%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW350+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 : n014.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 11:01:20 AM UTC 2026
% Result : Theorem 113.09s 22.93s
% Output : CNFRefutation 113.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 130
% Syntax : Number of formulae : 1921 (1079 unt; 0 typ; 0 def)
% Number of atoms : 11379 (5084 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 40037 (5032 ~;3353 |; 60 &;31223 @)
% ( 114 <=>; 255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 536 ( 533 usr; 68 con; 0-10 aty)
% Number of variables : 8845 ( 0 ^;8800 !; 45 ?;8845 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Big__Operators_Ocomm__monoid__add__class_Osetsum,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(tp_c_Big__Operators_Ocomm__monoid__big,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod,type,
c_Big__Operators_Ocomm__monoid__mult__class_Osetprod: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OInf__fin,type,
c_Big__Operators_Olattice_OInf__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OSup__fin,type,
c_Big__Operators_Olattice_OSup__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OInf__fin,type,
c_Big__Operators_Olattice__class_OInf__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OSup__fin,type,
c_Big__Operators_Olattice__class_OSup__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMax,type,
c_Big__Operators_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMin,type,
c_Big__Operators_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Big__Operators_Osemilattice__big,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i ).
thf(tp_c_COMBI,type,
c_COMBI: $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_OSuc__code__numeral,type,
c_Code__Numeral_OSuc__code__numeral: $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case: $i > $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__size,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size: $i > $i ).
thf(tp_c_Code__Numeral_Odiv__mod__code__numeral,type,
c_Code__Numeral_Odiv__mod__code__numeral: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oint__of,type,
c_Code__Numeral_Oint__of: $i ).
thf(tp_c_Code__Numeral_Onat__of,type,
c_Code__Numeral_Onat__of: $i ).
thf(tp_c_Code__Numeral_Onat__of__aux,type,
c_Code__Numeral_Onat__of__aux: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oof__nat,type,
c_Code__Numeral_Oof__nat: $i ).
thf(tp_c_Code__Numeral_Osubtract__code__numeral,type,
c_Code__Numeral_Osubtract__code__numeral: $i ).
thf(tp_c_Com_OArg,type,
c_Com_OArg: $i ).
thf(tp_c_Com_ORes,type,
c_Com_ORes: $i ).
thf(tp_c_Com_OWT,type,
c_Com_OWT: $i ).
thf(tp_c_Com_OWT__bodies,type,
c_Com_OWT__bodies: $o ).
thf(tp_c_Com_Obodies,type,
c_Com_Obodies: $i ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i ).
thf(tp_c_Com_Ocom_OAss,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(tp_c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i ).
thf(tp_c_Com_Ocom_OCall,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OCond,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OLocal,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Com_Ocom_OWhile,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(tp_c_Com_Ocom_Ocom__case,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_Ocom__rec,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_Ocom__size,type,
c_Com_Ocom_Ocom__size: $i > $i ).
thf(tp_c_Com_Ovname_OGlb,type,
c_Com_Ovname_OGlb: $i > $i ).
thf(tp_c_Com_Ovname_OLoc,type,
c_Com_Ovname_OLoc: $i > $i ).
thf(tp_c_Com_Ovname_Ovname__case,type,
c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).
thf(tp_c_Com_Ovname_Ovname__rec,type,
c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Com_Ovname_Ovname__size,type,
c_Com_Ovname_Ovname__size: $i > $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(tp_c_Divides_Oadjust,type,
c_Divides_Oadjust: $i > $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int__rel,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat__rel,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg__rel,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(tp_c_Divides_OnegateSnd,type,
c_Divides_OnegateSnd: $i ).
thf(tp_c_Divides_Opdivmod,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg__rel,type,
c_Divides_OposDivAlg__rel: $i ).
thf(tp_c_Enum_Oall__n__lists,type,
c_Enum_Oall__n__lists: $i > $i > $i > $o ).
thf(tp_c_Enum_Oenum__class_Oenum,type,
c_Enum_Oenum__class_Oenum: $i > $i ).
thf(tp_c_Enum_Oenum__class_Oenum__all,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(tp_c_Enum_Oenum__class_Oenum__ex,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(tp_c_Enum_Oenum__the,type,
c_Enum_Oenum__the: $i > $i > $i ).
thf(tp_c_Enum_Oex__n__lists,type,
c_Enum_Oex__n__lists: $i > $i > $i > $o ).
thf(tp_c_Enum_On__lists,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(tp_c_Enum_Oproduct,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Enum_Osublists,type,
c_Enum_Osublists: $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequivp,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(tp_c_Finite__Set_Ofold,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__image,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofolding,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__idem,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one__idem,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm__idem,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_Omax__strict,type,
c_FunDef_Omax__strict: $i ).
thf(tp_c_FunDef_Omax__weak,type,
c_FunDef_Omax__weak: $i ).
thf(tp_c_FunDef_Omin__strict,type,
c_FunDef_Omin__strict: $i ).
thf(tp_c_FunDef_Omin__weak,type,
c_FunDef_Omin__weak: $i ).
thf(tp_c_FunDef_Opair__leq,type,
c_FunDef_Opair__leq: $i ).
thf(tp_c_FunDef_Opair__less,type,
c_FunDef_Opair__less: $i ).
thf(tp_c_FunDef_Oreduction__pair,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(tp_c_FunDef_Orp__inv__image,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: $i > $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i ).
thf(tp_c_Fun_Oinj__on,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(tp_c_Fun_Ooverride__on,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Othe__inv__into,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tp_c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tp_c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(tp_c_Groups_Osgn__class_Osgn,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(tp_c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(tp_c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_HOL_OAll,type,
c_HOL_OAll: $i > $i ).
thf(tp_c_HOL_OEx,type,
c_HOL_OEx: $i > $i ).
thf(tp_c_HOL_OLet,type,
c_HOL_OLet: $i > $i > $i ).
thf(tp_c_HOL_OThe,type,
c_HOL_OThe: $i > $i > $i ).
thf(tp_c_HOL_Obool_Obool__size,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(tp_c_Hilbert__Choice_OEps,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(tp_c_Hilbert__Choice_OGreatest,type,
c_Hilbert__Choice_OGreatest: $i > $i ).
thf(tp_c_Hilbert__Choice_OGreatestM,type,
c_Hilbert__Choice_OGreatestM: $i > $i > $i > $i ).
thf(tp_c_Hilbert__Choice_OLeastM,type,
c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_OMGT,type,
c_Hoare__Mirabelle_OMGT: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Ohoare__valids,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Opeek__and,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ostate__not__singleton,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__case,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__rec,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__size,type,
c_Hoare__Mirabelle_Otriple_Otriple__size: $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple__valid,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(tp_c_If,type,
c_If: $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Ogfp,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Olfp,type,
c_Inductive_Ocomplete__lattice__class_Olfp: $i > $i > $i ).
thf(tp_c_Int_OAbs__Integ,type,
c_Int_OAbs__Integ: $i ).
thf(tp_c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
thf(tp_c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
thf(tp_c_Int_OInteg,type,
c_Int_OInteg: $i ).
thf(tp_c_Int_OMin,type,
c_Int_OMin: $i ).
thf(tp_c_Int_OPls,type,
c_Int_OPls: $i ).
thf(tp_c_Int_ORep__Integ,type,
c_Int_ORep__Integ: $i ).
thf(tp_c_Int_Oint__ge__less__than,type,
c_Int_Oint__ge__less__than: $i > $i ).
thf(tp_c_Int_Oint__ge__less__than2,type,
c_Int_Oint__ge__less__than2: $i > $i ).
thf(tp_c_Int_Ointrel,type,
c_Int_Ointrel: $i ).
thf(tp_c_Int_Oiszero,type,
c_Int_Oiszero: $i > $i > $o ).
thf(tp_c_Int_Onat,type,
c_Int_Onat: $i ).
thf(tp_c_Int_Onat__aux,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(tp_c_Int_Opred,type,
c_Int_Opred: $i > $i ).
thf(tp_c_Int_Oring__1__class_OInts,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(tp_c_Int_Oring__1__class_Oof__int,type,
c_Int_Oring__1__class_Oof__int: $i > $i ).
thf(tp_c_Int_Osucc,type,
c_Int_Osucc: $i > $i ).
thf(tp_c_Lattices_Osemilattice__inf__class_Oinf,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(tp_c_Lazy__Sequence_Oanamorph,type,
c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__not__seq,type,
c_Lazy__Sequence_Ohb__not__seq: $i > $i ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Oconcat,type,
c_List_Oconcat: $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(tp_c_List_Oembed__list,type,
c_List_Oembed__list: $i > $i ).
thf(tp_c_List_Ofilter,type,
c_List_Ofilter: $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i ).
thf(tp_c_List_Oinsert,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olenlex,type,
c_List_Olenlex: $i > $i > $i ).
thf(tp_c_List_Olex,type,
c_List_Olex: $i > $i > $i ).
thf(tp_c_List_Olexn,type,
c_List_Olexn: $i > $i > $i ).
thf(tp_c_List_Olexord,type,
c_List_Olexord: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__insert__key,type,
c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__key,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osort__key,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olinorder__class_Osorted__list__of__set,type,
c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_Olist__size,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(tp_c_List_Olist__all2,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i ).
thf(tp_c_List_Olistrel,type,
c_List_Olistrel: $i > $i > $i ).
thf(tp_c_List_Olistrel1,type,
c_List_Olistrel1: $i > $i > $i ).
thf(tp_c_List_Olistrelp,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(tp_c_List_Olists,type,
c_List_Olists: $i > $i > $i ).
thf(tp_c_List_Olistset,type,
c_List_Olistset: $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i ).
thf(tp_c_List_Omap__filter,type,
c_List_Omap__filter: $i > $i > $i > $i > $i ).
thf(tp_c_List_Omaps,type,
c_List_Omaps: $i > $i > $i > $i > $i ).
thf(tp_c_List_Omeasures,type,
c_List_Omeasures: $i > $i > $i ).
thf(tp_c_List_Omonoid__add__class_Olistsum,type,
c_List_Omonoid__add__class_Olistsum: $i > $i ).
thf(tp_c_List_Onat__list,type,
c_List_Onat__list: $i > $o ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i ).
thf(tp_c_List_Opartition,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(tp_c_List_Oremdups,type,
c_List_Oremdups: $i > $i > $i ).
thf(tp_c_List_Oremove1,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tp_c_List_OremoveAll,type,
c_List_OremoveAll: $i > $i > $i ).
thf(tp_c_List_Oreturn__list,type,
c_List_Oreturn__list: $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i ).
thf(tp_c_List_Oset__Cons,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $i > $i ).
thf(tp_c_List_Otranspose,type,
c_List_Otranspose: $i > $i > $i ).
thf(tp_c_List_Otranspose__rel,type,
c_List_Otranspose__rel: $i > $i ).
thf(tp_c_List_Oupt,type,
c_List_Oupt: $i > $i > $i ).
thf(tp_c_List_Oupto,type,
c_List_Oupto: $i > $i > $i ).
thf(tp_c_List_Oupto__rel,type,
c_List_Oupto__rel: $i ).
thf(tp_c_List_Ozip,type,
c_List_Ozip: $i > $i > $i ).
thf(tp_c_Map_Odom,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(tp_c_Map_Omap__add,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(tp_c_Map_Omap__comp,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Map_Omap__le,type,
c_Map_Omap__le: $i > $i > $i > $i > $o ).
thf(tp_c_Map_Omap__of,type,
c_Map_Omap__of: $i > $i > $i ).
thf(tp_c_Map_Omap__upds,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Map_Oran,type,
c_Map_Oran: $i > $i > $i > $i ).
thf(tp_c_Map_Orestrict__map,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_OSuc,type,
c_Nat_OSuc: $i ).
thf(tp_c_Nat_Ocompow,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(tp_c_Nat_Ofunpow,type,
c_Nat_Ofunpow: $i > $i ).
thf(tp_c_Nat_Onat_Onat__case,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__rec,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__size,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_ONats,type,
c_Nat_Osemiring__1__class_ONats: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tp_c_Nat__Numeral_Oneg,type,
c_Nat__Numeral_Oneg: $i ).
thf(tp_c_Nat__Transfer_Ois__nat,type,
c_Nat__Transfer_Ois__nat: $i > $o ).
thf(tp_c_Nat__Transfer_Onat__set,type,
c_Nat__Transfer_Onat__set: $i > $o ).
thf(tp_c_Nat__Transfer_Otransfer__morphism,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(tp_c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(tp_c_Natural_Oevalc,type,
c_Natural_Oevalc: $i > $i ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i ).
thf(tp_c_Natural_Ogetlocs,type,
c_Natural_Ogetlocs: $i ).
thf(tp_c_Natural_Onewlocs,type,
c_Natural_Onewlocs: $i ).
thf(tp_c_Natural_Osetlocs,type,
c_Natural_Osetlocs: $i ).
thf(tp_c_Natural_Oupdate,type,
c_Natural_Oupdate: $i ).
thf(tp_c_New__DSequence_Opos__not__seq,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__not__random__dseq,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_OAbs__Frac,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(tp_c_Nitpick_OFrac,type,
c_Nitpick_OFrac: $i ).
thf(tp_c_Nitpick_Ocard_H,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Ofrac,type,
c_Nitpick_Ofrac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oint__gcd,type,
c_Nitpick_Oint__gcd: $i ).
thf(tp_c_Nitpick_Oint__lcm,type,
c_Nitpick_Oint__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd__rel,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(tp_c_Nitpick_Onat__lcm,type,
c_Nitpick_Onat__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac__rel,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(tp_c_Nitpick_Onumber__of__frac,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oone__frac,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(tp_c_Nitpick_Opair__box_OPairBox,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__case,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__rec,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__size,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oprod,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osetsum_H,type,
c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ounknown,type,
c_Nitpick_Ounknown: $i > $o ).
thf(tp_c_Nitpick_Owf_H,type,
c_Nitpick_Owf_H: $i > $i > $o ).
thf(tp_c_Nitpick_Ozero__frac,type,
c_Nitpick_Ozero__frac: $i > $i ).
thf(tp_c_Option_Obind,type,
c_Option_Obind: $i > $i > $i ).
thf(tp_c_Option_Ois__none,type,
c_Option_Ois__none: $i > $i > $o ).
thf(tp_c_Option_Omap,type,
c_Option_Omap: $i > $i > $i ).
thf(tp_c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tp_c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: $i > $i ).
thf(tp_c_Option_Ooption_Ooption__case,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i ).
thf(tp_c_Option_Ooption_Ooption__rec,type,
c_Option_Ooption_Ooption__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Option_Ooption_Ooption__size,type,
c_Option_Ooption_Ooption__size: $i > $i > $i > $i ).
thf(tp_c_Option_Oset,type,
c_Option_Oset: $i > $i > $i ).
thf(tp_c_Option_Othe,type,
c_Option_Othe: $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord_Omax,type,
c_Orderings_Oord_Omax: $i > $i > $i ).
thf(tp_c_Orderings_Oord_Omin,type,
c_Orderings_Oord_Omin: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_OLeast,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(tp_c_Orderings_Oorder__class_Omono,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Partial__Function_Oflat__lub,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(tp_c_Power_Opower_Opower,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(tp_c_Predicate_ODomainP,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(tp_c_Predicate_OPowp,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(tp_c_Predicate_ORangeP,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(tp_c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Predicate_Oreflp,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(tp_c_Product__Type_OPair,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(tp_c_Product__Type_OSigma,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(tp_c_Product__Type_Oapfst,type,
c_Product__Type_Oapfst: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oapsnd,type,
c_Product__Type_Oapsnd: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ofst,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(tp_c_Product__Type_Omap__pair,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__case,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__size,type,
c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oscomp,type,
c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Osnd,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(tp_c_Random_Oinc__shift,type,
c_Random_Oinc__shift: $i > $i > $i ).
thf(tp_c_Random_Oiterate,type,
c_Random_Oiterate: $i > $i > $i > $i > $i ).
thf(tp_c_Random_Olog,type,
c_Random_Olog: $i > $i > $i ).
thf(tp_c_Random_Ominus__shift,type,
c_Random_Ominus__shift: $i > $i > $i > $i ).
thf(tp_c_Random_Opick,type,
c_Random_Opick: $i > $i > $i ).
thf(tp_c_Random_Orange,type,
c_Random_Orange: $i > $i ).
thf(tp_c_Random_Oselect,type,
c_Random_Oselect: $i > $i > $i ).
thf(tp_c_Random_Oselect__weight,type,
c_Random_Oselect__weight: $i > $i > $i ).
thf(tp_c_Recdef_Osame__fst,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i ).
thf(tp_c_Relation_OField,type,
c_Relation_OField: $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i ).
thf(tp_c_Relation_Oconverse,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(tp_c_Relation_Oirrefl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Rings_Oinverse__class_Odivide,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(tp_c_SMT_Oz3div,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(tp_c_SMT_Oz3mod,type,
c_SMT_Oz3mod: $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeast,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastAtMost,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastLessThan,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatMost,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThan,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanAtMost,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanLessThan,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OlessThan,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeast,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastLessThan,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatMost,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThan,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanAtMost,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanLessThan,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OlessThan,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(tp_c_Set_OBall,type,
c_Set_OBall: $i > $i ).
thf(tp_c_Set_OCollect,type,
c_Set_OCollect: $i > $i ).
thf(tp_c_Set_OPow,type,
c_Set_OPow: $i > $i ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i ).
thf(tp_c_Set_Othe__elem,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(tp_c_Set_Ovimage,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(tp_c_Smallcheck_Ofull__small_H,type,
c_Smallcheck_Ofull__small_H: $i > $i > $i > $i ).
thf(tp_c_Smallcheck_Ofull__small__class_Ofull__small,type,
c_Smallcheck_Ofull__small__class_Ofull__small: $i > $i > $i > $i ).
thf(tp_c_Smallcheck_Oorelse,type,
c_Smallcheck_Oorelse: $i > $i > $i > $i ).
thf(tp_c_Smallcheck_Osmall_H,type,
c_Smallcheck_Osmall_H: $i > $i > $i > $i ).
thf(tp_c_Smallcheck_Osmall_H__rel,type,
c_Smallcheck_Osmall_H__rel: $i ).
thf(tp_c_Smallcheck_Osmall__class_Osmall,type,
c_Smallcheck_Osmall__class_Osmall: $i > $i ).
thf(tp_c_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tp_c_Sum__Type_Osum_Osum__case,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Typedef_Otype__definition,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Ofinite__psubset,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(tp_c_Wellfounded_Oless__than,type,
c_Wellfounded_Oless__than: $i ).
thf(tp_c_Wellfounded_Olex__prod,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__ext,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__extp,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(tp_c_Wellfounded_Omin__ext,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Opred__nat,type,
c_Wellfounded_Opred__nat: $i ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fFalse,type,
c_fFalse: $i ).
thf(tp_c_fNot,type,
c_fNot: $i ).
thf(tp_c_fTrue,type,
c_fTrue: $i ).
thf(tp_c_fconj,type,
c_fconj: $i ).
thf(tp_c_fdisj,type,
c_fdisj: $i ).
thf(tp_c_fequal,type,
c_fequal: $i ).
thf(tp_c_fimplies,type,
c_fimplies: $i ).
thf(tp_c_member,type,
c_member: $i > $i ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Enum_Oenum,type,
class_Enum_Oenum: $i > $o ).
thf(tp_class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
thf(tp_class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(tp_class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(tp_class_Finite__Set_Ofinite,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tp_class_Groups_Oabs__if,type,
class_Groups_Oabs__if: $i > $o ).
thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__semigroup__add,type,
class_Groups_Olinordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
thf(tp_class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tp_class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(tp_class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(tp_class_Groups_Osemigroup__add,type,
class_Groups_Osemigroup__add: $i > $o ).
thf(tp_class_Groups_Osgn__if,type,
class_Groups_Osgn__if: $i > $o ).
thf(tp_class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_HOL_Oequal,type,
class_HOL_Oequal: $i > $o ).
thf(tp_class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__bot,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__top,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Osemilattice__inf,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(tp_class_Lattices_Osemilattice__sup,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
thf(tp_class_Orderings_Owellorder,type,
class_Orderings_Owellorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
thf(tp_class_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(tp_class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tp_class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(tp_class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(tp_class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
thf(tp_class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tp_class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(tp_class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
thf(tp_class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
thf(tp_class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
thf(tp_class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
thf(tp_class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(tp_class_Smallcheck_Osmall,type,
class_Smallcheck_Osmall: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK10_SY1376,type,
sK10_SY1376: $i > $i > $i > $i ).
thf(tp_sK11_SY1663,type,
sK11_SY1663: $i > $i > $i ).
thf(tp_sK12_SY1432,type,
sK12_SY1432: $i > $i > $i > $i ).
thf(tp_sK13_SY1664,type,
sK13_SY1664: $i > $i > $i > $i ).
thf(tp_sK14_SY1446,type,
sK14_SY1446: $i > $i > $i > $i ).
thf(tp_sK15_SY1144,type,
sK15_SY1144: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY1542,type,
sK16_SY1542: $i > $i > $i > $i > $i ).
thf(tp_sK17_SY1219,type,
sK17_SY1219: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY1602,type,
sK18_SY1602: $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY1536,type,
sK19_SY1536: $i > $i > $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY1441,type,
sK20_SY1441: $i > $i > $i > $i ).
thf(tp_sK21_SY1536,type,
sK21_SY1536: $i > $i > $i > $i > $i ).
thf(tp_sK22_SY1658,type,
sK22_SY1658: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK23_SY1550,type,
sK23_SY1550: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK24_SY1520,type,
sK24_SY1520: $i > $i > $i > $i > $i ).
thf(tp_sK25_SY1520,type,
sK25_SY1520: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY906,type,
sK2_SY906: $i > $i ).
thf(tp_sK3_SY1184,type,
sK3_SY1184: $i > $i > $i ).
thf(tp_sK4_SY1283,type,
sK4_SY1283: $i > $i > $i > $i ).
thf(tp_sK5_SY1532,type,
sK5_SY1532: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY887,type,
sK6_SY887: $i > $i > $i ).
thf(tp_sK7_SY1037,type,
sK7_SY1037: $i > $i > $i ).
thf(tp_sK8_SY1345,type,
sK8_SY1345: $i > $i > $i > $i ).
thf(tp_sK9_SY1348,type,
sK9_SY1348: $i > $i > $i > $i ).
thf(tp_tc_Code__Evaluation_Oterm,type,
tc_Code__Evaluation_Oterm: $i ).
thf(tp_tc_Code__Numeral_Ocode__numeral,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_tc_Com_Oloc,type,
tc_Com_Oloc: $i ).
thf(tp_tc_Com_Opname,type,
tc_Com_Opname: $i ).
thf(tp_tc_Com_Ostate,type,
tc_Com_Ostate: $i ).
thf(tp_tc_Com_Ovname,type,
tc_Com_Ovname: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lazy__Sequence_Olazy__sequence,type,
tc_Lazy__Sequence_Olazy__sequence: $i > $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_Nitpick_Opair__box,type,
tc_Nitpick_Opair__box: $i > $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_sum,type,
tc_sum: $i > $i > $i ).
thf(tp_v_Sledgehammer_058s__2,type,
v_Sledgehammer_058s__2: $i > $i > $i ).
thf(tp_v_Z,type,
v_Z: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_s_H,type,
v_s_H: $i ).
