ SV471 @ SV381 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV588 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6641]) ).

thf(6676,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ~ ( ( SV472 != SV247 )
              | ( SV382 != SV86 ) ) )
        = $true )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6642]) ).

thf(6677,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ~ ( ( SV472 != SV247 )
              | ( SV382 != SV86 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6643]) ).

thf(6678,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6643]) ).

thf(6679,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV89: $i,SV250: $i,SV527: $i] :
      ( ( ( ~ ( ( ( hAPP @ SV527 @ SV250 )
               != ( hAPP @ SV527 @ SV89 ) )
              | ( SV250 = SV89 ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6644]) ).

thf(6680,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV527: $i,SV89: $i,SV250: $i] :
      ( ( ( ~ ( ( SV250 != SV89 )
              | ( ( hAPP @ SV527 @ SV250 )
                = ( hAPP @ SV527 @ SV89 ) ) ) )
        = $false )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6644]) ).

thf(6681,plain,
    ! [SV108: $i,SV267: $i,SV394: $i,SV480: $i,SV529: $i,SV568: $i,SV591: $i,SV599: $i,SV603: $i] :
      ( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV603 @ SV599 @ SV591 @ SV568 ) @ SV529 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV480 @ SV599 @ SV591 @ SV394 ) @ SV267 ) )
        = $false )
      | ( ( ( hAPP @ SV568 @ ( hAPP @ SV529 @ SV108 ) )
          = ( hAPP @ SV394 @ ( hAPP @ SV267 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6645]) ).

thf(6682,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( SV572 = SV534 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = SV132 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6647]) ).

thf(6683,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( SV572 != SV534 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = ( hAPP @ SV290 @ SV572 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6648]) ).

thf(6684,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ! [SY1696: $i] :
              ~ ( ~ ( ( SV488
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1696 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV407 )
                     != SV133 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1696 )
                     != SV291 )
                    | ( SV407
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1696 ) @ SV133 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6649]) ).

thf(6685,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ! [SY1697: $i] :
              ~ ( ~ ( ( SV488
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SY1697 ) )
                    | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV407 )
                     != SV133 ) )
                | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SY1697 )
                     != SV291 )
                    | ( SV407
                     != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SY1697 ) @ SV133 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6650]) ).

thf(6686,plain,
    ! [SV135: $i,SV408: $i,SV536: $i,SV573: $i,SV293: $i,SV489: $i] :
      ( ( ( SV489 = SV293 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6651]) ).

thf(6687,plain,
    ! [SV293: $i,SV489: $i,SV536: $i,SV573: $i,SV135: $i,SV408: $i] :
      ( ( ( SV408 = SV135 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV489 ) @ SV408 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV573 @ SV536 ) @ SV293 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6652]) ).

thf(6688,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( SV296
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6653]) ).

thf(6689,plain,
    ! [SV296: $i,SV410: $i,SV138: $i] :
      ( ( ( SV138
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6654]) ).

thf(6690,plain,
    ! [SV138: $i,SV410: $i,SV296: $i] :
      ( ( ( SV296
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( SV138
         != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6655]) ).

thf(6691,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
         != ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ( SV575 != SV412 )
                    | ( SV538 != SV298 ) )
              | ( SV491 != SV140 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6656]) ).

thf(6692,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ( SV575 != SV412 )
                      | ( SV538 != SV298 ) )
                | ( SV491 != SV140 ) ) )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6657]) ).

thf(6693,plain,
    ! [SV492: $i,SV576: $i,SV539: $i,SV413: $i,SV300: $i,SV142: $i] :
      ( ( ( ! [SY1776: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ SY1776 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ SY1776 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6658]) ).

thf(6694,plain,
    ! [SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i,SV306: $i] :
      ( ( ( ! [SY1707: $i,SY1708: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ SY1707 ) @ SY1708 ) )
              | ! [SY1709: $i] :
                  ( ~ ! [SY1710: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1708 ) )
                        | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1709 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ SY1707 ) @ SY1709 ) ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6659]) ).

thf(6695,plain,
    ! [SV417: $i,SV578: $i,SV596: $i,SV600: $i,SV150: $i,SV308: $i,SV606: $i,SV494: $i,SV541: $i] :
      ( ( ( ( hAPP @ SV541 @ ( hAPP @ SV494 @ SV606 ) )
          = ( hAPP @ SV308 @ ( hAPP @ SV150 @ SV606 ) ) )
        = $true )
      | ( ( ( hAPP @ ( c_Fun_Ocomp @ SV600 @ SV596 @ SV578 @ SV541 ) @ SV494 )
          = ( hAPP @ ( c_Fun_Ocomp @ SV417 @ SV596 @ SV578 @ SV308 ) @ SV150 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6660]) ).

thf(6696,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( ( SV498 != SV312 )
          | ( SV421 != SV154 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6662]) ).

thf(6697,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( ( SV498 != SV312 )
          | ( SV421 != SV154 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6663]) ).

thf(6698,plain,
    ! [SV160: $i,SV580: $i,SV546: $i,SV500: $i,SV426: $i,SV318: $i] :
      ( ( ( ! [SY1777: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ SY1777 ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ SY1777 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6666]) ).

thf(6699,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( SV581 = SV547 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = SV162 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6667]) ).

thf(6700,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( SV581 != SV547 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = ( hAPP @ SV320 @ SV581 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6668]) ).

thf(6701,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( ( SV467 != SV240 )
          | ( SV375 != SV79 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6672]) ).

thf(6702,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( ( SV467 != SV240 )
          | ( SV375 != SV79 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6673]) ).

thf(6703,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i,SV602: $i,SV604: $i,SV605: $i] :
      ( ( ( ( hAPP @ SV605 @ ( hAPP @ SV604 @ SV602 ) )
         != ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SV605 ) @ SV604 ) @ SV602 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6674]) ).

thf(6704,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ( SV472 != SV247 )
          | ( SV382 != SV86 ) )
        = $false )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6676]) ).

thf(6705,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( ( SV472 != SV247 )
          | ( SV382 != SV86 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6677]) ).

thf(6706,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( ( SV472 != SV86 )
          | ( SV382 != SV247 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6678]) ).

thf(6707,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV89: $i,SV250: $i,SV527: $i] :
      ( ( ( ( ( hAPP @ SV527 @ SV250 )
           != ( hAPP @ SV527 @ SV89 ) )
          | ( SV250 = SV89 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6679]) ).

thf(6708,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV527: $i,SV89: $i,SV250: $i] :
      ( ( ( ( SV250 != SV89 )
          | ( ( hAPP @ SV527 @ SV250 )
            = ( hAPP @ SV527 @ SV89 ) ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6680]) ).

thf(6709,plain,
    ! [SV132: $i,SV290: $i,SV406: $i,SV487: $i,SV534: $i,SV572: $i] :
      ( ( ( SV572 = SV534 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV487 @ SV406 ) @ SV290 ) @ SV534 ) @ SV132 ) @ SV572 )
          = ( hAPP @ SV290 @ SV572 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6683]) ).

thf(6710,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ~ ( ( SV488
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
                   != SV133 ) )
              | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
                   != SV291 )
                  | ( SV407
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6684]) ).

thf(6711,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ~ ( ( SV488
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
                  | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
                   != SV133 ) )
              | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
                   != SV291 )
                  | ( SV407
                   != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6685]) ).

thf(6712,plain,
    ! [SV296: $i,SV410: $i,SV138: $i] :
      ( ( ( SV138
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( SV296
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) @ SV296 ) @ SV138 )
          = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV410 @ tc_HOL_Obool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6690]) ).

thf(6713,plain,
    ! [SV140: $i,SV298: $i,SV412: $i,SV491: $i,SV538: $i,SV575: $i,SV594: $i] :
      ( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ( SV575 != SV412 )
                    | ( SV538 != SV298 ) )
              | ( SV491 != SV140 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6691]) ).

thf(6714,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ( ~ ~ ( ( SV575 != SV412 )
                    | ( SV538 != SV298 ) )
              | ( SV491 != SV140 ) ) )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6692]) ).

thf(6715,plain,
    ! [SV492: $i,SV576: $i,SV539: $i,SV413: $i,SV300: $i,SV142: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ ( sK5_SY1776 @ SV492 @ SV576 @ SV539 @ SV413 @ SV300 @ SV142 ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ ( sK5_SY1776 @ SV492 @ SV576 @ SV539 @ SV413 @ SV300 @ SV142 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6693]) ).