thf(1,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(2,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(3,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(4,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(5,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(6,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(7,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(8,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(9,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(10,axiom,
! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(11,axiom,
! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(12,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(13,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(14,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(15,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(16,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19,axiom,
! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(20,axiom,
! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(296,axiom,
! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(333,axiom,
! [V_r_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(451,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(452,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(470,axiom,
! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(810,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(811,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(812,axiom,
! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(1153,axiom,
! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(1154,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(1155,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(1156,axiom,
! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(1157,axiom,
! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1269,axiom,
! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_ca_2
= ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1272,axiom,
! [T_a: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1273,axiom,
! [T_a: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1274,axiom,
! [T_a: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1275,axiom,
! [T_a: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(1346,axiom,
! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(1347,axiom,
! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(1401,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1402,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(1403,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1548,axiom,
! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1549,axiom,
! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1590,axiom,
! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1600,axiom,
! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
=> ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1604,axiom,
! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1605,axiom,
! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1626,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1652,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
thf(1653,axiom,
! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1654,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1725,axiom,
! [V_P_2: $i,T_a: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
= V_P_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(1750,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(1878,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(2139,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(2140,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(2187,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2499,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(2500,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(2501,axiom,
! [V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(2502,axiom,
! [V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(2852,axiom,
! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(2853,axiom,
! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(2854,axiom,
! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(2855,axiom,
! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(2898,axiom,
! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(2899,axiom,
! [T_b: $i,T_a: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(2900,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(2901,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(3785,axiom,
! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(4811,axiom,
! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(4812,axiom,
! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(4813,axiom,
! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(4816,axiom,
! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(4822,axiom,
! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(4824,axiom,
! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(4829,axiom,
! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(4877,axiom,
! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(4878,axiom,
! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(4879,axiom,
! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_ca_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(4880,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(4881,axiom,
! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(4905,axiom,
! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(4906,axiom,
! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(4907,axiom,
! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
( ( V_a_2 != V_ca_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(4908,axiom,
! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(4909,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(4910,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(4911,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(4917,axiom,
! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(4918,axiom,
! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(4927,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).
thf(4939,axiom,
! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
& ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_peek__and__def) ).
thf(4962,axiom,
! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(4963,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(4964,axiom,
! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(5028,axiom,
! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
<=> ( ( V_fun1_2 = V_fun1_H_2 )
& ( V_com_2 = V_com_H_2 )
& ( V_fun2_2 = V_fun2_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(5040,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5041,axiom,
! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5045,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5046,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5056,axiom,
! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(5080,axiom,
! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
=> ? [B_n: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__max2) ).
thf(5085,axiom,
! [V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(5135,axiom,
! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(5136,axiom,
! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
<=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(5142,axiom,
! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(5191,axiom,
! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( V_t_2 = V_s_2 )
=> ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(5192,axiom,
! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
=> ~ ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
thf(5208,axiom,
! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(5209,axiom,
! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(5210,axiom,
! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(5211,axiom,
! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
<=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(5212,axiom,
! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ( ( ( V_a5_2 = V_a2_2 )
& ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
| ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(5213,axiom,
! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
thf(5214,axiom,
! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(5215,axiom,
! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(5216,axiom,
! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(5217,axiom,
! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(5218,axiom,
! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(5219,axiom,
! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(5220,axiom,
! [V_t: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
=> ( V_t = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
thf(5221,axiom,
! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
thf(5224,axiom,
! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
=> ( V_u = V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
thf(5225,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(5226,axiom,
? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ B_x1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(5227,axiom,
! [B_Z_H: $i] :
( ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
=> ( B_Z_H = B_s1 ) )
=> ( B_Z_H = v_s_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(5229,conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(5230,negated_conjecture,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5229]) ).
thf(5231,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
= $false ),
inference(unfold_def,[status(thm)],[5230]) ).
thf(5232,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(5233,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(5234,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5235,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(5236,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(5237,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(5238,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(5239,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(5240,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(5241,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(5242,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(5243,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(5244,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(5245,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(5246,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(5247,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5248,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5249,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5250,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(5251,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5252,plain,
( ( ! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(5253,plain,
( ( ! [V_r_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(5254,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(5255,plain,
( ( ! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(5256,plain,
( ( ! [V_m_2: $i,V_n_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_n_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_n_2 = V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(5257,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(5258,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(5259,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(5260,plain,
( ( ! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1153]) ).
thf(5261,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(5262,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(5263,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1156]) ).
thf(5264,plain,
( ( ! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1157]) ).
thf(5265,plain,
( ( ! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_ca_2
= ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1269]) ).
thf(5266,plain,
( ( ! [T_a: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1272]) ).
thf(5267,plain,
( ( ! [T_a: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1273]) ).
thf(5268,plain,
( ( ! [T_a: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1274]) ).
thf(5269,plain,
( ( ! [T_a: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1275]) ).
thf(5270,plain,
( ( ! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1346]) ).
thf(5271,plain,
( ( ! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1347]) ).
thf(5272,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1401]) ).
thf(5273,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[1402]) ).
thf(5274,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1403]) ).
thf(5275,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1548]) ).
thf(5276,plain,
( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1549]) ).
thf(5277,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1590]) ).
thf(5278,plain,
( ( ! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
=> ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1600]) ).
thf(5279,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1604]) ).
thf(5280,plain,
( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1605]) ).
thf(5281,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1626]) ).
thf(5282,plain,
( ( ! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1652]) ).
thf(5283,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1653]) ).
thf(5284,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1654]) ).
thf(5285,plain,
( ( ! [V_P_2: $i,T_a: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1725]) ).
thf(5286,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1750]) ).
thf(5287,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1878]) ).
thf(5288,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2139]) ).
thf(5289,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2140]) ).
thf(5290,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2187]) ).
thf(5291,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2499]) ).
thf(5292,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2500]) ).
thf(5293,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2501]) ).
thf(5294,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2502]) ).
thf(5295,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2852]) ).
thf(5296,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2853]) ).
thf(5297,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2854]) ).
thf(5298,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2855]) ).
thf(5299,plain,
( ( ! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2898]) ).
thf(5300,plain,
( ( ! [T_b: $i,T_a: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2899]) ).
thf(5301,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2900]) ).
thf(5302,plain,
( ( ! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2901]) ).
thf(5303,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3785]) ).
thf(5304,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4811]) ).
thf(5305,plain,
( ( ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4812]) ).
thf(5306,plain,
( ( ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4813]) ).
thf(5307,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4816]) ).
thf(5308,plain,
( ( ! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4822]) ).
thf(5309,plain,
( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4824]) ).
thf(5310,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4829]) ).
thf(5311,plain,
( ( ! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4877]) ).
thf(5312,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4878]) ).
thf(5313,plain,
( ( ! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_ca_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ V_v_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4879]) ).
thf(5314,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4880]) ).
thf(5315,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4881]) ).
thf(5316,plain,
( ( ! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4905]) ).
thf(5317,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4906]) ).
thf(5318,plain,
( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
( ( V_a_2 != V_ca_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4907]) ).
thf(5319,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4908]) ).
thf(5320,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4909]) ).
thf(5321,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4910]) ).
thf(5322,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4911]) ).
thf(5323,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4917]) ).
thf(5324,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4918]) ).
thf(5325,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4927]) ).
thf(5326,plain,
( ( ! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
& ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4939]) ).
thf(5327,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4962]) ).
thf(5328,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4963]) ).
thf(5329,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4964]) ).
thf(5330,plain,
( ( ! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
<=> ( ( V_fun1_2 = V_fun1_H_2 )
& ( V_com_2 = V_com_H_2 )
& ( V_fun2_2 = V_fun2_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5028]) ).
thf(5331,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5040]) ).
thf(5332,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5041]) ).
thf(5333,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[5045]) ).
thf(5334,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5046]) ).
thf(5335,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5056]) ).
thf(5336,plain,
( ( ! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
=> ? [B_n: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5080]) ).
thf(5337,plain,
( ( ! [V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5085]) ).
thf(5338,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5135]) ).
thf(5339,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
<=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5136]) ).
thf(5340,plain,
( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5142]) ).
thf(5341,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( V_t_2 = V_s_2 )
=> ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5191]) ).
thf(5342,plain,
( ( ! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
=> ~ ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5192]) ).
thf(5343,plain,
( ( ! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5208]) ).
thf(5344,plain,
( ( ! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5209]) ).
thf(5345,plain,
( ( ! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5210]) ).
thf(5346,plain,
( ( ! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
<=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5211]) ).
thf(5347,plain,
( ( ! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ( ( ( V_a5_2 = V_a2_2 )
& ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
| ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5212]) ).
thf(5348,plain,
( ( ! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5213]) ).
thf(5349,plain,
( ( ! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5214]) ).
thf(5350,plain,
( ( ! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5215]) ).
thf(5351,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5216]) ).
thf(5352,plain,
( ( ! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5217]) ).
thf(5353,plain,
( ( ! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5218]) ).
thf(5354,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5219]) ).
thf(5355,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
=> ( V_t = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5220]) ).
thf(5356,plain,
( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5221]) ).
thf(5357,plain,
( ( ! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
=> ( V_u = V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5224]) ).
thf(5358,plain,
( ( ! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5225]) ).
thf(5359,plain,
( ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ B_x1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5226]) ).
thf(5360,plain,
( ( ! [B_Z_H: $i] :
( ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
=> ( B_Z_H = B_s1 ) )
=> ( B_Z_H = v_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5227]) ).
thf(5361,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5231]) ).
thf(5362,plain,
( ( ! [B_Z_H: $i] :
( ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B_s1 ) )
=> ( B_Z_H = B_s1 ) )
=> ( B_Z_H = v_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[5360]) ).
thf(5363,plain,
( ( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ B_x1 ) ) )
= $true ),
inference(copy,[status(thm)],[5359]) ).
thf(5364,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)],[5358]) ).
thf(5365,plain,
( ( ! [V_u: $i,V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
=> ( V_u = V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5357]) ).
thf(5366,plain,
( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[5356]) ).
thf(5367,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) )
=> ( V_t = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[5355]) ).
thf(5368,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_s0: $i,V_c0: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5354]) ).
thf(5369,plain,
( ( ! [V_c0_2: $i,V_s1_2: $i,V_c1_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5353]) ).
thf(5370,plain,
( ( ! [V_c1_2: $i,V_s1_2: $i,V_c0_2: $i,V_s_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0_2 ) @ V_s_2 ) @ V_s1_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c0_2 @ V_c1_2 ) ) @ V_s_2 ) @ V_s1_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5352]) ).
thf(5371,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_c2_2: $i,V_c1_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b_2 @ V_c1_2 @ V_c2_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1_2 ) @ V_s_2 ) @ V_t_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2_2 ) @ V_s_2 ) @ V_t_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5351]) ).
thf(5372,plain,
( ( ! [V_ca_2: $i,V_s_2: $i,V_b_2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_s_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5350]) ).
thf(5373,plain,
( ( ! [V_s2_2: $i,V_s1_2: $i,V_ca_2: $i,V_s0_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ V_b_2 @ V_s0_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s0_2 ) @ V_s1_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s1_2 ) @ V_s2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s0_2 ) @ V_s2_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5349]) ).
thf(5374,plain,
( ( ! [V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_a ) @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[5348]) ).
thf(5375,plain,
( ( ! [V_a5_2: $i,V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ( ( ( V_a5_2 = V_a2_2 )
& ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) ) )
| ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a5_2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5347]) ).
thf(5376,plain,
( ( ! [V_a2_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a2_2 ) )
<=> ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_a1_2 @ V_a3_2 ) ) @ B_s1 ) @ V_a2_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5346]) ).
thf(5377,plain,
( ( ! [V_a4_2: $i,V_a2_2: $i,V_a3_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a5_2 @ V_a3_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5345]) ).
thf(5378,plain,
( ( ! [V_a4_2: $i,V_a2_2: $i,V_a5_2: $i,V_a3_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_a1_2 @ V_a3_2 @ V_a5_2 ) ) @ V_a2_2 ) @ V_a4_2 ) )
<=> ( ( ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a3_2 ) @ V_a2_2 ) @ V_a4_2 ) ) )
| ( ~ ( hBOOL @ ( hAPP @ V_a1_2 @ V_a2_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a5_2 ) @ V_a2_2 ) @ V_a4_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5344]) ).
thf(5379,plain,
( ( ! [V_a5_2: $i,V_a2_2: $i,V_a4_2: $i,V_a1_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a4_2 ) ) @ V_a2_2 ) @ V_a5_2 ) )
<=> ? [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a1_2 ) @ V_a2_2 ) @ B_s1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_a4_2 ) @ B_s1 ) @ V_a5_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5343]) ).
thf(5380,plain,
( ( ! [V_t: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) )
=> ~ ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ B_s1 ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5342]) ).
thf(5381,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i,V_b_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ V_s_2 ) @ V_t_2 ) )
=> ( ( ( V_t_2 = V_s_2 )
=> ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_b_2 @ V_s_2 ) )
=> ! [B_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ B_s1 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b_2 @ V_ca_2 ) ) @ B_s1 ) @ V_t_2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5341]) ).
thf(5382,plain,
( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_2 )
= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5340]) ).
thf(5383,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_ca_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_ca_2 ) @ V_s_2 ) @ V_t_2 ) )
<=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_ca_2 ) @ V_s_2 ) @ B_n ) @ V_t_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5339]) ).
thf(5384,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ V_n ) @ V_t ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5338]) ).
thf(5385,plain,
( ( ! [V_t: $i,V_s: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) )
=> ? [B_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c ) @ V_s ) @ B_n ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5337]) ).
thf(5386,plain,
( ( ! [V_t2: $i,V_n2: $i,V_s2: $i,V_c2: $i,V_t1: $i,V_n1: $i,V_s1: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ V_n1 ) @ V_t1 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ V_n2 ) @ V_t2 ) )
=> ? [B_n: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c1 ) @ V_s1 ) @ B_n ) @ V_t1 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ V_c2 ) @ V_s2 ) @ B_n ) @ V_t2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5336]) ).
thf(5387,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5335]) ).
thf(5388,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5334]) ).
thf(5389,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5333]) ).
thf(5390,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)],[5332]) ).
thf(5391,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)],[5331]) ).
thf(5392,plain,
( ( ! [V_fun2_H_2: $i,V_com_H_2: $i,V_fun1_H_2: $i,V_fun2_2: $i,V_com_2: $i,V_fun1_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_2 ) @ V_com_2 ) @ V_fun2_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H_2 ) @ V_com_H_2 ) @ V_fun2_H_2 ) )
<=> ( ( V_fun1_2 = V_fun1_H_2 )
& ( V_com_2 = V_com_H_2 )
& ( V_fun2_2 = V_fun2_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5330]) ).
thf(5393,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5329]) ).
thf(5394,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5328]) ).
thf(5395,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_a ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5327]) ).
thf(5396,plain,
( ( ! [V_s_2: $i,V_Z_2: $i,V_p_2: $i,V_P_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ T_a @ V_P_2 @ V_p_2 ) @ V_Z_2 ) @ V_s_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_P_2 @ V_Z_2 ) @ V_s_2 ) )
& ( hBOOL @ ( hAPP @ V_p_2 @ V_s_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5326]) ).
thf(5397,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5325]) ).
thf(5398,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(copy,[status(thm)],[5324]) ).
thf(5399,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5323]) ).
thf(5400,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5322]) ).
thf(5401,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5321]) ).
thf(5402,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(copy,[status(thm)],[5320]) ).
thf(5403,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5319]) ).
thf(5404,plain,
( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_a_2: $i] :
( ( V_a_2 != V_ca_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_ca_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_m_2 ) @ V_ca_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5318]) ).
thf(5405,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_b: $i,T_a: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_a @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5317]) ).
thf(5406,plain,
( ( ! [T_a: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_a ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5316]) ).
thf(5407,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_d: $i,V_f_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_a @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5315]) ).
thf(5408,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5314]) ).
thf(5409,plain,
( ( ! [V_v_2: $i,V_ca_2: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= V_ca_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ V_v_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5313]) ).
thf(5410,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5312]) ).
thf(5411,plain,
( ( ! [V_d_2: $i,V_ca_2: $i,T_d: $i,V_b_2: $i,V_a_2: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_a @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_b @ T_a @ V_ca_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_ca_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5311]) ).
thf(5412,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i,T_a: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_a @ T_c @ T_b @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5310]) ).
thf(5413,plain,
( ( ! [T_e: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_b @ T_a @ T_c @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_a @ T_e @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5309]) ).
thf(5414,plain,
( ( ! [V_ca_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_ca_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5308]) ).
thf(5415,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(5416,plain,
( ( ! [V_x_2: $i,T_a: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5306]) ).
thf(5417,plain,
( ( ! [V_A_2: $i,T_a: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5305]) ).
thf(5418,plain,
( ( ! [V_A_2: $i,T_a: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_a ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5304]) ).
thf(5419,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_a @ T_b @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5303]) ).
thf(5420,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)],[5302]) ).
thf(5421,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5301]) ).
thf(5422,plain,
( ( ! [T_b: $i,T_a: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5300]) ).
thf(5423,plain,
( ( ! [V_ca_2: $i,T_c: $i,T_b: $i,T_a: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_a @ T_b @ T_c ) @ V_ca_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(5424,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5298]) ).
thf(5425,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(5426,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5296]) ).
thf(5427,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_a @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5428,plain,
( ( ! [V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(5429,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5293]) ).
thf(5430,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5292]) ).
thf(5431,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_a: $i] :
( ( c_Equiv__Relations_Oequivp @ T_a @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5291]) ).
thf(5432,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)],[5290]) ).
thf(5433,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5434,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_b: $i,T_a: $i] :
( ( c_Typedef_Otype__definition @ T_a @ T_b @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5435,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_a: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_a @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5436,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_a @ T_b @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5437,plain,
( ( ! [V_P_2: $i,T_a: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_a ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(5438,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(5439,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_a: $i] :
( ( c_Predicate_Oreflp @ T_a @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(5440,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)],[5282]) ).
thf(5441,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_d: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_c @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_c ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_a @ T_d @ T_b ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_d @ T_c @ T_b ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(5442,plain,
( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5280]) ).
thf(5443,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_a @ T_b @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(5444,plain,
( ( ! [T_c: $i,T_b: $i,T_a: $i,V_ca_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_ca_2 ) )
=> ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a_2 @ V_ca_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(5445,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Opred__comp @ T_a @ T_b @ T_c @ V_r_2 @ V_s_2 @ V_a1_2 @ V_a3_2 )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(5446,plain,
( ( ! [T_b: $i,T_a: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(5447,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_a @ T_b @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(5448,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5274]) ).
thf(5449,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)],[5273]) ).
thf(5450,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)],[5272]) ).
thf(5451,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)],[5271]) ).
thf(5452,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)],[5270]) ).
thf(5453,plain,
( ( ! [T_a: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5269]) ).
thf(5454,plain,
( ( ! [T_a: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_a @ B_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5268]) ).
thf(5455,plain,
( ( ! [T_a: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5267]) ).
thf(5456,plain,
( ( ! [T_a: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(5457,plain,
( ( ! [T_a: $i,V_ca_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_ca_2
= ( c_Hilbert__Choice_OEps @ T_a @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_ca_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5265]) ).
thf(5458,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)],[5264]) ).
thf(5459,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5263]) ).
thf(5460,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5262]) ).
thf(5461,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5261]) ).
thf(5462,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)],[5260]) ).
thf(5463,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)],[5259]) ).
thf(5464,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5258]) ).
thf(5465,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_a: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_a ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(5466,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)],[5256]) ).
thf(5467,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)],[5255]) ).
thf(5468,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)],[5254]) ).
thf(5469,plain,
( ( ! [V_r_2: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_a ) @ ( hAPP @ ( c_Relation_Oconverse @ T_a @ T_b ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(5470,plain,
( ( ! [V_x_2: $i,V_n_2: $i,T_a: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_a @ T_a ) @ V_n_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5252]) ).
thf(5471,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(5472,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)],[5250]) ).
thf(5473,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_b @ T_a @ T_c ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(5474,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5248]) ).
thf(5475,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_b @ T_c @ T_a ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5247]) ).
thf(5476,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5246]) ).
thf(5477,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(5478,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(5479,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(5480,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(5481,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(5482,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(5483,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(5484,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(5485,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(5486,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(5487,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(5488,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(5489,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5233]) ).
thf(5490,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5232]) ).
thf(5491,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[5361]) ).
thf(5492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5385]) ).
thf(5493,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5365]) ).
thf(5494,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX4 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX4 @ SX2 ) ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5373]) ).
thf(5495,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)],[5420]) ).
thf(5496,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5454]) ).
thf(5497,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5389]) ).
thf(5498,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5449]) ).
thf(5499,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)],[5468]) ).
thf(5500,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)],[5400]) ).
thf(5501,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX0 ) ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5372]) ).
thf(5502,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)],[5387]) ).
thf(5503,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5371]) ).
thf(5504,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)],[5410]) ).
thf(5505,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5377]) ).
thf(5506,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5418]) ).
thf(5507,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)],[5406]) ).
thf(5508,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5456]) ).
thf(5509,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)],[5404]) ).
thf(5510,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)],[5411]) ).
thf(5511,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5450]) ).
thf(5512,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)],[5465]) ).
thf(5513,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)],[5409]) ).
thf(5514,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX5 ) @ SX4 ) @ SX3 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ~ ( ( SX5 != SX2 )
| ( SX4 != SX1 ) )
| ( SX3 != SX0 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SX5 != SX2 )
| ( SX4 != SX1 ) )
| ( SX3 != SX0 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX5 ) @ SX4 ) @ SX3 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SX6 ) @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5392]) ).
thf(5515,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX0 @ SX2 ) ) @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5369]) ).
thf(5516,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX1 @ SX0 @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5446]) ).
thf(5517,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ SX4 @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX3 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX2 @ SX0 ) ) @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5370]) ).
thf(5518,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX7 ) @ SX6 ) @ SX5 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX8: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX7 ) @ SX6 ) @ SX8 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX8 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5386]) ).
thf(5519,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)],[5405]) ).
thf(5520,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX4 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SX4 @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5378]) ).
thf(5521,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)],[5467]) ).
thf(5522,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5424]) ).
thf(5523,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)],[5436]) ).
thf(5524,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX1 @ SX0 @ SX4 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5442]) ).
thf(5525,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5422]) ).
thf(5526,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5388]) ).
thf(5527,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)],[5423]) ).
thf(5528,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)],[5403]) ).
thf(5529,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)],[5413]) ).
thf(5530,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)],[5461]) ).
thf(5531,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5425]) ).
thf(5532,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5384]) ).
thf(5533,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5431]) ).
thf(5534,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)],[5391]) ).
thf(5535,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)],[5432]) ).
thf(5536,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)],[5448]) ).
thf(5537,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX0 != SX1 )
| ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SX0 != SX1 )
| ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5375]) ).
thf(5538,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5426]) ).
thf(5539,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( SX6 != SX5 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5412]) ).
thf(5540,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SX1 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SX1 )
= ( hAPP @ c_Com_Ocom_OBODY @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5382]) ).
thf(5541,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5443]) ).
thf(5542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5390]) ).
thf(5543,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5430]) ).
thf(5544,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)],[5460]) ).
thf(5545,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)],[5433]) ).
thf(5546,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)],[5459]) ).
thf(5547,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5380]) ).
thf(5548,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5396]) ).
thf(5549,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)],[5399]) ).
thf(5550,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5414]) ).
thf(5551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ( SX1
!= ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5457]) ).
thf(5552,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5415]) ).
thf(5553,plain,
( ( ~ ! [SX0: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5363]) ).
thf(5554,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP @ SX3 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX3 @ SX2 ) ) @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5381]) ).
thf(5555,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5419]) ).
thf(5556,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)],[5421]) ).
thf(5557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5364]) ).
thf(5558,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5477]) ).
thf(5559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SX1 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5367]) ).
thf(5560,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)],[5452]) ).
thf(5561,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5416]) ).
thf(5562,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX3 ) @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX4 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX3 @ SX2 ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5379]) ).
thf(5563,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)],[5395]) ).
thf(5564,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5417]) ).
thf(5565,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5455]) ).
thf(5566,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5428]) ).
thf(5567,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)],[5434]) ).
thf(5568,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)],[5466]) ).
thf(5569,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Predicate_Oreflp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5439]) ).
thf(5570,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
| ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) )
| ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5445]) ).
thf(5571,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SX1 ) )
| ( SX0 = SX1 ) )
| ( SX0 = v_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5362]) ).
thf(5572,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5447]) ).
thf(5573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5427]) ).
thf(5574,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)],[5464]) ).
thf(5575,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ SX2 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5453]) ).
thf(5576,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)],[5462]) ).
thf(5577,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX7 @ SX6 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX5 ) @ SX3 ) )
| ( c_Predicate_Opred__comp @ SX2 @ SX1 @ SX0 @ SX7 @ SX4 @ SX6 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5444]) ).
thf(5578,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX0 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX0 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX0 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SX2 @ SX1 ) ) @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5376]) ).
thf(5579,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5429]) ).
thf(5580,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX4 ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SX4 @ SX1 ) ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5368]) ).
thf(5581,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)],[5435]) ).
thf(5582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SX2 ) @ SX1 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5383]) ).
thf(5583,plain,
! [SV1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5366]) ).
thf(5584,plain,
! [SV2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5374]) ).
thf(5585,plain,
! [SV3: $i] :
( ( ! [SY530: $i,SY531: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY531 ) @ SY530 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY531 ) @ SY530 ) @ SV3 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY531 ) @ SY530 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5393]) ).
thf(5586,plain,
! [SV4: $i] :
( ( ! [SY532: $i,SY533: $i,SY534: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY534 ) @ SY533 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY534 ) @ SY532 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY534 ) @ SY532 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY534 ) @ SY533 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5394]) ).
thf(5587,plain,
! [SV5: $i] :
( ( ! [SY535: $i,SY536: $i,SY537: $i,SY538: $i,SY539: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY539 @ SY538 @ SY537 @ SY536 ) @ SY535 ) @ SV5 )
= ( hAPP @ SY536 @ ( hAPP @ SY535 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(5588,plain,
! [SV6: $i] :
( ( ! [SY540: $i,SY541: $i,SY542: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY542 @ SY541 ) @ SY540 ) @ SV6 ) @ ( hAPP @ SY540 @ SV6 ) )
= SY540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5398]) ).
thf(5589,plain,
! [SV7: $i] :
( ( ! [SY543: $i,SY544: $i,SY545: $i,SY546: $i,SY547: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY547 @ SY546 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY547 @ SY546 ) @ SY545 ) @ SY544 ) @ SY543 ) ) @ SY544 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY547 @ SY546 ) @ SY545 ) @ SY544 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5401]) ).
thf(5590,plain,
! [SV8: $i] :
( ( ! [SY548: $i,SY549: $i,SY550: $i,SY551: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY551 @ SY550 ) @ SY549 ) @ SY548 ) @ SV8 ) @ SY548 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5402]) ).
thf(5591,plain,
! [SV9: $i] :
( ( ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i,SY556: $i,SY557: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY557 @ SY556 @ SY555 @ SY554 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY553 @ SY557 @ SY555 @ SY552 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY553 @ SY556 @ SY555 @ ( hAPP @ ( c_Fun_Ocomp @ SY557 @ SY556 @ SY553 @ SY554 ) @ SY552 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5407]) ).
thf(5592,plain,
! [SV10: $i] :
( ( ! [SY558: $i,SY559: $i,SY560: $i,SY561: $i,SY562: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY562 @ SY561 @ SY560 @ SY559 ) @ SY558 ) @ SV10 )
= ( hAPP @ SY559 @ ( hAPP @ SY558 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5408]) ).
thf(5593,plain,
! [SV11: $i] :
( ( ! [SY563: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY563 ) @ SV11 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5437]) ).
thf(5594,plain,
! [SV12: $i] :
( ( ! [SY564: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY564 ) @ SV12 )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5438]) ).
thf(5595,plain,
! [SV13: $i] :
( ( ! [SY565: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY565 ) @ SV13 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(5596,plain,
! [SV14: $i] :
( ( ! [SY566: $i,SY567: $i,SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY571 @ SY570 @ SY569 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY571 @ SY568 @ SY570 ) @ SY567 ) @ SY566 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY571 @ SY568 @ SY569 ) @ SY567 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY568 @ SY570 @ SY569 ) @ SY566 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(5597,plain,
! [SV15: $i] :
( ( ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY575 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY575 @ SY574 ) @ SY573 ) @ SY572 ) ) @ SY573 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY575 @ SY574 ) @ SY573 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5451]) ).
thf(5598,plain,
! [SV16: $i] :
( ( ! [SY576: $i,SY577: $i,SY578: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY578 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY578 ) @ SY577 ) @ SY576 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY578 ) @ SY577 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY578 ) @ SY576 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5458]) ).
thf(5599,plain,
! [SV17: $i] :
( ( ! [SY579: $i] :
( ( hAPP @ ( c_List_Orev @ SY579 ) @ ( hAPP @ ( c_List_Orev @ SY579 ) @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5600,plain,
! [SV18: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY581 @ SY580 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY580 @ SY581 ) @ SV18 ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(5601,plain,
! [SV19: $i] :
( ( ! [SY582: $i,SY583: $i,SY584: $i] :
( ( hAPP @ SY584 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY583 @ SY583 ) @ SY582 ) @ SY584 ) @ SV19 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY583 @ SY583 ) @ SY582 ) @ SY584 ) @ ( hAPP @ SY584 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(5602,plain,
! [SV20: $i] :
( ( ! [SY585: $i] :
( ( hAPP @ ( c_COMBI @ SY585 ) @ SV20 )
= SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5471]) ).
thf(5603,plain,
! [SV21: $i] :
( ( ! [SY586: $i,SY587: $i,SY588: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY588 @ SY587 ) @ SY586 ) @ SV21 )
= SY586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5472]) ).
thf(5604,plain,
! [SV22: $i] :
( ( ! [SY589: $i,SY590: $i,SY591: $i,SY592: $i,SY593: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY593 @ SY592 @ SY591 ) @ SY590 ) @ SY589 ) @ SV22 )
= ( hAPP @ SY590 @ ( hAPP @ SY589 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5473]) ).
thf(5605,plain,
! [SV23: $i] :
( ( ! [SY594: $i,SY595: $i,SY596: $i,SY597: $i,SY598: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY598 @ SY597 @ SY596 ) @ SY595 ) @ SY594 ) @ SV23 )
= ( hAPP @ ( hAPP @ SY595 @ SV23 ) @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(5606,plain,
! [SV24: $i] :
( ( ! [SY599: $i,SY600: $i,SY601: $i,SY602: $i,SY603: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY603 @ SY602 @ SY601 ) @ SY600 ) @ SY599 ) @ SV24 )
= ( hAPP @ ( hAPP @ SY600 @ SV24 ) @ ( hAPP @ SY599 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5475]) ).
thf(5607,plain,
! [SV25: $i] :
( ( ! [SY604: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY604 ) @ SV25 ) )
| ( SY604 = SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(5608,plain,
( ( hBOOL @ c_fFalse )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5609,plain,
! [SV26: $i] :
( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
| ~ ( hBOOL @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5480]) ).
thf(5610,plain,
! [SV27: $i] :
( ( ~ ~ ( hBOOL @ SV27 )
| ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5481]) ).
thf(5611,plain,
! [SV28: $i] :
( ( ! [SY605: $i] :
( ~ ( hBOOL @ SY605 )
| ~ ( hBOOL @ SV28 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY605 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5482]) ).
thf(5612,plain,
! [SV29: $i] :
( ( ! [SY606: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY606 ) @ SV29 ) )
| ( hBOOL @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5483]) ).
thf(5613,plain,
! [SV30: $i] :
( ( ! [SY607: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY607 ) @ SV30 ) )
| ( hBOOL @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5484]) ).
thf(5614,plain,
! [SV31: $i] :
( ( ! [SY608: $i] :
( ~ ( hBOOL @ SY608 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY608 ) @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5485]) ).
thf(5615,plain,
! [SV32: $i] :
( ( ! [SY609: $i] :
( ~ ( hBOOL @ SY609 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SY609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(5616,plain,
! [SV33: $i] :
( ( ! [SY610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY610 ) @ SV33 ) )
| ( hBOOL @ SY610 )
| ( hBOOL @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(5617,plain,
! [SV34: $i] :
( ( ! [SY611: $i] :
( ( hBOOL @ SY611 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY611 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5488]) ).
thf(5618,plain,
! [SV35: $i] :
( ( ! [SY612: $i] :
( ~ ( hBOOL @ SY612 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5489]) ).
thf(5619,plain,
! [SV36: $i] :
( ( ! [SY613: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY613 ) @ SV36 ) )
| ~ ( hBOOL @ SY613 )
| ( hBOOL @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5490]) ).
thf(5620,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5621,plain,
! [SV37: $i] :
( ( ! [SY614: $i,SY615: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY615 ) @ SY614 ) @ SV37 ) )
| ~ ! [SY616: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY615 ) @ SY614 ) @ SY616 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5622,plain,
! [SV38: $i] :
( ( ! [SY617: $i,SY618: $i,SY619: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY619 ) @ SY618 ) @ SY617 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY619 ) @ SY618 ) @ SV38 ) )
| ( SV38 = SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(5623,plain,
! [SV39: $i] :
( ( ! [SY620: $i,SY621: $i,SY622: $i,SY623: $i] :
( ~ ( hBOOL @ ( hAPP @ SY623 @ SY622 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY621 ) @ SY622 ) @ SY620 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY623 @ SY621 ) ) @ SY620 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY623 @ SY621 ) ) @ SY622 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(5624,plain,
! [SV40: $i] :
( ( ! [SY624: $i,SY625: $i,SY626: $i,SY627: $i,SY628: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY628 @ SY627 ) @ SY626 ) @ SY625 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY628 @ SY627 ) @ SY624 ) @ SV40 ) )
| ~ ( ( SY626 != SY624 )
| ( SY625 != SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5495]) ).
thf(5625,plain,
! [SV41: $i] :
( ( ! [SY629: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY629 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY629 @ ( c_Hilbert__Choice_OEps @ SV41 @ SY629 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5496]) ).
thf(5626,plain,
! [SV42: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV42 )
!= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5497]) ).
thf(5627,plain,
! [SV43: $i] :
( ( ! [SY631: $i,SY632: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY632 ) @ SY631 ) @ SV43 )
!= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5498]) ).
thf(5628,plain,
! [SV44: $i] :
( ( ! [SY633: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY633 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SY633 = SV44 ) )
| ~ ( ( SY633 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY633 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(5629,plain,
! [SV45: $i] :
( ( ! [SY634: $i,SY635: $i,SY636: $i,SY637: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY637 @ SY636 ) @ SY635 ) @ SY634 ) @ SV45 )
!= SY635 )
| ( ( hAPP @ SY635 @ SY634 )
= SV45 ) )
| ~ ( ( ( hAPP @ SY635 @ SY634 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY637 @ SY636 ) @ SY635 ) @ SY634 ) @ SV45 )
= SY635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(5630,plain,
! [SV46: $i] :
( ( ! [SY638: $i,SY639: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY639 @ SY638 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY639 @ SV46 ) ) @ SY638 ) @ SY638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(5631,plain,
! [SV47: $i] :
( ( ! [SY640: $i,SY641: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY641 ) @ SY640 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY641 ) @ SV47 ) )
| ( SY640 = SV47 ) )
| ~ ( ( SY640 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY641 ) @ SY640 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY641 ) @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(5632,plain,
! [SV48: $i] :
( ( ! [SY642: $i,SY643: $i,SY644: $i,SY645: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY645 @ SY644 @ SY643 ) ) @ SY642 ) @ SV48 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY645 @ SY642 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY644 ) @ SY642 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY645 @ SY642 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY643 ) @ SY642 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5633,plain,
! [SV49: $i] :
( ( ! [SY646: $i,SY647: $i,SY648: $i,SY649: $i,SY650: $i,SY651: $i,SY652: $i,SY653: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY653 @ SY652 @ SY651 @ SY650 ) @ SY649 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY648 @ SY652 @ SY651 @ SY647 ) @ SY646 ) )
| ( ( hAPP @ SY650 @ ( hAPP @ SY649 @ SV49 ) )
= ( hAPP @ SY647 @ ( hAPP @ SY646 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5504]) ).
thf(5634,plain,
! [SV50: $i] :
( ( ! [SY654: $i,SY655: $i,SY656: $i,SY657: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY657 @ SY656 @ SY655 ) ) @ SY654 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY657 @ SY654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY656 ) @ SY654 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY657 @ SY654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY655 ) @ SY654 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY657 @ SY654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY656 ) @ SY654 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY657 @ SY654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY655 ) @ SY654 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY657 @ SY656 @ SY655 ) ) @ SY654 ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5505]) ).
thf(5635,plain,
! [SV51: $i] :
( ( ! [SY658: $i,SY659: $i,SY660: $i] :
( ( SY660 != SY659 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY658 ) @ SY659 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY658 ) @ SY660 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5636,plain,
! [SV52: $i] :
( ( ! [SY661: $i,SY662: $i,SY663: $i,SY664: $i] :
( ( ( hAPP @ SY664 @ SY663 )
!= SY662 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY661 @ SV52 ) @ SY664 ) @ SY663 ) @ SY662 )
= SY664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5507]) ).
thf(5637,plain,
! [SV53: $i] :
( ( ! [SY665: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY665 @ ( c_Hilbert__Choice_OEps @ SV53 @ SY665 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY665 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY665 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY665 @ ( c_Hilbert__Choice_OEps @ SV53 @ SY665 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5508]) ).
thf(5638,plain,
! [SV54: $i] :
( ( ! [SY668: $i,SY669: $i,SY670: $i,SY671: $i,SY672: $i,SY673: $i] :
( ~ ( ( SY673 != SY672 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY671 @ SY670 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY671 @ SY670 ) @ SY669 ) @ SY673 ) @ SY668 ) ) @ SY672 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY671 @ SY670 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY671 @ SY670 ) @ SY669 ) @ SY672 ) @ SV54 ) ) @ SY673 ) @ SY668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5509]) ).
thf(5639,plain,
! [SV55: $i] :
( ( ! [SY674: $i,SY675: $i,SY676: $i,SY677: $i,SY678: $i,SY679: $i,SY680: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY680 @ SY679 @ SY678 @ SY677 ) @ SY676 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY675 @ SY679 @ SY678 @ SY674 ) @ SV55 ) )
| ! [SY681: $i] :
( ( hAPP @ SY677 @ ( hAPP @ SY676 @ SY681 ) )
= ( hAPP @ SY674 @ ( hAPP @ SV55 @ SY681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5510]) ).
thf(5640,plain,
! [SV56: $i] :
( ( ! [SY682: $i,SY683: $i] :
( SY683
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY682 ) @ SV56 ) @ SY683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5641,plain,
! [SV57: $i] :
( ( ! [SY684: $i,SY685: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY685 ) @ SY684 )
!= ( hAPP @ ( c_List_Orev @ SY685 ) @ SV57 ) )
| ( SY684 = SV57 ) )
| ~ ( ( SY684 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SY685 ) @ SY684 )
= ( hAPP @ ( c_List_Orev @ SY685 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5512]) ).
thf(5642,plain,
! [SV58: $i] :
( ( ! [SY686: $i,SY687: $i,SY688: $i,SY689: $i,SY690: $i,SY691: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY691 @ SY690 @ SY689 @ SY688 ) @ SY687 )
!= SY686 )
| ( ( hAPP @ SY688 @ ( hAPP @ SY687 @ SV58 ) )
= ( hAPP @ SY686 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(5643,plain,
! [SV59: $i] :
( ( ! [SY692: $i,SY693: $i,SY694: $i,SY695: $i,SY696: $i,SY697: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY697 ) @ SY696 ) @ SY695 ) @ SY694 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY697 ) @ SY693 ) @ SY692 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SY696 != SY693 )
| ( SY695 != SY692 ) )
| ( SY694 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SY696 != SY693 )
| ( SY695 != SY692 ) )
| ( SY694 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY697 ) @ SY696 ) @ SY695 ) @ SY694 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY697 ) @ SY693 ) @ SY692 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(5644,plain,
! [SV60: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i,SY701: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY701 @ SY700 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY699 ) @ SY700 ) @ SY698 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY701 @ SV60 @ SY699 ) ) @ SY700 ) @ SY698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5515]) ).
thf(5645,plain,
! [SV61: $i] :
( ( ! [SY702: $i,SY703: $i,SY704: $i,SY705: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY705 @ SY704 ) @ SY703 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY702 @ SV61 @ SY705 ) @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5516]) ).
thf(5646,plain,
! [SV62: $i] :
( ( ! [SY706: $i,SY707: $i,SY708: $i,SY709: $i] :
( ~ ( hBOOL @ ( hAPP @ SY709 @ SY708 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY707 ) @ SY708 ) @ SY706 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY709 @ SY707 @ SV62 ) ) @ SY708 ) @ SY706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(5647,plain,
! [SV63: $i] :
( ( ! [SY710: $i,SY711: $i,SY712: $i,SY713: $i,SY714: $i,SY715: $i,SY716: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY716 ) @ SY715 ) @ SY714 ) @ SY713 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY712 ) @ SY711 ) @ SY710 ) @ SV63 ) )
| ~ ! [SY717: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY716 ) @ SY715 ) @ SY717 ) @ SY713 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY712 ) @ SY711 ) @ SY717 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5518]) ).
thf(5648,plain,
! [SV64: $i] :
( ( ! [SY718: $i,SY719: $i,SY720: $i,SY721: $i,SY722: $i] :
( ~ ( ( SY722 != SY721 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY720 @ SY719 ) @ SY718 ) @ SY721 ) @ SV64 ) @ SY722 )
= ( hAPP @ SY718 @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5519]) ).
thf(5649,plain,
! [SV65: $i] :
( ( ! [SY723: $i,SY724: $i,SY725: $i,SY726: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY726 @ SY725 @ SY724 ) ) @ SY723 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY726 @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY725 ) @ SY723 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY726 @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY724 ) @ SY723 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY726 @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY725 ) @ SY723 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY726 @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY724 ) @ SY723 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY726 @ SY725 @ SY724 ) ) @ SY723 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5520]) ).
thf(5650,plain,
! [SV66: $i] :
( ( ! [SY727: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY727 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
| ( SY727 = SV66 ) )
| ~ ( ( SY727 != SV66 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY727 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(5651,plain,
! [SV67: $i] :
( ( ! [SY728: $i,SY729: $i,SY730: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY730 @ SY729 ) @ SY728 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY730 @ SY729 ) @ SV67 ) )
| ( SY728 = SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5522]) ).
thf(5652,plain,
! [SV68: $i] :
( ( ! [SY731: $i,SY732: $i,SY733: $i,SY734: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY734 @ SY733 @ SY732 )
| ( ( hAPP @ ( hAPP @ SY732 @ SY731 ) @ ( hAPP @ ( hAPP @ SY732 @ SY731 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SY732 @ SY731 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5653,plain,
! [SV69: $i] :
( ( ! [SY735: $i,SY736: $i,SY737: $i,SY738: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY738 @ SY737 ) @ SY736 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY735 @ SV69 @ SY738 ) @ SY736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5654,plain,
! [SV70: $i] :
( ( ! [SY739: $i,SY740: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY740 @ SX3 ) )
| ! [SY742: $i,SY743: $i] : ( hBOOL @ ( hAPP @ SY740 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY739 @ SV70 ) @ SY742 ) @ SY743 ) ) ) )
| ~ ( ~ ! [SY744: $i,SY745: $i] : ( hBOOL @ ( hAPP @ SY740 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY739 @ SV70 ) @ SY744 ) @ SY745 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY740 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5655,plain,
! [SV71: $i] :
( ( SV71
!= ( hAPP @ c_Nat_OSuc @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5526]) ).
thf(5656,plain,
! [SV72: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i,SY750: $i,SY751: $i] :
( ( SY751 != SY750 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY749 @ SY748 @ SY747 ) @ SV72 ) @ SY751 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY749 @ SY748 @ SY747 ) @ SV72 ) @ SY750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(5657,plain,
! [SV73: $i] :
( ( ! [SY752: $i,SY753: $i,SY754: $i,SY755: $i,SY756: $i] :
~ ( ~ ( ( SY756 != SY755 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY754 @ SY753 ) @ SY752 ) @ SY755 ) @ SV73 ) @ SY756 )
= SV73 ) )
| ~ ( ~ ( ( SY756 != SY755 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY754 @ SY753 ) @ SY752 ) @ SY755 ) @ SV73 ) @ SY756 )
= ( hAPP @ SY752 @ SY756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(5658,plain,
! [SV74: $i] :
( ( ! [SY757: $i,SY758: $i,SY759: $i,SY760: $i,SY761: $i,SY762: $i,SY763: $i,SY764: $i,SY765: $i,SY766: $i] :
( ( ( hAPP @ SY766 @ ( hAPP @ SY765 @ SY764 ) )
!= ( hAPP @ SY763 @ ( hAPP @ SY762 @ SY761 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY760 @ SY759 @ SY758 @ SY766 ) @ SY765 ) @ SY764 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY757 @ SY759 @ SV74 @ SY763 ) @ SY762 ) @ SY761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5659,plain,
! [SV75: $i] :
( ( ! [SY767: $i,SY768: $i,SY769: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY769 ) @ SY768 ) @ SY767 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY769 ) @ SV75 ) @ SY767 ) )
| ( SY768 = SV75 ) )
| ~ ( ( SY768 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY769 ) @ SY768 ) @ SY767 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY769 ) @ SV75 ) @ SY767 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(5660,plain,
! [SV76: $i] :
( ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY772 @ SY771 ) @ SY770 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY771 @ SV76 ) @ SY770 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY772 @ SY771 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(5661,plain,
! [SV77: $i] :
( ( ! [SY773: $i,SY774: $i,SY775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY775 ) @ SY774 ) @ SY773 ) @ SV77 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY775 ) @ SY774 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5532]) ).
thf(5662,plain,
! [SV78: $i] :
( ( ! [SY776: $i,SY777: $i,SY778: $i,SY779: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY779 @ SY778 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY778 @ SY777 ) @ SY776 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY778 @ SY776 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY778 @ SY777 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5663,plain,
! [SV79: $i] :
( ( ! [SY780: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY780 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
| ( SY780 = SV79 ) )
| ~ ( ( SY780 != SV79 )
| ( ( hAPP @ c_Nat_OSuc @ SY780 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5534]) ).
thf(5664,plain,
! [SV80: $i] :
( ( ! [SY781: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY781 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
| ( SY781 = SV80 ) )
| ~ ( ( SY781 != SV80 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY781 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5665,plain,
! [SV81: $i] :
( ( ! [SY782: $i,SY783: $i,SY784: $i,SY785: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY785 ) @ SY784 ) @ SY783 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY785 ) @ SY782 ) @ SV81 ) )
| ~ ( ( SY784 != SY782 )
| ( SY783 != SV81 ) ) )
| ~ ( ~ ~ ( ( SY784 != SY782 )
| ( SY783 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY785 ) @ SY784 ) @ SY783 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY785 ) @ SY782 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5666,plain,
! [SV82: $i] :
( ( ! [SY786: $i,SY787: $i,SY788: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY788 @ SY787 ) ) @ SY786 ) @ SV82 ) )
| ~ ( ( SV82 != SY786 )
| ~ ~ ( hBOOL @ ( hAPP @ SY788 @ SY786 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY788 @ SY786 ) )
| ~ ~ ! [SY789: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY787 ) @ SY786 ) @ SY789 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY788 @ SY787 ) ) @ SY789 ) @ SV82 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SV82 != SY786 )
| ~ ~ ( hBOOL @ ( hAPP @ SY788 @ SY786 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY788 @ SY786 ) )
| ~ ~ ! [SY790: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY787 ) @ SY786 ) @ SY790 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY788 @ SY787 ) ) @ SY790 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY788 @ SY787 ) ) @ SY786 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5667,plain,
! [SV83: $i] :
( ( ! [SY791: $i,SY792: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY792 @ SY791 ) @ SV83 ) )
| ! [SY793: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY791 @ SY793 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY792 @ SY791 ) @ SY793 ) ) ) )
| ~ ( ~ ! [SY794: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY791 @ SY794 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY792 @ SY791 ) @ SY794 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY792 @ SY791 ) @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5668,plain,
! [SV84: $i] :
( ( ! [SY795: $i,SY796: $i,SY797: $i,SY798: $i,SY799: $i,SY800: $i] :
( ( SY800 != SY799 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY798 @ SY797 @ SY796 @ SY795 @ SV84 ) @ SY800 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY798 @ SY797 @ SY796 @ SY795 @ SV84 ) @ SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(5669,plain,
! [SV85: $i] :
( ( ! [SY801: $i] :
~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SY801 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
| ( SY801 = SV85 ) )
| ~ ( ( SY801 != SV85 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SY801 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5670,plain,
! [SV86: $i] :
( ( ! [SY802: $i,SY803: $i,SY804: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY804 @ SY803 @ SY802 ) @ SV86 ) )
| ~ ! [SY805: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY802 @ SY805 ) @ SV86 ) ) )
| ~ ( ~ ~ ! [SY806: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY802 @ SY806 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY804 @ SY803 @ SY802 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5541]) ).