thf(6716,plain,
    ! [SV540: $i,SV416: $i,SV148: $i,SV595: $i,SV577: $i,SV493: $i,SV306: $i] :
      ( ( ( ! [SY1778: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ SY1778 ) )
              | ! [SY1779: $i] :
                  ( ~ ! [SY1710: $i] :
                        ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1710 ) @ SY1778 ) )
                        | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1710 ) @ SY1779 ) ) )
                  | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ SY1779 ) ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6694]) ).

thf(6717,plain,
    ! [SV154: $i,SV421: $i,SV544: $i,SV312: $i,SV498: $i] :
      ( ( ( SV498 != SV312 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6696]) ).

thf(6718,plain,
    ! [SV312: $i,SV498: $i,SV544: $i,SV154: $i,SV421: $i] :
      ( ( ( SV421 != SV154 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6696]) ).

thf(6719,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( SV498 != SV312 )
        = $true )
      | ( ( SV421 != SV154 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6697]) ).

thf(6720,plain,
    ! [SV160: $i,SV580: $i,SV546: $i,SV500: $i,SV426: $i,SV318: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ ( sK7_SY1777 @ SV160 @ SV580 @ SV546 @ SV500 @ SV426 @ SV318 ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ ( sK7_SY1777 @ SV160 @ SV580 @ SV546 @ SV500 @ SV426 @ SV318 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6698]) ).

thf(6721,plain,
    ! [SV162: $i,SV320: $i,SV428: $i,SV501: $i,SV547: $i,SV581: $i] :
      ( ( ( SV581 = SV547 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV501 @ SV428 ) @ SV320 ) @ SV547 ) @ SV162 ) @ SV581 )
          = ( hAPP @ SV320 @ SV581 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6700]) ).

thf(6722,plain,
    ! [SV79: $i,SV375: $i,SV521: $i,SV561: $i,SV240: $i,SV467: $i] :
      ( ( ( SV467 != SV240 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6701]) ).

thf(6723,plain,
    ! [SV240: $i,SV467: $i,SV521: $i,SV561: $i,SV79: $i,SV375: $i] :
      ( ( ( SV375 != SV79 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6701]) ).

thf(6724,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( SV467 != SV240 )
        = $true )
      | ( ( SV375 != SV79 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6702]) ).

thf(6725,plain,
    ! [SV80: $i,SV241: $i,SV376: $i,SV468: $i,SV522: $i,SV562: $i,SV587: $i,SV598: $i,SV602: $i,SV604: $i,SV605: $i] :
      ( ( ( ( hAPP @ SV605 @ ( hAPP @ SV604 @ SV602 ) )
          = ( hAPP @ SV598 @ ( hAPP @ SV587 @ SV562 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV522 @ SV468 @ SV376 @ SV605 ) @ SV604 ) @ SV602 )
          = ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV241 @ SV468 @ SV80 @ SV598 ) @ SV587 ) @ SV562 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6703]) ).

thf(6726,plain,
    ! [SV525: $i,SV382: $i,SV86: $i,SV247: $i,SV472: $i] :
      ( ( ( SV472 != SV247 )
        = $false )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6704]) ).

thf(6727,plain,
    ! [SV525: $i,SV247: $i,SV472: $i,SV86: $i,SV382: $i] :
      ( ( ( SV382 != SV86 )
        = $false )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6704]) ).

thf(6728,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( SV472 != SV247 )
        = $true )
      | ( ( SV382 != SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6705]) ).

thf(6729,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 != SV86 )
        = $true )
      | ( ( SV382 != SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6706]) ).

thf(6730,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV89: $i,SV250: $i,SV527: $i] :
      ( ( ( ( hAPP @ SV527 @ SV250 )
         != ( hAPP @ SV527 @ SV89 ) )
        = $true )
      | ( ( SV250 = SV89 )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6707]) ).

thf(6731,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV527: $i,SV89: $i,SV250: $i] :
      ( ( ( SV250 != SV89 )
        = $true )
      | ( ( ( hAPP @ SV527 @ SV250 )
          = ( hAPP @ SV527 @ SV89 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6708]) ).

thf(6732,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ( SV488
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
               != SV133 ) )
          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6710]) ).

thf(6733,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ( SV488
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
               != SV133 ) )
          | ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6711]) ).

thf(6734,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ~ ( ( SV575 != SV412 )
                | ( SV538 != SV298 ) )
          | ( SV491 != SV140 ) )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6713]) ).