thf(5671,plain,
! [SV87: $i] :
( ( ! [SY807: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY807 )
!= ( hAPP @ c_Nat_OSuc @ SV87 ) )
| ( SY807 = SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5542]) ).
thf(5672,plain,
! [SV88: $i] :
( ( ! [SY808: $i,SY809: $i,SY810: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY810 @ SY809 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY809 @ SY808 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY809 @ SV88 ) @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(5673,plain,
! [SV89: $i] :
( ( ! [SY811: $i,SY812: $i,SY813: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY813 ) @ SY812 ) @ SY811 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY813 ) @ SY812 ) @ SV89 ) )
| ( SY811 = SV89 ) )
| ~ ( ( SY811 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY813 ) @ SY812 ) @ SY811 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY813 ) @ SY812 ) @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(5674,plain,
! [SV90: $i] :
( ( ! [SY814: $i,SY815: $i,SY816: $i,SY817: $i,SY818: $i] :
( ~ ( c_Typedef_Otype__definition @ SY818 @ SY817 @ SY816 @ SY815 @ SY814 )
| ( ( hAPP @ SY815 @ ( hAPP @ SY816 @ SV90 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(5675,plain,
! [SV91: $i] :
( ( ! [SY819: $i,SY820: $i,SY821: $i,SY822: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY821 ) @ SY820 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY819 ) @ SV91 ) )
| ~ ! [SY823: $i] :
~ ( ~ ( ( SY821
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY819 ) @ SY823 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY823 ) @ SY820 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY821 ) @ SY823 )
!= SY819 )
| ( SY820
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY823 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY824: $i] :
~ ( ~ ( ( SY821
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY819 ) @ SY824 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY824 ) @ SY820 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY821 ) @ SY824 )
!= SY819 )
| ( SY820
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY824 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY821 ) @ SY820 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY822 ) @ SY819 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5676,plain,
! [SV92: $i] :
( ( ! [SY825: $i,SY826: $i,SY827: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY827 @ SY826 ) ) @ SY825 ) @ SV92 ) )
| ~ ! [SY828: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY827 ) @ SY825 ) @ SY828 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY826 ) @ SY828 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(5677,plain,
! [SV93: $i] :
( ( ! [SY829: $i,SY830: $i,SY831: $i,SY832: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY832 @ SY831 @ SY830 ) @ SY829 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY831 @ SY829 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SY830 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY831 @ SY829 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SY830 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY832 @ SY831 @ SY830 ) @ SY829 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(5678,plain,
! [SV94: $i] :
( ( ! [SY833: $i,SY834: $i,SY835: $i,SY836: $i,SY837: $i] :
~ ( ~ ( ( SY837 != SY836 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY835 @ SY834 ) @ SY833 ) @ SY836 ) @ SV94 ) @ SY837 )
= SV94 ) )
| ~ ( ~ ( ( SY837 != SY836 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY835 @ SY834 ) @ SY833 ) @ SY836 ) @ SV94 ) @ SY837 )
= ( hAPP @ SY833 @ SY837 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(5679,plain,
! [SV95: $i] :
( ( ! [SY838: $i,SY839: $i,SY840: $i] :
( ( SY840 != SY839 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SV95 ) @ SY840 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SV95 ) @ SY839 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SV95 ) @ SY840 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SV95 ) @ SY839 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(5680,plain,
! [SV96: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY842 @ SX3 ) )
| ( SY841
!= ( c_Hilbert__Choice_OEps @ SV96 @ SY842 ) )
| ( hBOOL @ ( hAPP @ SY842 @ SY841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5551]) ).
thf(5681,plain,
! [SV97: $i] :
( ( ! [SY844: $i,SY845: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY845 ) @ SY844 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SY844 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV97 @ SY844 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY845 ) @ SY844 ) @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5552]) ).
thf(5682,plain,
( ( ! [SX0: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5553]) ).
thf(5683,plain,
! [SV98: $i] :
( ( ! [SY846: $i,SY847: $i,SY848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY848 @ SY847 ) ) @ SY846 ) @ SV98 ) )
| ~ ( ( SV98 != SY846 )
| ( hBOOL @ ( hAPP @ SY848 @ SY846 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY848 @ SY846 ) )
| ! [SY849: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY847 ) @ SY846 ) @ SY849 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY848 @ SY847 ) ) @ SY849 ) @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5684,plain,
! [SV99: $i] :
( ( ! [SY850: $i,SY851: $i,SY852: $i,SY853: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY853 @ SY852 @ SY851 ) @ SY850 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SY850 @ ( hAPP @ SY851 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY850 @ ( hAPP @ SY851 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY853 @ SY852 @ SY851 ) @ SY850 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(5685,plain,
! [SV100: $i] :
( ( ! [SY854: $i,SY855: $i,SY856: $i,SY857: $i,SY858: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY858 @ SY857 ) @ SY856 ) @ SY855 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY858 @ SY857 ) @ SY854 ) @ SV100 ) )
| ~ ( ( SY856 != SY854 )
| ( SY855 != SV100 ) ) )
| ~ ( ~ ~ ( ( SY856 != SY854 )
| ( SY855 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY858 @ SY857 ) @ SY856 ) @ SY855 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY858 @ SY857 ) @ SY854 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(5686,plain,
! [SV101: $i] :
( ( ! [SY859: $i] :
( ~ ! [SY860: $i] :
( ( hAPP @ SY859 @ SY860 )
= ( hAPP @ SV101 @ SY860 ) )
| ( SY859 = SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(5687,plain,
! [SV102: $i] :
( ( ! [SY861: $i] :
( ( SY861 != SV102 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY861 ) @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5558]) ).
thf(5688,plain,
! [SV103: $i] :
( ( ! [SY862: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SY862 ) @ SV103 ) )
| ( SV103 = SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5559]) ).
thf(5689,plain,
! [SV104: $i] :
( ( ! [SY863: $i,SY864: $i,SY865: $i,SY866: $i,SY867: $i] :
( ~ ( ( SY867 != SY866 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY865 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY865 @ SY864 ) @ SY867 ) @ SY863 ) ) @ SY866 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY865 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY865 @ SY864 ) @ SY866 ) @ SV104 ) ) @ SY867 ) @ SY863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5690,plain,
! [SV105: $i] :
( ( ! [SY868: $i,SY869: $i,SY870: $i] :
( ( SY870 != SY869 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY868 ) @ SV105 ) @ SY870 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY868 ) @ SV105 ) @ SY869 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY868 ) @ SV105 ) @ SY869 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY868 ) @ SV105 ) @ SY870 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5691,plain,
! [SV106: $i] :
( ( ! [SY871: $i,SY872: $i,SY873: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY873 @ SY872 ) ) @ SY871 ) @ SV106 ) )
| ~ ! [SY874: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY873 ) @ SY871 ) @ SY874 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY872 ) @ SY874 ) @ SV106 ) ) ) )
| ~ ( ~ ~ ! [SY875: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY873 ) @ SY871 ) @ SY875 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY872 ) @ SY875 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY873 @ SY872 ) ) @ SY871 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5562]) ).
thf(5692,plain,
! [SV107: $i] :
( ( ! [SY876: $i,SY877: $i,SY878: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY878 ) @ SY877 ) @ SY876 ) @ SV107 ) )
| ( SY877 = SV107 )
| ( hBOOL @ ( hAPP @ SY876 @ SV107 ) ) )
| ~ ( ~ ( ( SY877 = SV107 )
| ( hBOOL @ ( hAPP @ SY876 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY878 ) @ SY877 ) @ SY876 ) @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5563]) ).
thf(5693,plain,
! [SV108: $i] :
( ( ! [SY879: $i,SY880: $i,SY881: $i] :
( ( SY881 != SY880 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY879 ) @ SY881 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY879 ) @ SY880 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY879 ) @ SY880 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY879 ) @ SY881 ) @ SV108 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5564]) ).
thf(5694,plain,
! [SV109: $i] :
( ( ! [SY882: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY882 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY882 @ ( c_Hilbert__Choice_OEps @ SV109 @ SY882 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5695,plain,
! [SV110: $i] :
( ( ! [SY884: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SY884 @ SV110 )
| ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
| ~ ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SY884 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(5696,plain,
! [SV111: $i] :
( ( ! [SY889: $i,SY890: $i,SY891: $i,SY892: $i,SY893: $i,SY894: $i] :
( ~ ( c_Typedef_Otype__definition @ SY894 @ SY893 @ SY892 @ SY891 @ SY890 )
| ~ ( ~ ( ( ( hAPP @ SY892 @ SY889 )
!= ( hAPP @ SY892 @ SV111 ) )
| ( SY889 = SV111 ) )
| ~ ( ( SY889 != SV111 )
| ( ( hAPP @ SY892 @ SY889 )
= ( hAPP @ SY892 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5697,plain,
! [SV112: $i] :
( ( ! [SY895: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY895 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
| ( SY895 = SV112 ) )
| ~ ( ( SY895 != SV112 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY895 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5568]) ).
thf(5698,plain,
! [SV113: $i] :
( ( ! [SY896: $i,SY897: $i] :
( ~ ( c_Predicate_Oreflp @ SY897 @ SY896 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY896 @ SV113 ) @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5569]) ).
thf(5699,plain,
! [SV114: $i] :
( ( ! [SY898: $i,SY899: $i,SY900: $i,SY901: $i,SY902: $i,SY903: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY903 @ SY902 @ SY901 @ SY900 @ SY899 @ SY898 @ SV114 )
| ~ ! [SY904: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY900 @ SY898 ) @ SY904 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY899 @ SY904 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY905: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY900 @ SY898 ) @ SY905 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY899 @ SY905 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY903 @ SY902 @ SY901 @ SY900 @ SY899 @ SY898 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(5700,plain,
! [SV115: $i] :
( ( ~ ! [SY906: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY906 ) )
| ( SV115 = SY906 ) )
| ( SV115 = v_s_H ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5701,plain,
! [SV116: $i] :
( ( ! [SY907: $i,SY908: $i,SY909: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY909 @ SY908 @ SY907 ) @ SV116 ) )
| ~ ! [SY910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY907 @ SV116 ) @ SY910 ) ) )
| ~ ( ~ ~ ! [SY911: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY907 @ SV116 ) @ SY911 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY909 @ SY908 @ SY907 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5702,plain,
! [SV117: $i] :
( ( ! [SY912: $i,SY913: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY913 @ SY912 ) @ SV117 ) )
| ! [SY914: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY912 @ SY914 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY913 @ SY912 ) @ SY914 ) ) ) )
| ~ ( ~ ! [SY915: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY912 @ SY915 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY913 @ SY912 ) @ SY915 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY913 @ SY912 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5573]) ).
thf(5703,plain,
! [SV118: $i] :
( ( ! [SY916: $i,SY917: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY917 ) @ SY916 )
!= SV118 )
| ( SY916
= ( hAPP @ ( c_List_Orev @ SY917 ) @ SV118 ) ) )
| ~ ( ( SY916
!= ( hAPP @ ( c_List_Orev @ SY917 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SY917 ) @ SY916 )
= SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5704,plain,
! [SV119: $i] :
( ( ! [SY918: $i,SY919: $i] :
( ~ ( hBOOL @ ( hAPP @ SY919 @ SY918 ) )
| ( hBOOL @ ( hAPP @ SY919 @ ( c_Hilbert__Choice_OEps @ SV119 @ SY919 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5705,plain,
! [SV120: $i] :
( ( ! [SY920: $i,SY921: $i,SY922: $i,SY923: $i,SY924: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY924 ) @ SY923 ) @ SY922 )
!= SY921 )
| ( SY920
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY924 ) @ SY922 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY924 ) @ SY923 ) @ SY920 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY924 ) @ SY921 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(5706,plain,
! [SV121: $i] :
( ( ! [SY925: $i,SY926: $i,SY927: $i,SY928: $i,SY929: $i,SY930: $i,SY931: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY931 @ SY930 ) @ SY929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY928 @ SY929 ) @ SY927 ) )
| ( c_Predicate_Opred__comp @ SY926 @ SY925 @ SV121 @ SY931 @ SY928 @ SY930 @ SY927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(5707,plain,
! [SV122: $i] :
( ( ! [SY932: $i,SY933: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY933 @ SY932 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SY933 @ SV122 ) )
| ~ ! [SY934: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY932 ) @ SV122 ) @ SY934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY933 @ SY932 ) ) @ SY934 ) @ SV122 ) ) ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY933 @ SV122 ) )
| ~ ! [SY935: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY932 ) @ SV122 ) @ SY935 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY933 @ SY932 ) ) @ SY935 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY933 @ SY932 ) ) @ SV122 ) @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(5708,plain,
! [SV123: $i] :
( ( ! [SY936: $i,SY937: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY937 @ SY936 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY936 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5579]) ).
thf(5709,plain,
! [SV124: $i] :
( ( ! [SY938: $i,SY939: $i,SY940: $i,SY941: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY941 ) @ SY940 ) @ SY939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY938 ) @ SY939 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY941 @ SY938 ) ) @ SY940 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5580]) ).
thf(5710,plain,
! [SV125: $i] :
( ( ! [SY942: $i,SY943: $i,SY944: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY944 @ SY943 @ SY942 )
| ( ( hAPP @ ( hAPP @ SY943 @ SV125 ) @ SV125 )
= SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5581]) ).
thf(5711,plain,
! [SV126: $i] :
( ( ! [SY945: $i,SY946: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY946 ) @ SY945 ) @ SV126 ) )
| ~ ! [SY947: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY946 ) @ SY945 ) @ SY947 ) @ SV126 ) ) )
| ~ ( ~ ~ ! [SY948: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY946 ) @ SY945 ) @ SY948 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY946 ) @ SY945 ) @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5582]) ).
thf(5712,plain,
! [SV3: $i,SV127: $i] :
( ( ! [SY949: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY949 ) @ SV127 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY949 ) @ SV127 ) @ SV3 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY949 ) @ SV127 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(5713,plain,
! [SV4: $i,SV128: $i] :
( ( ! [SY950: $i,SY951: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY951 ) @ SY950 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY951 ) @ SV128 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY951 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY951 ) @ SY950 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(5714,plain,
! [SV5: $i,SV129: $i] :
( ( ! [SY952: $i,SY953: $i,SY954: $i,SY955: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY955 @ SY954 @ SY953 @ SY952 ) @ SV129 ) @ SV5 )
= ( hAPP @ SY952 @ ( hAPP @ SV129 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(5715,plain,
! [SV6: $i,SV130: $i] :
( ( ! [SY956: $i,SY957: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY957 @ SY956 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(5716,plain,
! [SV7: $i,SV131: $i] :
( ( ! [SY958: $i,SY959: $i,SY960: $i,SY961: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY961 @ SY960 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY961 @ SY960 ) @ SY959 ) @ SY958 ) @ SV131 ) ) @ SY958 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY961 @ SY960 ) @ SY959 ) @ SY958 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(5717,plain,
! [SV8: $i,SV132: $i] :
( ( ! [SY962: $i,SY963: $i,SY964: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY964 @ SY963 ) @ SY962 ) @ SV132 ) @ SV8 ) @ SV132 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(5718,plain,
! [SV9: $i,SV133: $i] :
( ( ! [SY965: $i,SY966: $i,SY967: $i,SY968: $i,SY969: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY969 @ SY968 @ SY967 @ SY966 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY965 @ SY969 @ SY967 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY965 @ SY968 @ SY967 @ ( hAPP @ ( c_Fun_Ocomp @ SY969 @ SY968 @ SY965 @ SY966 ) @ SV133 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(5719,plain,
! [SV10: $i,SV134: $i] :
( ( ! [SY970: $i,SY971: $i,SY972: $i,SY973: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY973 @ SY972 @ SY971 @ SY970 ) @ SV134 ) @ SV10 )
= ( hAPP @ SY970 @ ( hAPP @ SV134 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(5720,plain,
! [SV11: $i,SV135: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV135 ) @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(5721,plain,
! [SV12: $i,SV136: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV136 ) @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5594]) ).
thf(5722,plain,
! [SV13: $i,SV137: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV137 ) @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5595]) ).
thf(5723,plain,
! [SV14: $i,SV138: $i] :
( ( ! [SY974: $i,SY975: $i,SY976: $i,SY977: $i,SY978: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY978 @ SY977 @ SY976 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY978 @ SY975 @ SY977 ) @ SY974 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY978 @ SY975 @ SY976 ) @ SY974 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY975 @ SY977 @ SY976 ) @ SV138 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(5724,plain,
! [SV15: $i,SV139: $i] :
( ( ! [SY979: $i,SY980: $i,SY981: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY981 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY981 @ SY980 ) @ SY979 ) @ SV139 ) ) @ SY979 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY981 @ SY980 ) @ SY979 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(5725,plain,
! [SV16: $i,SV140: $i] :
( ( ! [SY982: $i,SY983: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY983 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY983 ) @ SY982 ) @ SV140 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY983 ) @ SY982 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY983 ) @ SV140 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5598]) ).
thf(5726,plain,
! [SV17: $i,SV141: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV141 ) @ ( hAPP @ ( c_List_Orev @ SV141 ) @ SV17 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5599]) ).
thf(5727,plain,
! [SV18: $i,SV142: $i] :
( ( ! [SY984: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY984 @ SV142 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV142 @ SY984 ) @ SV18 ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5600]) ).
thf(5728,plain,
! [SV19: $i,SV143: $i] :
( ( ! [SY985: $i,SY986: $i] :
( ( hAPP @ SY986 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY985 @ SY985 ) @ SV143 ) @ SY986 ) @ SV19 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY985 @ SY985 ) @ SV143 ) @ SY986 ) @ ( hAPP @ SY986 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5729,plain,
! [SV20: $i,SV144: $i] :
( ( ( hAPP @ ( c_COMBI @ SV144 ) @ SV20 )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(5730,plain,
! [SV21: $i,SV145: $i] :
( ( ! [SY987: $i,SY988: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY988 @ SY987 ) @ SV145 ) @ SV21 )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(5731,plain,
! [SV22: $i,SV146: $i] :
( ( ! [SY989: $i,SY990: $i,SY991: $i,SY992: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY992 @ SY991 @ SY990 ) @ SY989 ) @ SV146 ) @ SV22 )
= ( hAPP @ SY989 @ ( hAPP @ SV146 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5604]) ).
thf(5732,plain,
! [SV23: $i,SV147: $i] :
( ( ! [SY993: $i,SY994: $i,SY995: $i,SY996: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY996 @ SY995 @ SY994 ) @ SY993 ) @ SV147 ) @ SV23 )
= ( hAPP @ ( hAPP @ SY993 @ SV23 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(5733,plain,
! [SV24: $i,SV148: $i] :
( ( ! [SY997: $i,SY998: $i,SY999: $i,SY1000: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1000 @ SY999 @ SY998 ) @ SY997 ) @ SV148 ) @ SV24 )
= ( hAPP @ ( hAPP @ SY997 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(5734,plain,
! [SV25: $i,SV149: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) )
| ( SV149 = SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(5735,plain,
! [SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5609]) ).
thf(5736,plain,
! [SV27: $i] :
( ( ( ~ ~ ( hBOOL @ SV27 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5610]) ).
thf(5737,plain,
! [SV28: $i,SV150: $i] :
( ( ~ ( hBOOL @ SV150 )
| ~ ( hBOOL @ SV28 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5738,plain,
! [SV29: $i,SV151: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) )
| ( hBOOL @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(5739,plain,
! [SV30: $i,SV152: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) )
| ( hBOOL @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5613]) ).
thf(5740,plain,
! [SV31: $i,SV153: $i] :
( ( ~ ( hBOOL @ SV153 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5614]) ).
thf(5741,plain,
! [SV32: $i,SV154: $i] :
( ( ~ ( hBOOL @ SV154 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5615]) ).
thf(5742,plain,
! [SV33: $i,SV155: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
| ( hBOOL @ SV155 )
| ( hBOOL @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5616]) ).
thf(5743,plain,
! [SV34: $i,SV156: $i] :
( ( ( hBOOL @ SV156 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV156 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5617]) ).
thf(5744,plain,
! [SV35: $i,SV157: $i] :
( ( ~ ( hBOOL @ SV157 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5618]) ).
thf(5745,plain,
! [SV36: $i,SV158: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
| ~ ( hBOOL @ SV158 )
| ( hBOOL @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5619]) ).
thf(5746,plain,
! [SV37: $i,SV159: $i] :
( ( ! [SY1001: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1001 ) @ SV159 ) @ SV37 ) )
| ~ ! [SY1002: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1001 ) @ SV159 ) @ SY1002 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5621]) ).
thf(5747,plain,
! [SV38: $i,SV160: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1004 ) @ SY1003 ) @ SV160 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1004 ) @ SY1003 ) @ SV38 ) )
| ( SV38 = SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5622]) ).
thf(5748,plain,
! [SV39: $i,SV161: $i] :
( ( ! [SY1005: $i,SY1006: $i,SY1007: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1007 @ SY1006 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1005 ) @ SY1006 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1007 @ SY1005 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1007 @ SY1005 ) ) @ SY1006 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(5749,plain,
! [SV40: $i,SV162: $i] :
( ( ! [SY1008: $i,SY1009: $i,SY1010: $i,SY1011: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1011 @ SY1010 ) @ SY1009 ) @ SY1008 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1011 @ SY1010 ) @ SV162 ) @ SV40 ) )
| ~ ( ( SY1009 != SV162 )
| ( SY1008 != SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5624]) ).
thf(5750,plain,
! [SV41: $i,SV163: $i] :
( ( ~ ~ ! [SY1012: $i] :
~ ( hBOOL @ ( hAPP @ SV163 @ SY1012 ) )
| ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5625]) ).
thf(5751,plain,
! [SV42: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV42 )
= SV42 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5752,plain,
! [SV43: $i,SV164: $i] :
( ( ! [SY1013: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1013 ) @ SV164 ) @ SV43 )
!= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5627]) ).
thf(5753,plain,
! [SV44: $i,SV165: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV165 = SV44 ) )
| ~ ( ( SV165 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5628]) ).