thf(6735,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ~ ( ( SV575 != SV412 )
                | ( SV538 != SV298 ) )
          | ( SV491 != SV140 ) )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6714]) ).

thf(6736,plain,
    ! [SV492: $i,SV576: $i,SV539: $i,SV413: $i,SV300: $i,SV142: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ ( sK5_SY1776 @ SV492 @ SV576 @ SV539 @ SV413 @ SV300 @ SV142 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6715]) ).

thf(6737,plain,
    ! [SV142: $i,SV576: $i,SV539: $i,SV413: $i,SV300: $i,SV492: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ ( sK5_SY1776 @ SV492 @ SV576 @ SV539 @ SV413 @ SV300 @ SV142 ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6715]) ).

thf(6738,plain,
    ! [SV540: $i,SV416: $i,SV148: $i,SV595: $i,SV577: $i,SV493: $i,SV306: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
          | ! [SY1781: $i] :
              ( ~ ! [SY1782: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1782 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1782 ) @ SY1781 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ SY1781 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6716]) ).

thf(6739,plain,
    ! [SV154: $i,SV421: $i,SV544: $i,SV312: $i,SV498: $i] :
      ( ( ( SV498 = SV312 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6717]) ).

thf(6740,plain,
    ! [SV312: $i,SV498: $i,SV544: $i,SV154: $i,SV421: $i] :
      ( ( ( SV421 = SV154 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6718]) ).

thf(6741,plain,
    ! [SV544: $i,SV154: $i,SV421: $i,SV312: $i,SV498: $i] :
      ( ( ( SV498 = SV312 )
        = $false )
      | ( ( SV421 != SV154 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6719]) ).

thf(6742,plain,
    ! [SV160: $i,SV580: $i,SV546: $i,SV500: $i,SV426: $i,SV318: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ ( sK7_SY1777 @ SV160 @ SV580 @ SV546 @ SV500 @ SV426 @ SV318 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6720]) ).

thf(6743,plain,
    ! [SV318: $i,SV580: $i,SV546: $i,SV500: $i,SV426: $i,SV160: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV160 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ ( sK7_SY1777 @ SV160 @ SV580 @ SV546 @ SV500 @ SV426 @ SV318 ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6720]) ).

thf(6744,plain,
    ! [SV79: $i,SV375: $i,SV521: $i,SV561: $i,SV240: $i,SV467: $i] :
      ( ( ( SV467 = SV240 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6722]) ).

thf(6745,plain,
    ! [SV240: $i,SV467: $i,SV521: $i,SV561: $i,SV79: $i,SV375: $i] :
      ( ( ( SV375 = SV79 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6723]) ).

thf(6746,plain,
    ! [SV521: $i,SV561: $i,SV79: $i,SV375: $i,SV240: $i,SV467: $i] :
      ( ( ( SV467 = SV240 )
        = $false )
      | ( ( SV375 != SV79 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6724]) ).

thf(6747,plain,
    ! [SV525: $i,SV382: $i,SV86: $i,SV247: $i,SV472: $i] :
      ( ( ( SV472 = SV247 )
        = $true )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6726]) ).

thf(6748,plain,
    ! [SV525: $i,SV247: $i,SV472: $i,SV86: $i,SV382: $i] :
      ( ( ( SV382 = SV86 )
        = $true )
      | ( ( ~ ( ( SV472 != SV86 )
              | ( SV382 != SV247 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6727]) ).

thf(6749,plain,
    ! [SV525: $i,SV86: $i,SV382: $i,SV247: $i,SV472: $i] :
      ( ( ( SV472 = SV247 )
        = $false )
      | ( ( SV382 != SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6728]) ).

thf(6750,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 = SV86 )
        = $false )
      | ( ( SV382 != SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6729]) ).

thf(6751,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV89: $i,SV250: $i,SV527: $i] :
      ( ( ( ( hAPP @ SV527 @ SV250 )
          = ( hAPP @ SV527 @ SV89 ) )
        = $false )
      | ( ( SV250 = SV89 )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6730]) ).

thf(6752,plain,
    ! [SV384: $i,SV474: $i,SV566: $i,SV590: $i,SV527: $i,SV89: $i,SV250: $i] :
      ( ( ( SV250 = SV89 )
        = $false )
      | ( ( ( hAPP @ SV527 @ SV250 )
          = ( hAPP @ SV527 @ SV89 ) )
        = $true )
      | ( ( c_Typedef_Otype__definition @ SV590 @ SV566 @ SV527 @ SV474 @ SV384 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6731]) ).