thf(5754,plain,
! [SV45: $i,SV166: $i] :
( ( ! [SY1014: $i,SY1015: $i,SY1016: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1016 @ SY1015 ) @ SY1014 ) @ SV166 ) @ SV45 )
!= SY1014 )
| ( ( hAPP @ SY1014 @ SV166 )
= SV45 ) )
| ~ ( ( ( hAPP @ SY1014 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1016 @ SY1015 ) @ SY1014 ) @ SV166 ) @ SV45 )
= SY1014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(5755,plain,
! [SV46: $i,SV167: $i] :
( ( ! [SY1017: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY1017 @ SV167 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1017 @ SV46 ) ) @ SV167 ) @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(5756,plain,
! [SV47: $i,SV168: $i] :
( ( ! [SY1018: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1018 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY1018 ) @ SV47 ) )
| ( SV168 = SV47 ) )
| ~ ( ( SV168 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1018 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY1018 ) @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(5757,plain,
! [SV48: $i,SV169: $i] :
( ( ! [SY1019: $i,SY1020: $i,SY1021: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1021 @ SY1020 @ SY1019 ) ) @ SV169 ) @ SV48 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1021 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1020 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1021 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1019 ) @ SV169 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(5758,plain,
! [SV49: $i,SV170: $i] :
( ( ! [SY1022: $i,SY1023: $i,SY1024: $i,SY1025: $i,SY1026: $i,SY1027: $i,SY1028: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1028 @ SY1027 @ SY1026 @ SY1025 ) @ SY1024 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1023 @ SY1027 @ SY1026 @ SY1022 ) @ SV170 ) )
| ( ( hAPP @ SY1025 @ ( hAPP @ SY1024 @ SV49 ) )
= ( hAPP @ SY1022 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5633]) ).
thf(5759,plain,
! [SV50: $i,SV171: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1031 @ SY1030 @ SY1029 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1031 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1030 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1031 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1029 ) @ SV171 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1031 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1030 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1031 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1029 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1031 @ SY1030 @ SY1029 ) ) @ SV171 ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(5760,plain,
! [SV51: $i,SV172: $i] :
( ( ! [SY1032: $i,SY1033: $i] :
( ( SY1033 != SY1032 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SY1032 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SY1033 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5635]) ).
thf(5761,plain,
! [SV52: $i,SV173: $i] :
( ( ! [SY1034: $i,SY1035: $i,SY1036: $i] :
( ( ( hAPP @ SY1036 @ SY1035 )
!= SY1034 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SY1036 ) @ SY1035 ) @ SY1034 )
= SY1036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(5762,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
| ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
| ~ ( ~ ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) )
| ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(5763,plain,
! [SV54: $i,SV175: $i] :
( ( ! [SY1039: $i,SY1040: $i,SY1041: $i,SY1042: $i,SY1043: $i] :
( ~ ( ( SY1043 != SY1042 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1041 @ SY1040 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1041 @ SY1040 ) @ SY1039 ) @ SY1043 ) @ SV175 ) ) @ SY1042 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1041 @ SY1040 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1041 @ SY1040 ) @ SY1039 ) @ SY1042 ) @ SV54 ) ) @ SY1043 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(5764,plain,
! [SV55: $i,SV176: $i] :
( ( ! [SY1044: $i,SY1045: $i,SY1046: $i,SY1047: $i,SY1048: $i,SY1049: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1049 @ SY1048 @ SY1047 @ SY1046 ) @ SY1045 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1044 @ SY1048 @ SY1047 @ SV176 ) @ SV55 ) )
| ! [SY1050: $i] :
( ( hAPP @ SY1046 @ ( hAPP @ SY1045 @ SY1050 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1050 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(5765,plain,
! [SV56: $i,SV177: $i] :
( ( ! [SY1051: $i] :
( SY1051
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV177 ) @ SV56 ) @ SY1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(5766,plain,
! [SV57: $i,SV178: $i] :
( ( ! [SY1052: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1052 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SY1052 ) @ SV57 ) )
| ( SV178 = SV57 ) )
| ~ ( ( SV178 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SY1052 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SY1052 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5641]) ).
thf(5767,plain,
! [SV58: $i,SV179: $i] :
( ( ! [SY1053: $i,SY1054: $i,SY1055: $i,SY1056: $i,SY1057: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1057 @ SY1056 @ SY1055 @ SY1054 ) @ SY1053 )
!= SV179 )
| ( ( hAPP @ SY1054 @ ( hAPP @ SY1053 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(5768,plain,
! [SV59: $i,SV180: $i] :
( ( ! [SY1058: $i,SY1059: $i,SY1060: $i,SY1061: $i,SY1062: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1062 ) @ SY1061 ) @ SY1060 ) @ SY1059 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1062 ) @ SY1058 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SY1061 != SY1058 )
| ( SY1060 != SV180 ) )
| ( SY1059 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SY1061 != SY1058 )
| ( SY1060 != SV180 ) )
| ( SY1059 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1062 ) @ SY1061 ) @ SY1060 ) @ SY1059 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1062 ) @ SY1058 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5643]) ).
thf(5769,plain,
! [SV60: $i,SV181: $i] :
( ( ! [SY1063: $i,SY1064: $i,SY1065: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY1065 @ SY1064 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1063 ) @ SY1064 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1065 @ SV60 @ SY1063 ) ) @ SY1064 ) @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(5770,plain,
! [SV61: $i,SV182: $i] :
( ( ! [SY1066: $i,SY1067: $i,SY1068: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1068 @ SY1067 ) @ SY1066 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SY1068 ) @ SY1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5645]) ).
thf(5771,plain,
! [SV62: $i,SV183: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1071 @ SY1070 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1069 ) @ SY1070 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1071 @ SY1069 @ SV62 ) ) @ SY1070 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(5772,plain,
! [SV63: $i,SV184: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i,SY1075: $i,SY1076: $i,SY1077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1077 ) @ SY1076 ) @ SY1075 ) @ SY1074 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1073 ) @ SY1072 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY717: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1077 ) @ SY1076 ) @ SY717 ) @ SY1074 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1073 ) @ SY1072 ) @ SY717 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5647]) ).
thf(5773,plain,
! [SV64: $i,SV185: $i] :
( ( ! [SY1079: $i,SY1080: $i,SY1081: $i,SY1082: $i] :
( ~ ( ( SY1082 != SY1081 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1080 @ SY1079 ) @ SV185 ) @ SY1081 ) @ SV64 ) @ SY1082 )
= ( hAPP @ SV185 @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(5774,plain,
! [SV65: $i,SV186: $i] :
( ( ! [SY1083: $i,SY1084: $i,SY1085: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1085 @ SY1084 @ SY1083 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1085 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1084 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1085 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1083 ) @ SV186 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1085 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1084 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1085 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1083 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1085 @ SY1084 @ SY1083 ) ) @ SV186 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(5775,plain,
! [SV66: $i,SV187: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
| ( SV187 = SV66 ) )
| ~ ( ( SV187 != SV66 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(5776,plain,
! [SV67: $i,SV188: $i] :
( ( ! [SY1086: $i,SY1087: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1087 @ SY1086 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1087 @ SY1086 ) @ SV67 ) )
| ( SV188 = SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(5777,plain,
! [SV68: $i,SV189: $i] :
( ( ! [SY1088: $i,SY1089: $i,SY1090: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1090 @ SY1089 @ SY1088 )
| ( ( hAPP @ ( hAPP @ SY1088 @ SV189 ) @ ( hAPP @ ( hAPP @ SY1088 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SY1088 @ SV189 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(5778,plain,
! [SV69: $i,SV190: $i] :
( ( ! [SY1091: $i,SY1092: $i,SY1093: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1093 @ SY1092 ) @ SY1091 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SY1093 ) @ SY1091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5653]) ).
thf(5779,plain,
! [SV70: $i,SV191: $i] :
( ( ! [SY1094: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1094 @ SX3 ) )
| ! [SY1096: $i,SY1097: $i] : ( hBOOL @ ( hAPP @ SY1094 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1096 ) @ SY1097 ) ) ) )
| ~ ( ~ ! [SY1098: $i,SY1099: $i] : ( hBOOL @ ( hAPP @ SY1094 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1098 ) @ SY1099 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1094 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(5780,plain,
! [SV71: $i] :
( ( SV71
= ( hAPP @ c_Nat_OSuc @ SV71 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(5781,plain,
! [SV72: $i,SV192: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i,SY1104: $i] :
( ( SY1104 != SY1103 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1102 @ SY1101 @ SV192 ) @ SV72 ) @ SY1104 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1102 @ SY1101 @ SV192 ) @ SV72 ) @ SY1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5656]) ).
thf(5782,plain,
! [SV73: $i,SV193: $i] :
( ( ! [SY1105: $i,SY1106: $i,SY1107: $i,SY1108: $i] :
~ ( ~ ( ( SY1108 != SY1107 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1106 @ SY1105 ) @ SV193 ) @ SY1107 ) @ SV73 ) @ SY1108 )
= SV73 ) )
| ~ ( ~ ( ( SY1108 != SY1107 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1106 @ SY1105 ) @ SV193 ) @ SY1107 ) @ SV73 ) @ SY1108 )
= ( hAPP @ SV193 @ SY1108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(5783,plain,
! [SV74: $i,SV194: $i] :
( ( ! [SY1109: $i,SY1110: $i,SY1111: $i,SY1112: $i,SY1113: $i,SY1114: $i,SY1115: $i,SY1116: $i,SY1117: $i] :
( ( ( hAPP @ SY1117 @ ( hAPP @ SY1116 @ SY1115 ) )
!= ( hAPP @ SY1114 @ ( hAPP @ SY1113 @ SY1112 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1111 @ SY1110 @ SY1109 @ SY1117 ) @ SY1116 ) @ SY1115 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SY1110 @ SV74 @ SY1114 ) @ SY1113 ) @ SY1112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5658]) ).
thf(5784,plain,
! [SV75: $i,SV195: $i] :
( ( ! [SY1118: $i,SY1119: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1119 ) @ SY1118 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1119 ) @ SV75 ) @ SV195 ) )
| ( SY1118 = SV75 ) )
| ~ ( ( SY1118 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1119 ) @ SY1118 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1119 ) @ SV75 ) @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5785,plain,
! [SV76: $i,SV196: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1121 @ SY1120 ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1120 @ SV76 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1121 @ SY1120 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5660]) ).
thf(5786,plain,
! [SV77: $i,SV197: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1123 ) @ SY1122 ) @ SV197 ) @ SV77 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1123 ) @ SY1122 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5661]) ).
thf(5787,plain,
! [SV78: $i,SV198: $i] :
( ( ! [SY1124: $i,SY1125: $i,SY1126: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1126 @ SY1125 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1125 @ SY1124 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1125 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1125 @ SY1124 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5662]) ).
thf(5788,plain,
! [SV79: $i,SV199: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
| ( SV199 = SV79 ) )
| ~ ( ( SV199 != SV79 )
| ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(5789,plain,
! [SV80: $i,SV200: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
| ( SV200 = SV80 ) )
| ~ ( ( SV200 != SV80 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5664]) ).
thf(5790,plain,
! [SV81: $i,SV201: $i] :
( ( ! [SY1127: $i,SY1128: $i,SY1129: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1129 ) @ SY1128 ) @ SY1127 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1129 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SY1128 != SV201 )
| ( SY1127 != SV81 ) ) )
| ~ ( ~ ~ ( ( SY1128 != SV201 )
| ( SY1127 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1129 ) @ SY1128 ) @ SY1127 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1129 ) @ SV201 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5665]) ).
thf(5791,plain,
! [SV82: $i,SV202: $i] :
( ( ! [SY1130: $i,SY1131: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1131 @ SY1130 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SY1131 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1131 @ SV202 ) )
| ~ ~ ! [SY1132: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1130 ) @ SV202 ) @ SY1132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1131 @ SY1130 ) ) @ SY1132 ) @ SV82 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SY1131 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1131 @ SV202 ) )
| ~ ~ ! [SY1133: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1130 ) @ SV202 ) @ SY1133 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1131 @ SY1130 ) ) @ SY1133 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1131 @ SY1130 ) ) @ SV202 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5792,plain,
! [SV83: $i,SV203: $i] :
( ( ! [SY1134: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1134 @ SV203 ) @ SV83 ) )
| ! [SY1135: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1135 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1134 @ SV203 ) @ SY1135 ) ) ) )
| ~ ( ~ ! [SY1136: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1136 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1134 @ SV203 ) @ SY1136 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1134 @ SV203 ) @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5793,plain,
! [SV84: $i,SV204: $i] :
( ( ! [SY1137: $i,SY1138: $i,SY1139: $i,SY1140: $i,SY1141: $i] :
( ( SY1141 != SY1140 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1139 @ SY1138 @ SY1137 @ SV204 @ SV84 ) @ SY1141 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1139 @ SY1138 @ SY1137 @ SV204 @ SV84 ) @ SY1140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(5794,plain,
! [SV85: $i,SV205: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
| ( SV205 = SV85 ) )
| ~ ( ( SV205 != SV85 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5669]) ).
thf(5795,plain,
! [SV86: $i,SV206: $i] :
( ( ! [SY1142: $i,SY1143: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1143 @ SY1142 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
| ~ ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1143 @ SY1142 @ SV206 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5796,plain,
! [SV87: $i,SV207: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV207 )
!= ( hAPP @ c_Nat_OSuc @ SV87 ) )
| ( SV207 = SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5671]) ).
thf(5797,plain,
! [SV88: $i,SV208: $i] :
( ( ! [SY1146: $i,SY1147: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1147 @ SY1146 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1146 @ SV208 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1146 @ SV88 ) @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5672]) ).
thf(5798,plain,
! [SV89: $i,SV209: $i] :
( ( ! [SY1148: $i,SY1149: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1149 ) @ SY1148 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1149 ) @ SY1148 ) @ SV89 ) )
| ( SV209 = SV89 ) )
| ~ ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1149 ) @ SY1148 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1149 ) @ SY1148 ) @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5673]) ).
thf(5799,plain,
! [SV90: $i,SV210: $i] :
( ( ! [SY1150: $i,SY1151: $i,SY1152: $i,SY1153: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1153 @ SY1152 @ SY1151 @ SY1150 @ SV210 )
| ( ( hAPP @ SY1150 @ ( hAPP @ SY1151 @ SV90 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5674]) ).
thf(5800,plain,
! [SV91: $i,SV211: $i] :
( ( ! [SY1154: $i,SY1155: $i,SY1156: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1155 ) @ SY1154 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1157: $i] :
~ ( ~ ( ( SY1155
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SV211 ) @ SY1157 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1157 ) @ SY1154 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1155 ) @ SY1157 )
!= SV211 )
| ( SY1154
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1157 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY1158: $i] :
~ ( ~ ( ( SY1155
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SV211 ) @ SY1158 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1158 ) @ SY1154 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1155 ) @ SY1158 )
!= SV211 )
| ( SY1154
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1158 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SY1155 ) @ SY1154 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1156 ) @ SV211 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5675]) ).
thf(5801,plain,
! [SV92: $i,SV212: $i] :
( ( ! [SY1159: $i,SY1160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1160 @ SY1159 ) ) @ SV212 ) @ SV92 ) )
| ~ ! [SY1161: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1160 ) @ SV212 ) @ SY1161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1159 ) @ SY1161 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(5802,plain,
! [SV93: $i,SV213: $i] :
( ( ! [SY1162: $i,SY1163: $i,SY1164: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1164 @ SY1163 @ SY1162 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1163 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SY1162 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1163 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SY1162 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1164 @ SY1163 @ SY1162 ) @ SV213 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5677]) ).
thf(5803,plain,
! [SV94: $i,SV214: $i] :
( ( ! [SY1165: $i,SY1166: $i,SY1167: $i,SY1168: $i] :
~ ( ~ ( ( SY1168 != SY1167 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1166 @ SY1165 ) @ SV214 ) @ SY1167 ) @ SV94 ) @ SY1168 )
= SV94 ) )
| ~ ( ~ ( ( SY1168 != SY1167 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1166 @ SY1165 ) @ SV214 ) @ SY1167 ) @ SV94 ) @ SY1168 )
= ( hAPP @ SV214 @ SY1168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5678]) ).
thf(5804,plain,
! [SV95: $i,SV215: $i] :
( ( ! [SY1169: $i,SY1170: $i] :
( ( SY1170 != SY1169 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1170 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1169 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1170 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5679]) ).
thf(5805,plain,
! [SV96: $i,SV216: $i] :
( ( ! [SY1171: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY1171 @ SX3 ) )
| ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SY1171 ) )
| ( hBOOL @ ( hAPP @ SY1171 @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(5806,plain,
! [SV97: $i,SV217: $i] :
( ( ! [SY1173: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1173 ) @ SV217 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1173 ) @ SV217 ) @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5807,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5682]) ).
thf(5808,plain,
! [SV98: $i,SV218: $i] :
( ( ! [SY1174: $i,SY1175: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1175 @ SY1174 ) ) @ SV218 ) @ SV98 ) )
| ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SY1175 @ SV218 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1175 @ SV218 ) )
| ! [SY1176: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1174 ) @ SV218 ) @ SY1176 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1175 @ SY1174 ) ) @ SY1176 ) @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(5809,plain,
! [SV99: $i,SV219: $i] :
( ( ! [SY1177: $i,SY1178: $i,SY1179: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1179 @ SY1178 @ SY1177 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SY1177 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SY1177 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1179 @ SY1178 @ SY1177 ) @ SV219 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(5810,plain,
! [SV100: $i,SV220: $i] :
( ( ! [SY1180: $i,SY1181: $i,SY1182: $i,SY1183: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1183 @ SY1182 ) @ SY1181 ) @ SY1180 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1183 @ SY1182 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SY1181 != SV220 )
| ( SY1180 != SV100 ) ) )
| ~ ( ~ ~ ( ( SY1181 != SV220 )
| ( SY1180 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1183 @ SY1182 ) @ SY1181 ) @ SY1180 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1183 @ SY1182 ) @ SV220 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(5811,plain,
! [SV101: $i,SV221: $i] :
( ( ~ ! [SY1184: $i] :
( ( hAPP @ SV221 @ SY1184 )
= ( hAPP @ SV101 @ SY1184 ) )
| ( SV221 = SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(5812,plain,
! [SV102: $i,SV222: $i] :
( ( ( SV222 != SV102 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV222 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(5813,plain,
! [SV103: $i,SV223: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV223 ) @ SV103 ) )
| ( SV103 = SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(5814,plain,
! [SV104: $i,SV224: $i] :
( ( ! [SY1185: $i,SY1186: $i,SY1187: $i,SY1188: $i] :
( ~ ( ( SY1188 != SY1187 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1186 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1186 @ SY1185 ) @ SY1188 ) @ SV224 ) ) @ SY1187 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1186 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1186 @ SY1185 ) @ SY1187 ) @ SV104 ) ) @ SY1188 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(5815,plain,
! [SV105: $i,SV225: $i] :
( ( ! [SY1189: $i,SY1190: $i] :
( ( SY1190 != SY1189 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1189 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(5816,plain,
! [SV106: $i,SV226: $i] :
( ( ! [SY1191: $i,SY1192: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1192 @ SY1191 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1193: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1192 ) @ SV226 ) @ SY1193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1191 ) @ SY1193 ) @ SV106 ) ) ) )
| ~ ( ~ ~ ! [SY1194: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1192 ) @ SV226 ) @ SY1194 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1191 ) @ SY1194 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1192 @ SY1191 ) ) @ SV226 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5691]) ).
thf(5817,plain,
! [SV107: $i,SV227: $i] :
( ( ! [SY1195: $i,SY1196: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1196 ) @ SY1195 ) @ SV227 ) @ SV107 ) )
| ( SY1195 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ~ ( ~ ( ( SY1195 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1196 ) @ SY1195 ) @ SV227 ) @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5692]) ).
thf(5818,plain,
! [SV108: $i,SV228: $i] :
( ( ! [SY1197: $i,SY1198: $i] :
( ( SY1198 != SY1197 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1198 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1197 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1197 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1198 ) @ SV108 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(5819,plain,
! [SV109: $i,SV229: $i] :
( ( ~ ~ ! [SY1199: $i] :
~ ( hBOOL @ ( hAPP @ SV229 @ SY1199 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5694]) ).
thf(5820,plain,
! [SV110: $i,SV230: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
| ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
| ~ ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5695]) ).
thf(5821,plain,
! [SV111: $i,SV231: $i] :
( ( ! [SY1204: $i,SY1205: $i,SY1206: $i,SY1207: $i,SY1208: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1208 @ SY1207 @ SY1206 @ SY1205 @ SY1204 )
| ~ ( ~ ( ( ( hAPP @ SY1206 @ SV231 )
!= ( hAPP @ SY1206 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SY1206 @ SV231 )
= ( hAPP @ SY1206 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5696]) ).
thf(5822,plain,
! [SV112: $i,SV232: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
| ( SV232 = SV112 ) )
| ~ ( ( SV232 != SV112 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(5823,plain,
! [SV113: $i,SV233: $i] :
( ( ! [SY1209: $i] :
( ~ ( c_Predicate_Oreflp @ SY1209 @ SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV233 @ SV113 ) @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(5824,plain,
! [SV114: $i,SV234: $i] :
( ( ! [SY1210: $i,SY1211: $i,SY1212: $i,SY1213: $i,SY1214: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1214 @ SY1213 @ SY1212 @ SY1211 @ SY1210 @ SV234 @ SV114 )
| ~ ! [SY1215: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1211 @ SV234 ) @ SY1215 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1210 @ SY1215 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1216: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1211 @ SV234 ) @ SY1216 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1210 @ SY1216 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY1214 @ SY1213 @ SY1212 @ SY1211 @ SY1210 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(5825,plain,
! [SV115: $i] :
( ( ( ~ ! [SY906: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY906 ) )
| ( SV115 = SY906 ) ) )
= $true )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5700]) ).
thf(5826,plain,
! [SV116: $i,SV235: $i] :
( ( ! [SY1217: $i,SY1218: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1218 @ SY1217 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
| ~ ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1218 @ SY1217 @ SV235 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5701]) ).
thf(5827,plain,
! [SV117: $i,SV236: $i] :
( ( ! [SY1221: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1221 @ SV236 ) @ SV117 ) )
| ! [SY1222: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1222 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1221 @ SV236 ) @ SY1222 ) ) ) )
| ~ ( ~ ! [SY1223: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1223 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1221 @ SV236 ) @ SY1223 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1221 @ SV236 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(5828,plain,
! [SV118: $i,SV237: $i] :
( ( ! [SY1224: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1224 ) @ SV237 )
!= SV118 )
| ( SV237
= ( hAPP @ ( c_List_Orev @ SY1224 ) @ SV118 ) ) )
| ~ ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SY1224 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1224 ) @ SV237 )
= SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(5829,plain,
! [SV119: $i,SV238: $i] :
( ( ! [SY1225: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1225 @ SV238 ) )
| ( hBOOL @ ( hAPP @ SY1225 @ ( c_Hilbert__Choice_OEps @ SV119 @ SY1225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5704]) ).
thf(5830,plain,
! [SV120: $i,SV239: $i] :
( ( ! [SY1226: $i,SY1227: $i,SY1228: $i,SY1229: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1229 ) @ SY1228 ) @ SY1227 )
!= SY1226 )
| ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1229 ) @ SY1227 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1229 ) @ SY1228 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1229 ) @ SY1226 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(5831,plain,
! [SV121: $i,SV240: $i] :
( ( ! [SY1230: $i,SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i,SY1235: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1235 @ SY1234 ) @ SY1233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1232 @ SY1233 ) @ SY1231 ) )
| ( c_Predicate_Opred__comp @ SY1230 @ SV240 @ SV121 @ SY1235 @ SY1232 @ SY1234 @ SY1231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(5832,plain,
! [SV122: $i,SV241: $i] :
( ( ! [SY1236: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1236 @ SV241 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SY1236 @ SV122 ) )
| ~ ! [SY1237: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1237 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1236 @ SV241 ) ) @ SY1237 ) @ SV122 ) ) ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1236 @ SV122 ) )
| ~ ! [SY1238: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1238 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1236 @ SV241 ) ) @ SY1238 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1236 @ SV241 ) ) @ SV122 ) @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5707]) ).