thf(6753,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ( SV488
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
               != SV133 ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6732]) ).

thf(6754,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ~ ( ( SV488
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
              | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
               != SV133 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6733]) ).

thf(6755,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV607: $i,SV488: $i,SV535: $i] :
      ( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[6733]) ).

thf(6756,plain,
    ! [SV140: $i,SV491: $i,SV594: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ~ ( ( SV575 != SV412 )
                | ( SV538 != SV298 ) ) )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6734]) ).

thf(6757,plain,
    ! [SV298: $i,SV412: $i,SV538: $i,SV575: $i,SV594: $i,SV140: $i,SV491: $i] :
      ( ( ( SV491 != SV140 )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6734]) ).

thf(6758,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ~ ( ( SV575 != SV412 )
                | ( SV538 != SV298 ) ) )
        = $true )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6735]) ).

thf(6759,plain,
    ! [SV492: $i,SV576: $i,SV539: $i,SV413: $i,SV300: $i,SV142: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ ( sK2_SY1626 @ SV300 @ SV413 @ SV539 @ SV576 @ SV492 @ SV142 ) ) @ ( sK5_SY1776 @ SV492 @ SV576 @ SV539 @ SV413 @ SV300 @ SV142 ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV142 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV576 @ SV539 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV576 @ SV492 @ SV413 @ SV300 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV576 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6736]) ).

thf(6760,plain,
    ! [SV540: $i,SV416: $i,SV148: $i,SV595: $i,SV577: $i,SV493: $i,SV306: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6738]) ).

thf(6761,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i] :
      ( ( ( ! [SY1781: $i] :
              ( ~ ! [SY1782: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1782 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
                    | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1782 ) @ SY1781 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ SY1781 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6738]) ).

thf(6762,plain,
    ! [SV544: $i,SV312: $i,SV498: $i,SV154: $i,SV421: $i] :
      ( ( ( SV421 = SV154 )
        = $false )
      | ( ( SV498 = SV312 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV498 ) @ SV421 )
          = ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV544 ) @ SV312 ) @ SV154 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6741]) ).

thf(6763,plain,
    ! [SV160: $i,SV580: $i,SV546: $i,SV500: $i,SV426: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV318 @ ( sK3_SY1341 @ SV426 @ SV500 @ SV546 @ SV580 @ SV160 @ SV318 ) ) @ ( sK7_SY1777 @ SV160 @ SV580 @ SV546 @ SV500 @ SV426 @ SV318 ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV160 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV580 @ SV546 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV580 @ SV500 @ SV426 @ SV318 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV580 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6742]) ).

thf(6764,plain,
    ! [SV521: $i,SV561: $i,SV240: $i,SV467: $i,SV79: $i,SV375: $i] :
      ( ( ( SV375 = SV79 )
        = $false )
      | ( ( SV467 = SV240 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV467 ) @ SV375 )
          = ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV561 @ SV521 ) @ SV240 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6746]) ).

thf(6765,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( ( SV472 != SV86 )
          | ( SV382 != SV247 ) )
        = $false )
      | ( ( SV472 = SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6747]) ).

thf(6766,plain,
    ! [SV525: $i,SV247: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( ( SV472 != SV86 )
          | ( SV382 != SV247 ) )
        = $false )
      | ( ( SV382 = SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6748]) ).

thf(6767,plain,
    ! [SV525: $i,SV247: $i,SV472: $i,SV86: $i,SV382: $i] :
      ( ( ( SV382 = SV86 )
        = $false )
      | ( ( SV472 = SV247 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6749]) ).

thf(6768,plain,
    ! [SV525: $i,SV86: $i,SV472: $i,SV247: $i,SV382: $i] :
      ( ( ( SV382 = SV247 )
        = $false )
      | ( ( SV472 = SV86 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6750]) ).

thf(6769,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ( SV488
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
           != SV133 ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6753]) ).

thf(6770,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( ( SV488
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
          | ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
           != SV133 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6754]) ).

thf(6771,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV607: $i,SV488: $i,SV535: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
           != SV291 )
          | ( SV407
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6755]) ).

thf(6772,plain,
    ! [SV140: $i,SV491: $i,SV594: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ( ( SV575 != SV412 )
              | ( SV538 != SV298 ) ) )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6756]) ).

thf(6773,plain,
    ! [SV298: $i,SV412: $i,SV538: $i,SV575: $i,SV594: $i,SV140: $i,SV491: $i] :
      ( ( ( SV491 = SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6757]) ).

thf(6774,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ~ ( ( SV575 != SV412 )
              | ( SV538 != SV298 ) ) )
        = $false )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6758]) ).

thf(6775,plain,
    ! [SV540: $i,SV416: $i,SV148: $i,SV595: $i,SV577: $i,SV493: $i,SV306: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV306 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6760]) ).

thf(6776,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i] :
      ( ( ( ~ ! [SY1783: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1783 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1783 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[6761]) ).

thf(6777,plain,
    ! [SV382: $i,SV525: $i,SV247: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 != SV86 )
        = $false )
      | ( ( SV472 = SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6765]) ).

thf(6778,plain,
    ! [SV86: $i,SV525: $i,SV472: $i,SV247: $i,SV382: $i] :
      ( ( ( SV382 != SV247 )
        = $false )
      | ( ( SV472 = SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6765]) ).

thf(6779,plain,
    ! [SV247: $i,SV525: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 != SV86 )
        = $false )
      | ( ( SV382 = SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6766]) ).

thf(6780,plain,
    ! [SV472: $i,SV525: $i,SV86: $i,SV247: $i,SV382: $i] :
      ( ( ( SV382 != SV247 )
        = $false )
      | ( ( SV382 = SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6766]) ).

thf(6781,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( SV488
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6769]) ).

thf(6782,plain,
    ! [SV488: $i,SV291: $i,SV407: $i,SV133: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
         != SV133 )
        = $false )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6769]) ).

thf(6783,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( SV488
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
         != SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6770]) ).

thf(6784,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV607: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
         != SV291 )
        = $true )
      | ( ( SV407
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6771]) ).

thf(6785,plain,
    ! [SV140: $i,SV491: $i,SV594: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ( SV575 != SV412 )
          | ( SV538 != SV298 ) )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6772]) ).

thf(6786,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( ( SV575 != SV412 )
          | ( SV538 != SV298 ) )
        = $true )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[6774]) ).

thf(6787,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i] :
      ( ( ( ~ ! [SY1783: $i] :
                ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1783 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
                | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1783 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6776]) ).

thf(6788,plain,
    ! [SV306: $i,SV540: $i,SV416: $i,SV595: $i,SV577: $i,SV493: $i,SV148: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV148 @ ( sK6_SY1707 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 @ SV306 ) ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) )
        = $false )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6776]) ).

thf(6789,plain,
    ! [SV382: $i,SV525: $i,SV247: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 = SV86 )
        = $true )
      | ( ( SV472 = SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6777]) ).

thf(6790,plain,
    ! [SV86: $i,SV525: $i,SV472: $i,SV247: $i,SV382: $i] :
      ( ( ( SV382 = SV247 )
        = $true )
      | ( ( SV472 = SV247 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6778]) ).

thf(6791,plain,
    ! [SV247: $i,SV525: $i,SV382: $i,SV86: $i,SV472: $i] :
      ( ( ( SV472 = SV86 )
        = $true )
      | ( ( SV382 = SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6779]) ).

thf(6792,plain,
    ! [SV472: $i,SV525: $i,SV86: $i,SV247: $i,SV382: $i] :
      ( ( ( SV382 = SV247 )
        = $true )
      | ( ( SV382 = SV86 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV472 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV525 ) @ SV86 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV525 @ tc_HOL_Obool ) ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6780]) ).

thf(6793,plain,
    ! [SV407: $i,SV133: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6781]) ).

thf(6794,plain,
    ! [SV488: $i,SV291: $i,SV407: $i,SV133: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
               != SV291 )
              | ( SV407
               != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6782]) ).

thf(6795,plain,
    ! [SV133: $i,SV407: $i,SV607: $i,SV291: $i,SV535: $i,SV488: $i] :
      ( ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
         != SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6783]) ).

thf(6796,plain,
    ! [SV133: $i,SV407: $i,SV291: $i,SV607: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
          = SV291 )
        = $false )
      | ( ( SV407
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6784]) ).