thf(5833,plain,
! [SV123: $i,SV242: $i] :
( ( ! [SY1239: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1239 @ SV242 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV242 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(5834,plain,
! [SV124: $i,SV243: $i] :
( ( ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1242 ) @ SY1241 ) @ SY1240 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SY1240 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1242 @ SV243 ) ) @ SY1241 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5835,plain,
! [SV125: $i,SV244: $i] :
( ( ! [SY1243: $i,SY1244: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1244 @ SY1243 @ SV244 )
| ( ( hAPP @ ( hAPP @ SY1243 @ SV125 ) @ SV125 )
= SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5710]) ).
thf(5836,plain,
! [SV126: $i,SV245: $i] :
( ( ! [SY1245: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1245 ) @ SV245 ) @ SV126 ) )
| ~ ! [SY1246: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1245 ) @ SV245 ) @ SY1246 ) @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1247: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1245 ) @ SV245 ) @ SY1247 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1245 ) @ SV245 ) @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5711]) ).
thf(5837,plain,
! [SV3: $i,SV127: $i,SV246: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ SV3 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV246 ) @ SV127 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5712]) ).
thf(5838,plain,
! [SV4: $i,SV128: $i,SV247: $i] :
( ( ! [SY1248: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SV128 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SV247 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(5839,plain,
! [SV5: $i,SV129: $i,SV248: $i] :
( ( ! [SY1249: $i,SY1250: $i,SY1251: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1251 @ SY1250 @ SY1249 @ SV248 ) @ SV129 ) @ SV5 )
= ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5714]) ).
thf(5840,plain,
! [SV6: $i,SV130: $i,SV249: $i] :
( ( ! [SY1252: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1252 @ SV249 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5715]) ).
thf(5841,plain,
! [SV7: $i,SV131: $i,SV250: $i] :
( ( ! [SY1253: $i,SY1254: $i,SY1255: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1255 @ SY1254 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1255 @ SY1254 ) @ SY1253 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1255 @ SY1254 ) @ SY1253 ) @ SV250 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(5842,plain,
! [SV8: $i,SV132: $i,SV251: $i] :
( ( ! [SY1256: $i,SY1257: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1257 @ SY1256 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5717]) ).
thf(5843,plain,
! [SV9: $i,SV133: $i,SV252: $i] :
( ( ! [SY1258: $i,SY1259: $i,SY1260: $i,SY1261: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1261 @ SY1260 @ SY1259 @ SY1258 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1261 @ SY1259 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1260 @ SY1259 @ ( hAPP @ ( c_Fun_Ocomp @ SY1261 @ SY1260 @ SV252 @ SY1258 ) @ SV133 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5718]) ).
thf(5844,plain,
! [SV10: $i,SV134: $i,SV253: $i] :
( ( ! [SY1262: $i,SY1263: $i,SY1264: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1264 @ SY1263 @ SY1262 @ SV253 ) @ SV134 ) @ SV10 )
= ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5719]) ).
thf(5845,plain,
! [SV14: $i,SV138: $i,SV254: $i] :
( ( ! [SY1265: $i,SY1266: $i,SY1267: $i,SY1268: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1268 @ SY1267 @ SY1266 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1268 @ SY1265 @ SY1267 ) @ SV254 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1268 @ SY1265 @ SY1266 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1265 @ SY1267 @ SY1266 ) @ SV138 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5723]) ).
thf(5846,plain,
! [SV15: $i,SV139: $i,SV255: $i] :
( ( ! [SY1269: $i,SY1270: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ SY1269 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ SY1269 ) @ SV255 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5724]) ).
thf(5847,plain,
! [SV16: $i,SV140: $i,SV256: $i] :
( ( ! [SY1271: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1271 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1271 ) @ SV256 ) @ SV140 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1271 ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1271 ) @ SV140 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(5848,plain,
! [SV18: $i,SV142: $i,SV257: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV257 @ SV142 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV142 @ SV257 ) @ SV18 ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5727]) ).
thf(5849,plain,
! [SV19: $i,SV143: $i,SV258: $i] :
( ( ! [SY1272: $i] :
( ( hAPP @ SY1272 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SY1272 ) @ SV19 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SY1272 ) @ ( hAPP @ SY1272 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5728]) ).
thf(5850,plain,
! [SV21: $i,SV145: $i,SV259: $i] :
( ( ! [SY1273: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1273 @ SV259 ) @ SV145 ) @ SV21 )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5730]) ).
thf(5851,plain,
! [SV22: $i,SV146: $i,SV260: $i] :
( ( ! [SY1274: $i,SY1275: $i,SY1276: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1276 @ SY1275 @ SY1274 ) @ SV260 ) @ SV146 ) @ SV22 )
= ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5731]) ).
thf(5852,plain,
! [SV23: $i,SV147: $i,SV261: $i] :
( ( ! [SY1277: $i,SY1278: $i,SY1279: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1279 @ SY1278 @ SY1277 ) @ SV261 ) @ SV147 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5732]) ).
thf(5853,plain,
! [SV24: $i,SV148: $i,SV262: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1282 @ SY1281 @ SY1280 ) @ SV262 ) @ SV148 ) @ SV24 )
= ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5733]) ).
thf(5854,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) ) )
= $true )
| ( ( SV149 = SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(5855,plain,
! [SV26: $i] :
( ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
= $false )
| ( ( ~ ( hBOOL @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5735]) ).
thf(5856,plain,
! [SV27: $i] :
( ( ( ~ ( hBOOL @ SV27 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5736]) ).
thf(5857,plain,
! [SV28: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ SV150 )
| ~ ( hBOOL @ SV28 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5858,plain,
! [SV29: $i,SV151: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) ) )
= $true )
| ( ( hBOOL @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5859,plain,
! [SV30: $i,SV152: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) ) )
= $true )
| ( ( hBOOL @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(5860,plain,
! [SV31: $i,SV153: $i] :
( ( ( ~ ( hBOOL @ SV153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5740]) ).
thf(5861,plain,
! [SV32: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ SV154 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5862,plain,
! [SV33: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
| ( hBOOL @ SV155 ) )
= $true )
| ( ( hBOOL @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5863,plain,
! [SV34: $i,SV156: $i] :
( ( ( hBOOL @ SV156 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV156 ) @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5743]) ).
thf(5864,plain,
! [SV35: $i,SV157: $i] :
( ( ( ~ ( hBOOL @ SV157 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5744]) ).
thf(5865,plain,
! [SV36: $i,SV158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
| ~ ( hBOOL @ SV158 ) )
= $true )
| ( ( hBOOL @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5745]) ).
thf(5866,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) )
| ~ ! [SY1283: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ SY1283 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5746]) ).
thf(5867,plain,
! [SV38: $i,SV160: $i,SV264: $i] :
( ( ! [SY1284: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1284 ) @ SV264 ) @ SV160 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1284 ) @ SV264 ) @ SV38 ) )
| ( SV38 = SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(5868,plain,
! [SV39: $i,SV161: $i,SV265: $i] :
( ( ! [SY1285: $i,SY1286: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1286 @ SY1285 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SY1285 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1286 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1286 @ SV265 ) ) @ SY1285 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(5869,plain,
! [SV40: $i,SV162: $i,SV266: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1289 @ SY1288 ) @ SY1287 ) @ SV266 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1289 @ SY1288 ) @ SV162 ) @ SV40 ) )
| ~ ( ( SY1287 != SV162 )
| ( SV266 != SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5749]) ).
thf(5870,plain,
! [SV41: $i,SV163: $i] :
( ( ( ~ ~ ! [SY1012: $i] :
~ ( hBOOL @ ( hAPP @ SV163 @ SY1012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5750]) ).
thf(5871,plain,
! [SV43: $i,SV164: $i,SV267: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV267 ) @ SV164 ) @ SV43 )
!= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5752]) ).
thf(5872,plain,
! [SV44: $i,SV165: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV165 = SV44 ) )
| ~ ( ( SV165 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5873,plain,
! [SV45: $i,SV166: $i,SV268: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1291 @ SY1290 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) )
| ~ ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1291 @ SY1290 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(5874,plain,
! [SV46: $i,SV167: $i,SV269: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP @ SV269 @ SV167 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV269 @ SV46 ) ) @ SV167 ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5755]) ).
thf(5875,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
| ( SV168 = SV47 ) )
| ~ ( ( SV168 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(5876,plain,
! [SV48: $i,SV169: $i,SV271: $i] :
( ( ! [SY1292: $i,SY1293: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1293 @ SY1292 @ SV271 ) ) @ SV169 ) @ SV48 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1293 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1292 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1293 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(5877,plain,
! [SV49: $i,SV170: $i,SV272: $i] :
( ( ! [SY1294: $i,SY1295: $i,SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1299 @ SY1298 @ SY1297 @ SY1296 ) @ SY1295 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1294 @ SY1298 @ SY1297 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SY1296 @ ( hAPP @ SY1295 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5758]) ).
thf(5878,plain,
! [SV50: $i,SV171: $i,SV273: $i] :
( ( ! [SY1300: $i,SY1301: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1301 @ SY1300 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1301 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1300 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1301 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1301 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1300 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1301 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1301 @ SY1300 @ SV273 ) ) @ SV171 ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5759]) ).
thf(5879,plain,
! [SV51: $i,SV172: $i,SV274: $i] :
( ( ! [SY1302: $i] :
( ( SY1302 != SV274 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SY1302 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5760]) ).
thf(5880,plain,
! [SV52: $i,SV173: $i,SV275: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( ( hAPP @ SY1304 @ SY1303 )
!= SV275 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SY1304 ) @ SY1303 ) @ SV275 )
= SY1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(5881,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
| ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
| ~ ( ~ ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) )
| ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(5882,plain,
! [SV54: $i,SV175: $i,SV276: $i] :
( ( ! [SY1305: $i,SY1306: $i,SY1307: $i,SY1308: $i] :
( ~ ( ( SY1308 != SY1307 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1306 @ SY1305 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1306 @ SY1305 ) @ SV276 ) @ SY1308 ) @ SV175 ) ) @ SY1307 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1306 @ SY1305 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1306 @ SY1305 ) @ SV276 ) @ SY1307 ) @ SV54 ) ) @ SY1308 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5763]) ).
thf(5883,plain,
! [SV55: $i,SV176: $i,SV277: $i] :
( ( ! [SY1309: $i,SY1310: $i,SY1311: $i,SY1312: $i,SY1313: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1313 @ SY1312 @ SY1311 @ SY1310 ) @ SY1309 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SY1312 @ SY1311 @ SV176 ) @ SV55 ) )
| ! [SY1050: $i] :
( ( hAPP @ SY1310 @ ( hAPP @ SY1309 @ SY1050 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1050 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(5884,plain,
! [SV56: $i,SV177: $i,SV278: $i] :
( ( SV278
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV177 ) @ SV56 ) @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5765]) ).
thf(5885,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
| ( SV178 = SV57 ) )
| ~ ( ( SV178 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5766]) ).
thf(5886,plain,
! [SV58: $i,SV179: $i,SV280: $i] :
( ( ! [SY1315: $i,SY1316: $i,SY1317: $i,SY1318: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1318 @ SY1317 @ SY1316 @ SY1315 ) @ SV280 )
!= SV179 )
| ( ( hAPP @ SY1315 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5767]) ).
thf(5887,plain,
! [SV59: $i,SV180: $i,SV281: $i] :
( ( ! [SY1319: $i,SY1320: $i,SY1321: $i,SY1322: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1322 ) @ SY1321 ) @ SY1320 ) @ SY1319 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1322 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SY1321 != SV281 )
| ( SY1320 != SV180 ) )
| ( SY1319 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SY1321 != SV281 )
| ( SY1320 != SV180 ) )
| ( SY1319 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1322 ) @ SY1321 ) @ SY1320 ) @ SY1319 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1322 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5768]) ).
thf(5888,plain,
! [SV60: $i,SV181: $i,SV282: $i] :
( ( ! [SY1323: $i,SY1324: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY1324 @ SY1323 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SY1323 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1324 @ SV60 @ SV282 ) ) @ SY1323 ) @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(5889,plain,
! [SV61: $i,SV182: $i,SV283: $i] :
( ( ! [SY1325: $i,SY1326: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1326 @ SY1325 ) @ SV283 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SY1326 ) @ SY1325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5770]) ).
thf(5890,plain,
! [SV62: $i,SV183: $i,SV284: $i] :
( ( ! [SY1327: $i,SY1328: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1328 @ SY1327 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SY1327 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1328 @ SV284 @ SV62 ) ) @ SY1327 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(5891,plain,
! [SV63: $i,SV184: $i,SV285: $i] :
( ( ! [SY1329: $i,SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1333 ) @ SY1332 ) @ SY1331 ) @ SY1330 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1329 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1334: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1333 ) @ SY1332 ) @ SY1334 ) @ SY1330 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1329 ) @ SV285 ) @ SY1334 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5772]) ).
thf(5892,plain,
! [SV64: $i,SV185: $i,SV286: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i] :
( ~ ( ( SY1337 != SY1336 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1335 @ SV286 ) @ SV185 ) @ SY1336 ) @ SV64 ) @ SY1337 )
= ( hAPP @ SV185 @ SY1337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(5893,plain,
! [SV65: $i,SV186: $i,SV287: $i] :
( ( ! [SY1338: $i,SY1339: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1339 @ SY1338 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1339 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1338 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1339 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1339 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1338 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1339 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1339 @ SY1338 @ SV287 ) ) @ SV186 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5774]) ).
thf(5894,plain,
! [SV66: $i,SV187: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
| ( SV187 = SV66 ) )
| ~ ( ( SV187 != SV66 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(5895,plain,
! [SV67: $i,SV188: $i,SV288: $i] :
( ( ! [SY1340: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1340 @ SV288 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1340 @ SV288 ) @ SV67 ) )
| ( SV188 = SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5776]) ).
thf(5896,plain,
! [SV68: $i,SV189: $i,SV289: $i] :
( ( ! [SY1341: $i,SY1342: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1342 @ SY1341 @ SV289 )
| ( ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5777]) ).
thf(5897,plain,
! [SV69: $i,SV190: $i,SV290: $i] :
( ( ! [SY1343: $i,SY1344: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1344 @ SY1343 ) @ SV290 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SY1344 ) @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5778]) ).
thf(5898,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ( ~ ( ~ ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) )
| ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
| ~ ( ~ ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) )
| ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(5899,plain,
! [SV72: $i,SV192: $i,SV292: $i] :
( ( ! [SY1351: $i,SY1352: $i,SY1353: $i] :
( ( SY1353 != SY1352 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1351 @ SV292 @ SV192 ) @ SV72 ) @ SY1353 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1351 @ SV292 @ SV192 ) @ SV72 ) @ SY1352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5781]) ).
thf(5900,plain,
! [SV73: $i,SV193: $i,SV293: $i] :
( ( ! [SY1354: $i,SY1355: $i,SY1356: $i] :
~ ( ~ ( ( SY1356 != SY1355 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1354 @ SV293 ) @ SV193 ) @ SY1355 ) @ SV73 ) @ SY1356 )
= SV73 ) )
| ~ ( ~ ( ( SY1356 != SY1355 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1354 @ SV293 ) @ SV193 ) @ SY1355 ) @ SV73 ) @ SY1356 )
= ( hAPP @ SV193 @ SY1356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5782]) ).
thf(5901,plain,
! [SV74: $i,SV194: $i,SV294: $i] :
( ( ! [SY1357: $i,SY1358: $i,SY1359: $i,SY1360: $i,SY1361: $i,SY1362: $i,SY1363: $i,SY1364: $i] :
( ( ( hAPP @ SY1364 @ ( hAPP @ SY1363 @ SY1362 ) )
!= ( hAPP @ SY1361 @ ( hAPP @ SY1360 @ SY1359 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1358 @ SY1357 @ SV294 @ SY1364 ) @ SY1363 ) @ SY1362 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SY1357 @ SV74 @ SY1361 ) @ SY1360 ) @ SY1359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5783]) ).
thf(5902,plain,
! [SV75: $i,SV195: $i,SV295: $i] :
( ( ! [SY1365: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1365 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1365 ) @ SV75 ) @ SV195 ) )
| ( SV295 = SV75 ) )
| ~ ( ( SV295 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1365 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1365 ) @ SV75 ) @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5784]) ).
thf(5903,plain,
! [SV76: $i,SV196: $i,SV296: $i] :
( ( ! [SY1366: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1366 @ SV296 ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1366 @ SV296 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5785]) ).
thf(5904,plain,
! [SV77: $i,SV197: $i,SV297: $i] :
( ( ! [SY1367: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1367 ) @ SV297 ) @ SV197 ) @ SV77 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1367 ) @ SV297 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5786]) ).
thf(5905,plain,
! [SV78: $i,SV198: $i,SV298: $i] :
( ( ! [SY1368: $i,SY1369: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1369 @ SY1368 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1368 @ SV298 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1368 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1368 @ SV298 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5787]) ).
thf(5906,plain,
! [SV79: $i,SV199: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
| ( SV199 = SV79 ) )
| ~ ( ( SV199 != SV79 )
| ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5907,plain,
! [SV80: $i,SV200: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
| ( SV200 = SV80 ) )
| ~ ( ( SV200 != SV80 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5908,plain,
! [SV81: $i,SV201: $i,SV299: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1371 ) @ SY1370 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1371 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SY1370 != SV201 )
| ( SV299 != SV81 ) ) )
| ~ ( ~ ~ ( ( SY1370 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1371 ) @ SY1370 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1371 ) @ SV201 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5790]) ).
thf(5909,plain,
! [SV82: $i,SV202: $i,SV300: $i] :
( ( ! [SY1372: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1372 @ SV300 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SY1372 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1372 @ SV202 ) )
| ~ ~ ! [SY1373: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1373 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1372 @ SV300 ) ) @ SY1373 ) @ SV82 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SY1372 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1372 @ SV202 ) )
| ~ ~ ! [SY1374: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1374 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1372 @ SV300 ) ) @ SY1374 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1372 @ SV300 ) ) @ SV202 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5791]) ).
thf(5910,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
| ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) )
| ~ ( ~ ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5792]) ).
thf(5911,plain,
! [SV84: $i,SV204: $i,SV302: $i] :
( ( ! [SY1377: $i,SY1378: $i,SY1379: $i,SY1380: $i] :
( ( SY1380 != SY1379 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1378 @ SY1377 @ SV302 @ SV204 @ SV84 ) @ SY1380 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1378 @ SY1377 @ SV302 @ SV204 @ SV84 ) @ SY1379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(5912,plain,
! [SV85: $i,SV205: $i] :
( ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
| ( SV205 = SV85 ) )
| ~ ( ( SV205 != SV85 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5794]) ).
thf(5913,plain,
! [SV86: $i,SV206: $i,SV303: $i] :
( ( ! [SY1381: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1381 @ SV303 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
| ~ ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1381 @ SV303 @ SV206 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5795]) ).
thf(5914,plain,
! [SV87: $i,SV207: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV207 )
!= ( hAPP @ c_Nat_OSuc @ SV87 ) )
= $true )
| ( ( SV207 = SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(5915,plain,
! [SV88: $i,SV208: $i,SV304: $i] :
( ( ! [SY1384: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1384 @ SV304 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(5916,plain,
! [SV89: $i,SV209: $i,SV305: $i] :
( ( ! [SY1385: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1385 ) @ SV305 ) @ SV89 ) )
| ( SV209 = SV89 ) )
| ~ ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1385 ) @ SV305 ) @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(5917,plain,
! [SV90: $i,SV210: $i,SV306: $i] :
( ( ! [SY1386: $i,SY1387: $i,SY1388: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1388 @ SY1387 @ SY1386 @ SV306 @ SV210 )
| ( ( hAPP @ SV306 @ ( hAPP @ SY1386 @ SV90 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(5918,plain,
! [SV91: $i,SV211: $i,SV307: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1389 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1391: $i] :
~ ( ~ ( ( SY1389
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SV211 ) @ SY1391 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1391 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1389 ) @ SY1391 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1391 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY1392: $i] :
~ ( ~ ( ( SY1389
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SV211 ) @ SY1392 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1392 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1389 ) @ SY1392 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1392 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SY1389 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1390 ) @ SV211 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(5919,plain,
! [SV92: $i,SV212: $i,SV308: $i] :
( ( ! [SY1393: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1393 @ SV308 ) ) @ SV212 ) @ SV92 ) )
| ~ ! [SY1394: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1393 ) @ SV212 ) @ SY1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ SY1394 ) @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5801]) ).
thf(5920,plain,
! [SV93: $i,SV213: $i,SV309: $i] :
( ( ! [SY1395: $i,SY1396: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1396 @ SY1395 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1395 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1395 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1396 @ SY1395 @ SV309 ) @ SV213 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5802]) ).
thf(5921,plain,
! [SV94: $i,SV214: $i,SV310: $i] :
( ( ! [SY1397: $i,SY1398: $i,SY1399: $i] :
~ ( ~ ( ( SY1399 != SY1398 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1397 @ SV310 ) @ SV214 ) @ SY1398 ) @ SV94 ) @ SY1399 )
= SV94 ) )
| ~ ( ~ ( ( SY1399 != SY1398 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1397 @ SV310 ) @ SV214 ) @ SY1398 ) @ SV94 ) @ SY1399 )
= ( hAPP @ SV214 @ SY1399 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5803]) ).
thf(5922,plain,
! [SV95: $i,SV215: $i,SV311: $i] :
( ( ! [SY1400: $i] :
( ( SY1400 != SV311 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SY1400 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(5923,plain,
! [SV96: $i,SV216: $i,SV312: $i] :
( ( ~ ~ ! [SY1401: $i] :
~ ( hBOOL @ ( hAPP @ SV312 @ SY1401 ) )
| ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5805]) ).
thf(5924,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5806]) ).
thf(5925,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5807]) ).
thf(5926,plain,
! [SV98: $i,SV218: $i,SV314: $i] :
( ( ! [SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1402 @ SV314 ) ) @ SV218 ) @ SV98 ) )
| ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SY1402 @ SV218 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1402 @ SV218 ) )
| ! [SY1403: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1402 @ SV314 ) ) @ SY1403 ) @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(5927,plain,
! [SV99: $i,SV219: $i,SV315: $i] :
( ( ! [SY1404: $i,SY1405: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1405 @ SY1404 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1405 @ SY1404 @ SV315 ) @ SV219 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(5928,plain,
! [SV100: $i,SV220: $i,SV316: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1408 @ SY1407 ) @ SY1406 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1408 @ SY1407 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SY1406 != SV220 )
| ( SV316 != SV100 ) ) )
| ~ ( ~ ~ ( ( SY1406 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1408 @ SY1407 ) @ SY1406 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1408 @ SY1407 ) @ SV220 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(5929,plain,
! [SV101: $i,SV221: $i] :
( ( ( ~ ! [SY1184: $i] :
( ( hAPP @ SV221 @ SY1184 )
= ( hAPP @ SV101 @ SY1184 ) ) )
= $true )
| ( ( SV221 = SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5811]) ).
thf(5930,plain,
! [SV102: $i,SV222: $i] :
( ( ( SV222 != SV102 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV222 ) @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5812]) ).
thf(5931,plain,
! [SV103: $i,SV223: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV223 ) @ SV103 ) ) )
= $true )
| ( ( SV103 = SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5813]) ).
thf(5932,plain,
! [SV104: $i,SV224: $i,SV317: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i] :
( ~ ( ( SY1411 != SY1410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1409 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1409 @ SV317 ) @ SY1411 ) @ SV224 ) ) @ SY1410 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1409 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1409 @ SV317 ) @ SY1410 ) @ SV104 ) ) @ SY1411 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5814]) ).
thf(5933,plain,
! [SV105: $i,SV225: $i,SV318: $i] :
( ( ! [SY1412: $i] :
( ( SY1412 != SV318 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1412 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SY1412 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(5934,plain,
! [SV106: $i,SV226: $i,SV319: $i] :
( ( ! [SY1413: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1413 @ SV319 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1414: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1413 ) @ SV226 ) @ SY1414 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1414 ) @ SV106 ) ) ) )
| ~ ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1413 ) @ SV226 ) @ SY1415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1415 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1413 @ SV319 ) ) @ SV226 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5816]) ).
thf(5935,plain,
! [SV107: $i,SV227: $i,SV320: $i] :
( ( ! [SY1416: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1416 ) @ SV320 ) @ SV227 ) @ SV107 ) )
| ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ~ ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1416 ) @ SV320 ) @ SV227 ) @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5817]) ).
thf(5936,plain,
! [SV108: $i,SV228: $i,SV321: $i] :
( ( ! [SY1417: $i] :
( ( SY1417 != SV321 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1417 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SY1417 ) @ SV108 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(5937,plain,
! [SV109: $i,SV229: $i] :
( ( ( ~ ~ ! [SY1199: $i] :
~ ( hBOOL @ ( hAPP @ SV229 @ SY1199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5819]) ).
thf(5938,plain,
! [SV110: $i,SV230: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
| ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
| ~ ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5939,plain,
! [SV111: $i,SV231: $i,SV322: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i,SY1421: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1421 @ SY1420 @ SY1419 @ SY1418 @ SV322 )
| ~ ( ~ ( ( ( hAPP @ SY1419 @ SV231 )
!= ( hAPP @ SY1419 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SY1419 @ SV231 )
= ( hAPP @ SY1419 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5821]) ).
thf(5940,plain,
! [SV112: $i,SV232: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
| ( SV232 = SV112 ) )
| ~ ( ( SV232 != SV112 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(5941,plain,
! [SV113: $i,SV233: $i,SV323: $i] :
( ( ~ ( c_Predicate_Oreflp @ SV323 @ SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV233 @ SV113 ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5823]) ).
thf(5942,plain,
! [SV114: $i,SV234: $i,SV324: $i] :
( ( ! [SY1422: $i,SY1423: $i,SY1424: $i,SY1425: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1425 @ SY1424 @ SY1423 @ SY1422 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1426: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1422 @ SV234 ) @ SY1426 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1426 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1427: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1422 @ SV234 ) @ SY1427 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1427 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY1425 @ SY1424 @ SY1423 @ SY1422 @ SV324 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(5943,plain,
! [SV115: $i] :
( ( ( ! [SY906: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ SY906 ) )
| ( SV115 = SY906 ) ) )
= $false )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5825]) ).
thf(5944,plain,
! [SV116: $i,SV235: $i,SV325: $i] :
( ( ! [SY1428: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1428 @ SV325 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
| ~ ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1428 @ SV325 @ SV235 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5826]) ).
thf(5945,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
| ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) )
| ~ ( ~ ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5827]) ).
thf(5946,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
!= SV118 )
| ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) ) )
| ~ ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5828]) ).
thf(5947,plain,
! [SV119: $i,SV238: $i,SV328: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV328 @ SV238 ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( c_Hilbert__Choice_OEps @ SV119 @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5829]) ).
thf(5948,plain,
! [SV120: $i,SV239: $i,SV329: $i] :
( ( ! [SY1433: $i,SY1434: $i,SY1435: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1435 ) @ SY1434 ) @ SY1433 )
!= SV329 )
| ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1435 ) @ SY1433 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1435 ) @ SY1434 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1435 ) @ SV329 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5830]) ).
thf(5949,plain,
! [SV121: $i,SV240: $i,SV330: $i] :
( ( ! [SY1436: $i,SY1437: $i,SY1438: $i,SY1439: $i,SY1440: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1440 @ SY1439 ) @ SY1438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1438 ) @ SY1436 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SY1440 @ SY1437 @ SY1439 @ SY1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5831]) ).
thf(5950,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5832]) ).
thf(5951,plain,
! [SV123: $i,SV242: $i,SV332: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV332 @ SV242 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV242 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5833]) ).
thf(5952,plain,
! [SV124: $i,SV243: $i,SV333: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1444 ) @ SY1443 ) @ SV333 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1444 @ SV243 ) ) @ SY1443 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(5953,plain,
! [SV125: $i,SV244: $i,SV334: $i] :
( ( ! [SY1445: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1445 @ SV334 @ SV244 )
| ( ( hAPP @ ( hAPP @ SV334 @ SV125 ) @ SV125 )
= SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5835]) ).
thf(5954,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
| ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5836]) ).
thf(5955,plain,
! [SV4: $i,SV128: $i,SV247: $i,SV336: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV247 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV128 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV128 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV336 ) @ SV247 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5838]) ).
thf(5956,plain,
! [SV5: $i,SV129: $i,SV248: $i,SV337: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1449 @ SY1448 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
= ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5839]) ).
thf(5957,plain,
! [SV6: $i,SV130: $i,SV249: $i,SV338: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV338 @ SV249 ) @ SV130 ) @ SV6 ) @ ( hAPP @ SV130 @ SV6 ) )
= SV130 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5840]) ).
thf(5958,plain,
! [SV7: $i,SV131: $i,SV250: $i,SV339: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1451 @ SY1450 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1451 @ SY1450 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1451 @ SY1450 ) @ SV339 ) @ SV250 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5841]) ).
thf(5959,plain,
! [SV8: $i,SV132: $i,SV251: $i,SV340: $i] :
( ( ! [SY1452: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1452 @ SV340 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5842]) ).
thf(5960,plain,
! [SV9: $i,SV133: $i,SV252: $i,SV341: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1455 @ SY1454 @ SY1453 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1455 @ SY1453 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1454 @ SY1453 @ ( hAPP @ ( c_Fun_Ocomp @ SY1455 @ SY1454 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5843]) ).
thf(5961,plain,
! [SV10: $i,SV134: $i,SV253: $i,SV342: $i] :
( ( ! [SY1456: $i,SY1457: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1457 @ SY1456 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
= ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(5962,plain,
! [SV14: $i,SV138: $i,SV254: $i,SV343: $i] :
( ( ! [SY1458: $i,SY1459: $i,SY1460: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1460 @ SY1459 @ SY1458 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1460 @ SV343 @ SY1459 ) @ SV254 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1460 @ SV343 @ SY1458 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SY1459 @ SY1458 ) @ SV138 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5845]) ).
thf(5963,plain,
! [SV15: $i,SV139: $i,SV255: $i,SV344: $i] :
( ( ! [SY1461: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1461 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1461 @ SV344 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1461 @ SV344 ) @ SV255 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5846]) ).
thf(5964,plain,
! [SV16: $i,SV140: $i,SV256: $i,SV345: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV256 ) @ SV140 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV256 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV345 ) @ SV140 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5847]) ).
thf(5965,plain,
! [SV19: $i,SV143: $i,SV258: $i,SV346: $i] :
( ( ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SV346 ) @ SV19 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV258 @ SV258 ) @ SV143 ) @ SV346 ) @ ( hAPP @ SV346 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5849]) ).
thf(5966,plain,
! [SV21: $i,SV145: $i,SV259: $i,SV347: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV347 @ SV259 ) @ SV145 ) @ SV21 )
= SV145 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5850]) ).
thf(5967,plain,
! [SV22: $i,SV146: $i,SV260: $i,SV348: $i] :
( ( ! [SY1462: $i,SY1463: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1463 @ SY1462 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
= ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5851]) ).
thf(5968,plain,
! [SV23: $i,SV147: $i,SV261: $i,SV349: $i] :
( ( ! [SY1464: $i,SY1465: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1465 @ SY1464 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5852]) ).
thf(5969,plain,
! [SV24: $i,SV148: $i,SV262: $i,SV350: $i] :
( ( ! [SY1466: $i,SY1467: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1467 @ SY1466 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
= ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5853]) ).
thf(5970,plain,
! [SV25: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV149 ) @ SV25 ) )
= $false )
| ( ( SV149 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5971,plain,
! [SV26: $i] :
( ( ( hBOOL @ SV26 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5855]) ).
thf(5972,plain,
! [SV27: $i] :
( ( ( hBOOL @ SV27 )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5856]) ).
thf(5973,plain,
! [SV28: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ SV150 ) )
= $true )
| ( ( ~ ( hBOOL @ SV28 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5857]) ).
thf(5974,plain,
! [SV29: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV151 ) @ SV29 ) )
= $false )
| ( ( hBOOL @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(5975,plain,
! [SV30: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV152 ) @ SV30 ) )
= $false )
| ( ( hBOOL @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(5976,plain,
! [SV31: $i,SV153: $i] :
( ( ( hBOOL @ SV153 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV153 ) @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5860]) ).
thf(5977,plain,
! [SV32: $i,SV154: $i] :
( ( ( hBOOL @ SV154 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV32 ) @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5861]) ).
thf(5978,plain,
! [SV33: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) ) )
= $true )
| ( ( hBOOL @ SV155 )
= $true )
| ( ( hBOOL @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5862]) ).
thf(5979,plain,
! [SV35: $i,SV157: $i] :
( ( ( hBOOL @ SV157 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV35 ) @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(5980,plain,
! [SV36: $i,SV158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV158 ) )
= $true )
| ( ( hBOOL @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5865]) ).
thf(5981,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) ) )
= $true )
| ( ( ~ ! [SY1283: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ SY1283 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5866]) ).
thf(5982,plain,
! [SV38: $i,SV160: $i,SV264: $i,SV351: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV160 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV38 ) )
| ( SV38 = SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5867]) ).
thf(5983,plain,
! [SV39: $i,SV161: $i,SV265: $i,SV352: $i] :
( ( ! [SY1468: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1468 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1468 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SY1468 @ SV265 ) ) @ SV352 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5868]) ).
thf(5984,plain,
! [SV40: $i,SV162: $i,SV266: $i,SV353: $i] :
( ( ! [SY1469: $i,SY1470: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1470 @ SY1469 ) @ SV353 ) @ SV266 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1470 @ SY1469 ) @ SV162 ) @ SV40 ) )
| ~ ( ( SV353 != SV162 )
| ( SV266 != SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5869]) ).
thf(5985,plain,
! [SV41: $i,SV163: $i] :
( ( ( ~ ! [SY1012: $i] :
~ ( hBOOL @ ( hAPP @ SV163 @ SY1012 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5870]) ).
thf(5986,plain,
! [SV43: $i,SV164: $i,SV267: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV267 ) @ SV164 ) @ SV43 )
= SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5987,plain,
! [SV44: $i,SV165: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV165 = SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5872]) ).
thf(5988,plain,
! [SV44: $i,SV165: $i] :
( ( ~ ( ( SV165 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5872]) ).
thf(5989,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i] :
( ( ! [SY1471: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1471 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) )
| ~ ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1471 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5873]) ).
thf(5990,plain,
! [SV46: $i,SV167: $i,SV269: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV269 @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV269 @ SV46 ) ) @ SV167 ) @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5874]) ).
thf(5991,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
| ( SV168 = SV47 ) )
| ~ ( ( SV168 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5875]) ).
thf(5992,plain,
! [SV48: $i,SV169: $i,SV271: $i,SV355: $i] :
( ( ! [SY1472: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1472 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1472 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1472 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5876]) ).
thf(5993,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i] :
( ( ! [SY1473: $i,SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1477 @ SY1476 @ SY1475 @ SY1474 ) @ SY1473 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SY1476 @ SY1475 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SY1474 @ ( hAPP @ SY1473 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5877]) ).
thf(5994,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i] :
( ( ! [SY1478: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1478 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1478 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1478 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1478 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1478 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1478 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5878]) ).
thf(5995,plain,
! [SV51: $i,SV172: $i,SV274: $i,SV358: $i] :
( ( ( SV358 != SV274 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV358 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5879]) ).
thf(5996,plain,
! [SV52: $i,SV173: $i,SV275: $i,SV359: $i] :
( ( ! [SY1479: $i] :
( ( ( hAPP @ SY1479 @ SV359 )
!= SV275 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SY1479 ) @ SV359 ) @ SV275 )
= SY1479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5880]) ).
thf(5997,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
| ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5881]) ).
thf(5998,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ( ~ ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) )
| ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5881]) ).
thf(5999,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i] :
( ( ! [SY1480: $i,SY1481: $i,SY1482: $i] :
( ~ ( ( SY1482 != SY1481 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1480 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1480 @ SV360 ) @ SV276 ) @ SY1482 ) @ SV175 ) ) @ SY1481 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1480 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1480 @ SV360 ) @ SV276 ) @ SY1481 ) @ SV54 ) ) @ SY1482 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5882]) ).
thf(6000,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i] :
( ( ! [SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1486 @ SY1485 @ SY1484 @ SY1483 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SY1485 @ SY1484 @ SV176 ) @ SV55 ) )
| ! [SY1487: $i] :
( ( hAPP @ SY1483 @ ( hAPP @ SV361 @ SY1487 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5883]) ).
thf(6001,plain,
! [SV56: $i,SV177: $i,SV278: $i] :
( ( SV278
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV177 ) @ SV56 ) @ SV278 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5884]) ).
thf(6002,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
| ( SV178 = SV57 ) )
| ~ ( ( SV178 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5885]) ).
thf(6003,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i] :
( ( ! [SY1488: $i,SY1489: $i,SY1490: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1490 @ SY1489 @ SY1488 @ SV362 ) @ SV280 )
!= SV179 )
| ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5886]) ).
thf(6004,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i] :
( ( ! [SY1491: $i,SY1492: $i,SY1493: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1493 ) @ SY1492 ) @ SY1491 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1493 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SY1492 != SV281 )
| ( SY1491 != SV180 ) )
| ( SV363 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SY1492 != SV281 )
| ( SY1491 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1493 ) @ SY1492 ) @ SY1491 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1493 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5887]) ).
thf(6005,plain,
! [SV60: $i,SV181: $i,SV282: $i,SV364: $i] :
( ( ! [SY1494: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ SY1494 @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1494 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5888]) ).
thf(6006,plain,
! [SV61: $i,SV182: $i,SV283: $i,SV365: $i] :
( ( ! [SY1495: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1495 @ SV365 ) @ SV283 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SY1495 ) @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5889]) ).
thf(6007,plain,
! [SV62: $i,SV183: $i,SV284: $i,SV366: $i] :
( ( ! [SY1496: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1496 @ SV366 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1496 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5890]) ).
thf(6008,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i] :
( ( ! [SY1497: $i,SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1500 ) @ SY1499 ) @ SY1498 ) @ SY1497 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1501: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1500 ) @ SY1499 ) @ SY1501 ) @ SY1497 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1501 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5891]) ).
thf(6009,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i] :
( ( ! [SY1502: $i,SY1503: $i] :
( ~ ( ( SY1503 != SY1502 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SY1502 ) @ SV64 ) @ SY1503 )
= ( hAPP @ SV185 @ SY1503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5892]) ).
thf(6010,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i] :
( ( ! [SY1504: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1504 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1504 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1504 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1504 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1504 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY1504 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5893]) ).
thf(6011,plain,
! [SV66: $i,SV187: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
| ( SV187 = SV66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5894]) ).
thf(6012,plain,
! [SV66: $i,SV187: $i] :
( ( ~ ( ( SV187 != SV66 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5894]) ).
thf(6013,plain,
! [SV67: $i,SV188: $i,SV288: $i,SV370: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV67 ) )
| ( SV188 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5895]) ).
thf(6014,plain,
! [SV68: $i,SV189: $i,SV289: $i,SV371: $i] :
( ( ! [SY1505: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1505 @ SV371 @ SV289 )
| ( ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5896]) ).
thf(6015,plain,
! [SV69: $i,SV190: $i,SV290: $i,SV372: $i] :
( ( ! [SY1506: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1506 @ SV372 ) @ SV290 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SY1506 ) @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5897]) ).
thf(6016,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ( ~ ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) )
| ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
| ~ ( ~ ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) )
| ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5898]) ).
thf(6017,plain,
! [SV72: $i,SV192: $i,SV292: $i,SV373: $i] :
( ( ! [SY1507: $i,SY1508: $i] :
( ( SY1508 != SY1507 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SY1508 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SY1507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5899]) ).
thf(6018,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i] :
( ( ! [SY1509: $i,SY1510: $i] :
~ ( ~ ( ( SY1510 != SY1509 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SY1509 ) @ SV73 ) @ SY1510 )
= SV73 ) )
| ~ ( ~ ( ( SY1510 != SY1509 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SY1509 ) @ SV73 ) @ SY1510 )
= ( hAPP @ SV193 @ SY1510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5900]) ).
thf(6019,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i] :
( ( ! [SY1511: $i,SY1512: $i,SY1513: $i,SY1514: $i,SY1515: $i,SY1516: $i,SY1517: $i] :
( ( ( hAPP @ SY1517 @ ( hAPP @ SY1516 @ SY1515 ) )
!= ( hAPP @ SY1514 @ ( hAPP @ SY1513 @ SY1512 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1511 @ SV375 @ SV294 @ SY1517 ) @ SY1516 ) @ SY1515 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SY1514 ) @ SY1513 ) @ SY1512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5901]) ).
thf(6020,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
| ( SV295 = SV75 ) )
| ~ ( ( SV295 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5902]) ).
thf(6021,plain,
! [SV76: $i,SV196: $i,SV296: $i,SV377: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5903]) ).
thf(6022,plain,
! [SV77: $i,SV197: $i,SV297: $i,SV378: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV378 ) @ SV297 ) @ SV197 ) @ SV77 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV378 ) @ SV297 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(6023,plain,
! [SV78: $i,SV198: $i,SV298: $i,SV379: $i] :
( ( ! [SY1518: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1518 @ SV379 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(6024,plain,
! [SV79: $i,SV199: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
| ( SV199 = SV79 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5906]) ).
thf(6025,plain,
! [SV79: $i,SV199: $i] :
( ( ~ ( ( SV199 != SV79 )
| ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5906]) ).
thf(6026,plain,
! [SV80: $i,SV200: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
| ( SV200 = SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5907]) ).
thf(6027,plain,
! [SV80: $i,SV200: $i] :
( ( ~ ( ( SV200 != SV80 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5907]) ).
thf(6028,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i] :
( ( ! [SY1519: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1519 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1519 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
| ~ ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1519 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1519 ) @ SV201 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5908]) ).
thf(6029,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5909]) ).
thf(6030,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
| ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) )
| ~ ( ~ ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6031,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i] :
( ( ! [SY1522: $i,SY1523: $i,SY1524: $i] :
( ( SY1524 != SY1523 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1522 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SY1524 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1522 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SY1523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5911]) ).
thf(6032,plain,
! [SV85: $i,SV205: $i] :
( ( ~ ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
| ( SV205 = SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5912]) ).
thf(6033,plain,
! [SV85: $i,SV205: $i] :
( ( ~ ( ( SV205 != SV85 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5912]) ).
thf(6034,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
| ~ ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5913]) ).
thf(6035,plain,
! [SV87: $i,SV207: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV207 )
= ( hAPP @ c_Nat_OSuc @ SV87 ) )
= $false )
| ( ( SV207 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5914]) ).
thf(6036,plain,
! [SV88: $i,SV208: $i,SV304: $i,SV384: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV384 @ SV304 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5915]) ).
thf(6037,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
| ( SV209 = SV89 ) )
| ~ ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5916]) ).
thf(6038,plain,
! [SV90: $i,SV210: $i,SV306: $i,SV386: $i] :
( ( ! [SY1527: $i,SY1528: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1528 @ SY1527 @ SV386 @ SV306 @ SV210 )
| ( ( hAPP @ SV306 @ ( hAPP @ SV386 @ SV90 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5917]) ).
thf(6039,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i] :
( ( ! [SY1529: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1530: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV211 ) @ SY1530 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SY1530 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV387 ) @ SY1530 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SY1530 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY1531: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV211 ) @ SY1531 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SY1531 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV387 ) @ SY1531 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SY1531 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1529 ) @ SV211 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5918]) ).
thf(6040,plain,
! [SV92: $i,SV212: $i,SV308: $i,SV388: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
| ~ ! [SY1532: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ SY1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ SY1532 ) @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5919]) ).
thf(6041,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i] :
( ( ! [SY1533: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1533 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SY1533 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5920]) ).
thf(6042,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i] :
( ( ! [SY1534: $i,SY1535: $i] :
~ ( ~ ( ( SY1535 != SY1534 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SY1534 ) @ SV94 ) @ SY1535 )
= SV94 ) )
| ~ ( ~ ( ( SY1535 != SY1534 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SY1534 ) @ SV94 ) @ SY1535 )
= ( hAPP @ SV214 @ SY1535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5921]) ).
thf(6043,plain,
! [SV95: $i,SV215: $i,SV311: $i,SV391: $i] :
( ( ( SV391 != SV311 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5922]) ).
thf(6044,plain,
! [SV96: $i,SV216: $i,SV312: $i] :
( ( ( ~ ~ ! [SY1401: $i] :
~ ( hBOOL @ ( hAPP @ SV312 @ SY1401 ) ) )
= $true )
| ( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5923]) ).
thf(6045,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(6046,plain,
! [SV98: $i,SV218: $i,SV314: $i,SV392: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
| ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(6047,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i] :
( ( ! [SY1537: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1537 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1537 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5927]) ).
thf(6048,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i] :
( ( ! [SY1538: $i,SY1539: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1539 @ SY1538 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1539 @ SY1538 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
| ~ ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1539 @ SY1538 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1539 @ SY1538 ) @ SV220 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5928]) ).
thf(6049,plain,
! [SV101: $i,SV221: $i] :
( ( ( ! [SY1184: $i] :
( ( hAPP @ SV221 @ SY1184 )
= ( hAPP @ SV101 @ SY1184 ) ) )
= $false )
| ( ( SV221 = SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5929]) ).
thf(6050,plain,
! [SV102: $i,SV222: $i] :
( ( ( SV222 = SV102 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV222 ) @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(6051,plain,
! [SV103: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV223 ) @ SV103 ) )
= $false )
| ( ( SV103 = SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(6052,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i] :
( ( ! [SY1540: $i,SY1541: $i] :
( ~ ( ( SY1541 != SY1540 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SY1541 ) @ SV224 ) ) @ SY1540 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SY1540 ) @ SV104 ) ) @ SY1541 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(6053,plain,
! [SV105: $i,SV225: $i,SV318: $i,SV396: $i] :
( ( ( SV396 != SV318 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5933]) ).
thf(6054,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
| ~ ( ~ ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5934]) ).
thf(6055,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
| ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ~ ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5935]) ).
thf(6056,plain,
! [SV108: $i,SV228: $i,SV321: $i,SV399: $i] :
( ( ( SV399 != SV321 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5936]) ).
thf(6057,plain,
! [SV109: $i,SV229: $i] :
( ( ( ~ ! [SY1199: $i] :
~ ( hBOOL @ ( hAPP @ SV229 @ SY1199 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(6058,plain,
! [SV110: $i,SV230: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
| ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5938]) ).
thf(6059,plain,
! [SV230: $i,SV110: $i] :
( ( ~ ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5938]) ).
thf(6060,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i] :
( ( ! [SY1544: $i,SY1545: $i,SY1546: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1546 @ SY1545 @ SY1544 @ SV400 @ SV322 )
| ~ ( ~ ( ( ( hAPP @ SY1544 @ SV231 )
!= ( hAPP @ SY1544 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SY1544 @ SV231 )
= ( hAPP @ SY1544 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5939]) ).
thf(6061,plain,
! [SV112: $i,SV232: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
| ( SV232 = SV112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5940]) ).
thf(6062,plain,
! [SV112: $i,SV232: $i] :
( ( ~ ( ( SV232 != SV112 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5940]) ).
thf(6063,plain,
! [SV113: $i,SV233: $i,SV323: $i] :
( ( ( ~ ( c_Predicate_Oreflp @ SV323 @ SV233 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV233 @ SV113 ) @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5941]) ).
thf(6064,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1549 @ SY1548 @ SY1547 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY1549 @ SY1548 @ SY1547 @ SV401 @ SV324 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5942]) ).