thf(6797,plain,
    ! [SV140: $i,SV298: $i,SV491: $i,SV538: $i,SV594: $i,SV412: $i,SV575: $i] :
      ( ( ( SV575 != SV412 )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6785]) ).

thf(6798,plain,
    ! [SV140: $i,SV412: $i,SV491: $i,SV575: $i,SV594: $i,SV298: $i,SV538: $i] :
      ( ( ( SV538 != SV298 )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6785]) ).

thf(6799,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( SV575 != SV412 )
        = $true )
      | ( ( SV538 != SV298 )
        = $true )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6786]) ).

thf(6800,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV540: $i] :
      ( ( ( ! [SY1783: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SY1783 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
              | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SY1783 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6787]) ).

thf(6801,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
           != SV291 )
          | ( SV407
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) )
        = $false )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6793]) ).

thf(6802,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
           != SV291 )
          | ( SV407
           != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6794]) ).

thf(6803,plain,
    ! [SV291: $i,SV488: $i,SV133: $i,SV407: $i,SV607: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV407 )
          = SV133 )
        = $false )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV607 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6795]) ).

thf(6804,plain,
    ! [SV291: $i,SV488: $i,SV133: $i,SV607: $i,SV535: $i,SV407: $i] :
      ( ( ( SV407
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV607 ) @ SV133 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV607 )
          = SV291 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6796]) ).

thf(6805,plain,
    ! [SV140: $i,SV298: $i,SV491: $i,SV538: $i,SV594: $i,SV412: $i,SV575: $i] :
      ( ( ( SV575 = SV412 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6797]) ).

thf(6806,plain,
    ! [SV140: $i,SV412: $i,SV491: $i,SV575: $i,SV594: $i,SV298: $i,SV538: $i] :
      ( ( ( SV538 = SV298 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6798]) ).

thf(6807,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i] :
      ( ( ( SV575 = SV412 )
        = $false )
      | ( ( SV538 != SV298 )
        = $true )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6799]) ).

thf(6808,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV608: $i,SV540: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SV608 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
          | ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SV608 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6800]) ).

thf(6809,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
         != SV291 )
        = $false )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6801]) ).

thf(6810,plain,
    ! [SV488: $i,SV291: $i,SV133: $i,SV535: $i,SV407: $i] :
      ( ( ( SV407
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) )
        = $false )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6801]) ).

thf(6811,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
         != SV291 )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6802]) ).

thf(6812,plain,
    ! [SV488: $i,SV291: $i,SV133: $i,SV535: $i,SV407: $i] :
      ( ( ( SV407
         != ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) )
        = $false )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[6802]) ).

thf(6813,plain,
    ! [SV594: $i,SV140: $i,SV491: $i,SV412: $i,SV575: $i,SV298: $i,SV538: $i] :
      ( ( ( SV538 = SV298 )
        = $false )
      | ( ( SV575 = SV412 )
        = $false )
      | ( ( SV491 != SV140 )
        = $true )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6807]) ).

thf(6814,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV608: $i,SV540: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SV608 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SV608 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[6808]) ).

thf(6815,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
          = SV291 )
        = $true )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6809]) ).

thf(6816,plain,
    ! [SV488: $i,SV291: $i,SV133: $i,SV535: $i,SV407: $i] :
      ( ( ( SV407
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) )
        = $true )
      | ( ( SV488
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6810]) ).

thf(6817,plain,
    ! [SV291: $i,SV407: $i,SV133: $i,SV488: $i,SV535: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) )
          = SV291 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6811]) ).

thf(6818,plain,
    ! [SV488: $i,SV291: $i,SV133: $i,SV535: $i,SV407: $i] :
      ( ( ( SV407
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV133 ) )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ ( sK4_SY1696 @ SV133 @ SV407 @ SV291 @ SV535 @ SV488 ) ) @ SV407 )
          = SV133 )
        = $true )
      | ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV488 ) @ SV407 )
          = ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV535 ) @ SV291 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[6812]) ).

thf(6819,plain,
    ! [SV594: $i,SV298: $i,SV538: $i,SV412: $i,SV575: $i,SV140: $i,SV491: $i] :
      ( ( ( SV491 = SV140 )
        = $false )
      | ( ( SV575 = SV412 )
        = $false )
      | ( ( SV538 = SV298 )
        = $false )
      | ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV575 @ SV538 @ SV491 )
          = ( c_Hoare__Mirabelle_Otriple_Otriple @ SV594 @ SV412 @ SV298 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6813]) ).

thf(6820,plain,
    ! [SV306: $i,SV493: $i,SV577: $i,SV595: $i,SV148: $i,SV416: $i,SV608: $i,SV540: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV540 @ SV608 ) @ ( sK8_SY1778 @ SV540 @ SV416 @ SV148 @ SV595 @ SV577 @ SV493 @ SV306 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hAPP @ SV416 @ SV608 ) @ ( sK9_SY1781 @ SV306 @ SV493 @ SV577 @ SV595 @ SV148 @ SV416 @ SV540 ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV306 @ SV493 @ SV148 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $true )
      | ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV595 @ SV577 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV595 @ SV540 @ SV493 @ SV416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV595 ) @ tc_HOL_Obool ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[6814]) ).

thf(6821,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[5577,6820,6819,6818,6817,6816,6815,6806,6805,6804,6803,6792,6791,6790,6789,6788,6775,6773,6768,6767,6764,6763,6762,6759,6752,6751,6745,6744,6743,6740,6739,6737,6725,6721,6712,6709,6699,6695,6689,6688,6687,6686,6682,6681,6675,6671,6670,6669,6665,6664,6661,6646,6620,6613,6611,6610,6609,6608,6607,6606,6604,6600,6599,6598,6594,6593,6592,6581,6578,6577,6576,6575,6569,6562,6560,6559,6553,6550,6549,6548,6547,6541,6540,6539,6538,6518,6497,6496,6495,6490,6489,6485,6484,6483,6482,6461,6460,6459,6458,6452,6422,6417,6386,6385,6384,6382,6381,6379,6377,6376,6369,6340,6339,6338,6324,6302,6300,6299,6297,6296,6284,6282,6281,6278,6272,6268,6267,6266,6264,6262,6257,6250,6246,6244,6243,6240,6239,6224,6221,6220,6217,6202,6201,6200,6199,6194,6193,6190,6189,6188,6187,6186,6185,6184,6183,6181,6180,6179,6174,6136,6132,6130,6126,6116,6100,6099,6079,6076,6074,6071,6070,6064,6059,6057,6056,6055,6051,6048,6047,6041,6037,6036,5986,5976,5964,5942,5939,5937,5933,5932,5926,5925,5914,5913,5912,5911,5910,5904,5900,5899,5892,5891,5887,5886,5883,5877,5875,5785,5779,5778,5771,5759,5725,5610,5609,5608,5607,5606,5605,5604,5603,5602,5601,5600,5599,5598,5597,5596,5595,5594,5593,5592]) ).

thf(6822,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[6821]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW317+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
% 0.07/0.20  % Computer : n020.cluster.edu
% 0.07/0.20  % Model    : x86_64 x86_64
% 0.07/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20  % Memory   : 8046.5625MB
% 0.07/0.20  % OS       : Linux 6.8.0-71-generic
% 0.07/0.20  % CPULimit : 300
% 0.07/0.20  % WCLimit  : 300
% 0.07/0.20  % DateTime : Tue Oct  6 16:54:36 UTC 2026
% 0.07/0.20  % CPUTime  : 
% 0.07/0.20  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.71/16.16  .....................................
% 79.71/16.16  
% 79.71/16.16   No.of.Axioms: 186
% 79.71/16.16  
% 79.71/16.16   Length.of.Defs: 0
% 79.71/16.16  
% 79.71/16.16   Contains.Choice.Funs: false
% 79.71/16.16  ..............................................................................................................................
% 79.71/16.16  
% 79.71/16.16  ********************************
% 79.71/16.16  *   All subproblems solved!    *
% 79.71/16.16  ********************************
% 79.71/16.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:186,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:293,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6821,loop_count:0,foatp_calls:1,translation:fof_full)
% 79.71/16.16  
% 79.71/16.16  %**** Beginning of derivation protocol ****
% 79.71/16.16  % SZS output start CNFRefutation
% See solution above
% 79.71/16.17  
% 79.71/16.17  %**** End of derivation protocol ****
% 79.71/16.17  %**** no. of clauses in derivation: 1767 ****
% 79.71/16.17  %**** clause counter: 6821 ****
% 79.71/16.17  
% 79.71/16.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:186,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:293,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6821,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------