thf(6065,plain,
! [SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK2_SY906 @ SV115 ) ) )
| ( SV115
= ( sK2_SY906 @ SV115 ) ) )
= $false )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5943]) ).
thf(6066,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
| ~ ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5944]) ).
thf(6067,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
| ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) )
| ~ ( ~ ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5945]) ).
thf(6068,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
!= SV118 )
| ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) ) )
| ~ ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5946]) ).
thf(6069,plain,
! [SV119: $i,SV238: $i,SV328: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV328 @ SV238 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV328 @ ( c_Hilbert__Choice_OEps @ SV119 @ SV328 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5947]) ).
thf(6070,plain,
! [SV120: $i,SV239: $i,SV329: $i,SV403: $i] :
( ( ! [SY1554: $i,SY1555: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1555 ) @ SY1554 ) @ SV403 )
!= SV329 )
| ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1555 ) @ SV403 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1555 ) @ SY1554 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1555 ) @ SV329 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6071,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i] :
( ( ! [SY1556: $i,SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1559 @ SY1558 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1556 @ SY1557 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SY1559 @ SY1556 @ SY1558 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5949]) ).
thf(6072,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5950]) ).
thf(6073,plain,
! [SV123: $i,SV242: $i,SV332: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV332 @ SV242 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV242 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5951]) ).
thf(6074,plain,
! [SV124: $i,SV243: $i,SV333: $i,SV405: $i] :
( ( ! [SY1560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY1560 ) @ SV405 ) @ SV333 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY1560 @ SV243 ) ) @ SV405 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5952]) ).
thf(6075,plain,
! [SV125: $i,SV244: $i,SV334: $i,SV406: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV406 @ SV334 @ SV244 )
| ( ( hAPP @ ( hAPP @ SV334 @ SV125 ) @ SV125 )
= SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5953]) ).
thf(6076,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
| ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6077,plain,
! [SV5: $i,SV129: $i,SV248: $i,SV337: $i,SV407: $i] :
( ( ! [SY1561: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1561 @ SV407 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
= ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(6078,plain,
! [SV7: $i,SV131: $i,SV250: $i,SV339: $i,SV408: $i] :
( ( ! [SY1562: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1562 @ SV408 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1562 @ SV408 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1562 @ SV408 ) @ SV339 ) @ SV250 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5958]) ).
thf(6079,plain,
! [SV8: $i,SV132: $i,SV251: $i,SV340: $i,SV409: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV409 @ SV340 ) @ SV251 ) @ SV132 ) @ SV8 ) @ SV132 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5959]) ).
thf(6080,plain,
! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i] :
( ( ! [SY1563: $i,SY1564: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1564 @ SY1563 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1564 @ SV410 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1563 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SY1564 @ SY1563 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(6081,plain,
! [SV10: $i,SV134: $i,SV253: $i,SV342: $i,SV411: $i] :
( ( ! [SY1565: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1565 @ SV411 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
= ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5961]) ).
thf(6082,plain,
! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SY1566 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SV343 @ SY1566 ) @ SV254 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1567 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SY1566 @ SV412 ) @ SV138 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5962]) ).
thf(6083,plain,
! [SV15: $i,SV139: $i,SV255: $i,SV344: $i,SV413: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ SV344 ) @ SV255 ) @ SV139 ) ) @ SV255 ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV413 @ SV344 ) @ SV255 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5963]) ).
thf(6084,plain,
! [SV22: $i,SV146: $i,SV260: $i,SV348: $i,SV414: $i] :
( ( ! [SY1568: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1568 @ SV414 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
= ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5967]) ).
thf(6085,plain,
! [SV23: $i,SV147: $i,SV261: $i,SV349: $i,SV415: $i] :
( ( ! [SY1569: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1569 @ SV415 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5968]) ).
thf(6086,plain,
! [SV24: $i,SV148: $i,SV262: $i,SV350: $i,SV416: $i] :
( ( ! [SY1570: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1570 @ SV416 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
= ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5969]) ).
thf(6087,plain,
! [SV28: $i,SV150: $i] :
( ( ( hBOOL @ SV150 )
= $false )
| ( ( ~ ( hBOOL @ SV28 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(6088,plain,
! [SV33: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV155 ) @ SV33 ) )
= $false )
| ( ( hBOOL @ SV155 )
= $true )
| ( ( hBOOL @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5978]) ).
thf(6089,plain,
! [SV36: $i,SV158: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
= $false )
| ( ( ~ ( hBOOL @ SV158 ) )
= $true )
| ( ( hBOOL @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(6090,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) )
= $false )
| ( ( ~ ! [SY1283: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ SY1283 ) @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5981]) ).
thf(6091,plain,
! [SV38: $i,SV160: $i,SV264: $i,SV351: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV160 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV38 ) )
| ( SV38 = SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5982]) ).
thf(6092,plain,
! [SV39: $i,SV161: $i,SV265: $i,SV352: $i,SV417: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6093,plain,
! [SV40: $i,SV162: $i,SV266: $i,SV353: $i,SV418: $i] :
( ( ! [SY1571: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1571 @ SV418 ) @ SV353 ) @ SV266 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1571 @ SV418 ) @ SV162 ) @ SV40 ) )
| ~ ( ( SV353 != SV162 )
| ( SV266 != SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5984]) ).
thf(6094,plain,
! [SV41: $i,SV163: $i] :
( ( ( ! [SY1012: $i] :
~ ( hBOOL @ ( hAPP @ SV163 @ SY1012 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5985]) ).
thf(6095,plain,
! [SV44: $i,SV165: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV165 = SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5987]) ).
thf(6096,plain,
! [SV44: $i,SV165: $i] :
( ( ( SV165 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5988]) ).
thf(6097,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) )
| ~ ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5989]) ).
thf(6098,plain,
! [SV46: $i,SV167: $i,SV269: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV269 @ SV167 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV269 @ SV46 ) ) @ SV167 ) @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5990]) ).
thf(6099,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
| ( SV168 = SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5991]) ).
thf(6100,plain,
! [SV270: $i,SV47: $i,SV168: $i] :
( ( ~ ( ( SV168 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5991]) ).
thf(6101,plain,
! [SV48: $i,SV169: $i,SV271: $i,SV355: $i,SV420: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6102,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i] :
( ( ! [SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1575 @ SY1574 @ SY1573 @ SY1572 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SY1574 @ SY1573 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SY1572 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5993]) ).
thf(6103,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5994]) ).
thf(6104,plain,
! [SV51: $i,SV172: $i,SV274: $i,SV358: $i] :
( ( ( SV358 != SV274 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV358 ) @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5995]) ).
thf(6105,plain,
! [SV52: $i,SV173: $i,SV275: $i,SV359: $i,SV423: $i] :
( ( ( ( hAPP @ SV423 @ SV359 )
!= SV275 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SV423 ) @ SV359 ) @ SV275 )
= SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5996]) ).
thf(6106,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
| ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5997]) ).
thf(6107,plain,
! [SV53: $i,SV174: $i] :
( ( ~ ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) )
| ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5998]) ).
thf(6108,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i] :
( ( ! [SY1576: $i,SY1577: $i] :
( ~ ( ( SY1577 != SY1576 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SY1577 ) @ SV175 ) ) @ SY1576 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SY1576 ) @ SV54 ) ) @ SY1577 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5999]) ).
thf(6109,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i] :
( ( ! [SY1578: $i,SY1579: $i,SY1580: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1580 @ SY1579 @ SY1578 @ SV425 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SY1579 @ SY1578 @ SV176 ) @ SV55 ) )
| ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6110,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
| ( SV178 = SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6002]) ).
thf(6111,plain,
! [SV279: $i,SV57: $i,SV178: $i] :
( ( ~ ( ( SV178 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6002]) ).
thf(6112,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i,SV426: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1583 @ SY1582 @ SV426 @ SV362 ) @ SV280 )
!= SV179 )
| ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6003]) ).
thf(6113,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i] :
( ( ! [SY1584: $i,SY1585: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1585 ) @ SY1584 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1585 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SY1584 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SY1584 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1585 ) @ SY1584 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1585 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6004]) ).
thf(6114,plain,
! [SV60: $i,SV181: $i,SV282: $i,SV364: $i,SV428: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP @ SV428 @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6115,plain,
! [SV61: $i,SV182: $i,SV283: $i,SV365: $i,SV429: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV429 @ SV365 ) @ SV283 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SV429 ) @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6116,plain,
! [SV62: $i,SV183: $i,SV284: $i,SV366: $i,SV430: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV430 @ SV366 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV430 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6007]) ).
thf(6117,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i] :
( ( ! [SY1586: $i,SY1587: $i,SY1588: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1588 ) @ SY1587 ) @ SY1586 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1589: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1588 ) @ SY1587 ) @ SY1589 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1589 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6118,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i,SV432: $i] :
( ( ! [SY1590: $i] :
( ~ ( ( SY1590 != SV432 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SV432 ) @ SV64 ) @ SY1590 )
= ( hAPP @ SV185 @ SY1590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6009]) ).
thf(6119,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6010]) ).
thf(6120,plain,
! [SV66: $i,SV187: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
| ( SV187 = SV66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6011]) ).
thf(6121,plain,
! [SV66: $i,SV187: $i] :
( ( ( SV187 != SV66 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6012]) ).
thf(6122,plain,
! [SV67: $i,SV188: $i,SV288: $i,SV370: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV188 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV67 ) )
| ( SV188 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6013]) ).
thf(6123,plain,
! [SV68: $i,SV189: $i,SV289: $i,SV371: $i,SV434: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV434 @ SV371 @ SV289 )
| ( ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6124,plain,
! [SV69: $i,SV190: $i,SV290: $i,SV372: $i,SV435: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV372 ) @ SV290 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SV435 ) @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6125,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ( ~ ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) )
| ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6016]) ).
thf(6126,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ( ~ ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) )
| ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6016]) ).
thf(6127,plain,
! [SV72: $i,SV192: $i,SV292: $i,SV373: $i,SV436: $i] :
( ( ! [SY1591: $i] :
( ( SY1591 != SV436 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SY1591 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6017]) ).
thf(6128,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i] :
( ( ! [SY1592: $i] :
~ ( ~ ( ( SY1592 != SV437 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SY1592 )
= SV73 ) )
| ~ ( ~ ( ( SY1592 != SV437 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SY1592 )
= ( hAPP @ SV193 @ SY1592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6018]) ).
thf(6129,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i] :
( ( ! [SY1593: $i,SY1594: $i,SY1595: $i,SY1596: $i,SY1597: $i,SY1598: $i] :
( ( ( hAPP @ SY1598 @ ( hAPP @ SY1597 @ SY1596 ) )
!= ( hAPP @ SY1595 @ ( hAPP @ SY1594 @ SY1593 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1598 ) @ SY1597 ) @ SY1596 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SY1595 ) @ SY1594 ) @ SY1593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6019]) ).
thf(6130,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
| ( SV295 = SV75 ) )
| ~ ( ( SV295 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6020]) ).
thf(6131,plain,
! [SV76: $i,SV196: $i,SV296: $i,SV377: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV196 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6021]) ).
thf(6132,plain,
! [SV77: $i,SV197: $i,SV297: $i,SV378: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV378 ) @ SV297 ) @ SV197 ) @ SV77 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV378 ) @ SV297 ) @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6022]) ).
thf(6133,plain,
! [SV78: $i,SV198: $i,SV298: $i,SV379: $i,SV439: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6134,plain,
! [SV79: $i,SV199: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
| ( SV199 = SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6024]) ).
thf(6135,plain,
! [SV79: $i,SV199: $i] :
( ( ( SV199 != SV79 )
| ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6025]) ).
thf(6136,plain,
! [SV80: $i,SV200: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
| ( SV200 = SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6026]) ).
thf(6137,plain,
! [SV80: $i,SV200: $i] :
( ( ( SV200 != SV80 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6027]) ).
thf(6138,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
| ~ ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6028]) ).
thf(6139,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
| ~ ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6029]) ).
thf(6140,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
| ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6030]) ).
thf(6141,plain,
! [SV301: $i,SV83: $i,SV203: $i] :
( ( ~ ( ~ ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6030]) ).
thf(6142,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i,SV441: $i] :
( ( ! [SY1599: $i,SY1600: $i] :
( ( SY1600 != SY1599 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SY1600 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SY1599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6031]) ).
thf(6143,plain,
! [SV85: $i,SV205: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
| ( SV205 = SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6032]) ).
thf(6144,plain,
! [SV85: $i,SV205: $i] :
( ( ( SV205 != SV85 )
| ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6033]) ).
thf(6145,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
| ~ ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6034]) ).
thf(6146,plain,
! [SV88: $i,SV208: $i,SV304: $i,SV384: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV384 @ SV304 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6036]) ).
thf(6147,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
| ( SV209 = SV89 ) )
| ~ ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6148,plain,
! [SV90: $i,SV210: $i,SV306: $i,SV386: $i,SV442: $i] :
( ( ! [SY1601: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1601 @ SV442 @ SV386 @ SV306 @ SV210 )
| ( ( hAPP @ SV306 @ ( hAPP @ SV386 @ SV90 ) )
= SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6038]) ).
thf(6149,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6039]) ).
thf(6150,plain,
! [SV92: $i,SV212: $i,SV308: $i,SV388: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) ) )
= $true )
| ( ( ~ ! [SY1532: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ SY1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ SY1532 ) @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6040]) ).
thf(6151,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6041]) ).
thf(6152,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i] :
( ( ! [SY1604: $i] :
~ ( ~ ( ( SY1604 != SV445 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SY1604 )
= SV94 ) )
| ~ ( ~ ( ( SY1604 != SV445 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SY1604 )
= ( hAPP @ SV214 @ SY1604 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6042]) ).
thf(6153,plain,
! [SV95: $i,SV215: $i,SV311: $i,SV391: $i] :
( ( ( SV391 != SV311 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6043]) ).
thf(6154,plain,
! [SV96: $i,SV216: $i,SV312: $i] :
( ( ( ~ ! [SY1401: $i] :
~ ( hBOOL @ ( hAPP @ SV312 @ SY1401 ) ) )
= $false )
| ( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(6155,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6045]) ).
thf(6156,plain,
! [SV313: $i,SV217: $i,SV97: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6045]) ).
thf(6157,plain,
! [SV98: $i,SV218: $i,SV314: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) ) )
= $true )
| ( ( ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6046]) ).
thf(6158,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6047]) ).
thf(6159,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i] :
( ( ! [SY1605: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1605 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1605 @ SV447 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
| ~ ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1605 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1605 @ SV447 ) @ SV220 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6048]) ).
thf(6160,plain,
! [SV101: $i,SV221: $i] :
( ( ( ( hAPP @ SV221 @ ( sK3_SY1184 @ SV101 @ SV221 ) )
= ( hAPP @ SV101 @ ( sK3_SY1184 @ SV101 @ SV221 ) ) )
= $false )
| ( ( SV221 = SV101 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6049]) ).
thf(6161,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i,SV448: $i] :
( ( ! [SY1606: $i] :
( ~ ( ( SY1606 != SV448 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SY1606 ) @ SV224 ) ) @ SV448 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV448 ) @ SV104 ) ) @ SY1606 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6052]) ).
thf(6162,plain,
! [SV105: $i,SV225: $i,SV318: $i,SV396: $i] :
( ( ( SV396 != SV318 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6053]) ).
thf(6163,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
| ~ ( ~ ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(6164,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
| ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ~ ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6055]) ).
thf(6165,plain,
! [SV108: $i,SV228: $i,SV321: $i,SV399: $i] :
( ( ( SV399 != SV321 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6056]) ).
thf(6166,plain,
! [SV109: $i,SV229: $i] :
( ( ( ! [SY1199: $i] :
~ ( hBOOL @ ( hAPP @ SV229 @ SY1199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6057]) ).
thf(6167,plain,
! [SV110: $i,SV230: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
| ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6058]) ).
thf(6168,plain,
! [SV230: $i,SV110: $i] :
( ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6059]) ).
thf(6169,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i,SV449: $i] :
( ( ! [SY1607: $i,SY1608: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1608 @ SY1607 @ SV449 @ SV400 @ SV322 )
| ~ ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6170,plain,
! [SV112: $i,SV232: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
| ( SV232 = SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6061]) ).
thf(6171,plain,
! [SV112: $i,SV232: $i] :
( ( ( SV232 != SV112 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6062]) ).
thf(6172,plain,
! [SV113: $i,SV233: $i,SV323: $i] :
( ( ( c_Predicate_Oreflp @ SV323 @ SV233 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV233 @ SV113 ) @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(6173,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i] :
( ( ! [SY1609: $i,SY1610: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1610 @ SY1609 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY1610 @ SY1609 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6064]) ).
thf(6174,plain,
! [SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK2_SY906 @ SV115 ) ) ) )
= $false )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6065]) ).
thf(6175,plain,
! [SV115: $i] :
( ( ( SV115
= ( sK2_SY906 @ SV115 ) )
= $false )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6065]) ).
thf(6176,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
| ~ ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(6177,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
| ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6067]) ).
thf(6178,plain,
! [SV326: $i,SV117: $i,SV236: $i] :
( ( ~ ( ~ ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6067]) ).
thf(6179,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
!= SV118 )
| ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6068]) ).
thf(6180,plain,
! [SV118: $i,SV327: $i,SV237: $i] :
( ( ~ ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6068]) ).
thf(6181,plain,
! [SV119: $i,SV238: $i,SV328: $i] :
( ( ( hBOOL @ ( hAPP @ SV328 @ SV238 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV328 @ ( c_Hilbert__Choice_OEps @ SV119 @ SV328 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(6182,plain,
! [SV120: $i,SV239: $i,SV329: $i,SV403: $i,SV451: $i] :
( ( ! [SY1613: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1613 ) @ SV451 ) @ SV403 )
!= SV329 )
| ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1613 ) @ SV403 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1613 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1613 ) @ SV329 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6070]) ).
thf(6183,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i] :
( ( ! [SY1614: $i,SY1615: $i,SY1616: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1616 @ SY1615 ) @ SY1614 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SY1614 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SY1616 @ SV452 @ SY1615 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6071]) ).
thf(6184,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6072]) ).
thf(6185,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6072]) ).
thf(6186,plain,
! [SV123: $i,SV242: $i,SV332: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV332 @ SV242 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV242 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6073]) ).
thf(6187,plain,
! [SV124: $i,SV243: $i,SV333: $i,SV405: $i,SV453: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV453 ) @ SV405 ) @ SV333 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV453 @ SV243 ) ) @ SV405 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6074]) ).
thf(6188,plain,
! [SV125: $i,SV244: $i,SV334: $i,SV406: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV406 @ SV334 @ SV244 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV334 @ SV125 ) @ SV125 )
= SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6189,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
| ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6076]) ).
thf(6190,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ( ~ ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6076]) ).
thf(6191,plain,
! [SV5: $i,SV129: $i,SV248: $i,SV337: $i,SV407: $i,SV454: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV454 @ SV407 @ SV337 @ SV248 ) @ SV129 ) @ SV5 )
= ( hAPP @ SV248 @ ( hAPP @ SV129 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6077]) ).
thf(6192,plain,
! [SV7: $i,SV131: $i,SV250: $i,SV339: $i,SV408: $i,SV455: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ SV339 ) @ SV250 ) @ SV131 ) ) @ SV250 ) @ SV7 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV455 @ SV408 ) @ SV339 ) @ SV250 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6078]) ).
thf(6193,plain,
! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i,SV456: $i] :
( ( ! [SY1617: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1617 @ SV456 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SY1617 @ SV410 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV456 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SY1617 @ SV456 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6080]) ).
thf(6194,plain,
! [SV10: $i,SV134: $i,SV253: $i,SV342: $i,SV411: $i,SV457: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV457 @ SV411 @ SV342 @ SV253 ) @ SV134 ) @ SV10 )
= ( hAPP @ SV253 @ ( hAPP @ SV134 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6081]) ).
thf(6195,plain,
! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i,SV458: $i] :
( ( ! [SY1618: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1618 @ SV458 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1618 @ SV343 @ SV458 ) @ SV254 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1618 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SV458 @ SV412 ) @ SV138 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6082]) ).
thf(6196,plain,
! [SV22: $i,SV146: $i,SV260: $i,SV348: $i,SV414: $i,SV459: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV459 @ SV414 @ SV348 ) @ SV260 ) @ SV146 ) @ SV22 )
= ( hAPP @ SV260 @ ( hAPP @ SV146 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6084]) ).
thf(6197,plain,
! [SV23: $i,SV147: $i,SV261: $i,SV349: $i,SV415: $i,SV460: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV460 @ SV415 @ SV349 ) @ SV261 ) @ SV147 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV261 @ SV23 ) @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6085]) ).
thf(6198,plain,
! [SV24: $i,SV148: $i,SV262: $i,SV350: $i,SV416: $i,SV461: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV461 @ SV416 @ SV350 ) @ SV262 ) @ SV148 ) @ SV24 )
= ( hAPP @ ( hAPP @ SV262 @ SV24 ) @ ( hAPP @ SV148 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6086]) ).
thf(6199,plain,
! [SV150: $i,SV28: $i] :
( ( ( hBOOL @ SV28 )
= $false )
| ( ( hBOOL @ SV150 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV150 ) @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6087]) ).
thf(6200,plain,
! [SV36: $i,SV158: $i] :
( ( ( hBOOL @ SV158 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV158 ) @ SV36 ) )
= $false )
| ( ( hBOOL @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6089]) ).
thf(6201,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ( ! [SY1283: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ SY1283 ) @ SV37 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(6202,plain,
! [SV38: $i,SV160: $i,SV264: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV160 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV38 ) )
| ( SV38 = SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(6203,plain,
! [SV39: $i,SV161: $i,SV265: $i,SV352: $i,SV417: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV417 @ SV352 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6092]) ).
thf(6204,plain,
! [SV40: $i,SV162: $i,SV266: $i,SV353: $i,SV418: $i,SV462: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
| ~ ( ( SV353 != SV162 )
| ( SV266 != SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6093]) ).
thf(6205,plain,
! [SV41: $i,SV463: $i,SV163: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV163 @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6094]) ).
thf(6206,plain,
! [SV44: $i,SV165: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true )
| ( ( SV165 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6207,plain,
! [SV44: $i,SV165: $i] :
( ( ( SV165 != SV44 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6096]) ).
thf(6208,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) )
| ~ ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6097]) ).
thf(6209,plain,
! [SV46: $i,SV167: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP @ SV269 @ SV167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV269 @ SV46 ) ) @ SV167 ) @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6098]) ).
thf(6210,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
| ( SV168 = SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6099]) ).
thf(6211,plain,
! [SV270: $i,SV47: $i,SV168: $i] :
( ( ( SV168 != SV47 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6100]) ).
thf(6212,plain,
! [SV48: $i,SV169: $i,SV271: $i,SV355: $i,SV420: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6213,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i] :
( ( ! [SY1619: $i,SY1620: $i,SY1621: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1621 @ SY1620 @ SY1619 @ SV464 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SY1620 @ SY1619 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6102]) ).
thf(6214,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6103]) ).
thf(6215,plain,
! [SV51: $i,SV172: $i,SV274: $i,SV358: $i] :
( ( ( SV358 = SV274 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV358 ) @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6104]) ).
thf(6216,plain,
! [SV52: $i,SV173: $i,SV275: $i,SV359: $i,SV423: $i] :
( ( ( ( hAPP @ SV423 @ SV359 )
!= SV275 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SV423 ) @ SV359 ) @ SV275 )
= SV423 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6105]) ).
thf(6217,plain,
! [SV53: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6106]) ).
thf(6218,plain,
! [SV53: $i,SV174: $i] :
( ( ( ~ ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6107]) ).
thf(6219,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i,SV465: $i] :
( ( ! [SY1622: $i] :
( ~ ( ( SY1622 != SV465 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SY1622 ) @ SV175 ) ) @ SV465 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV465 ) @ SV54 ) ) @ SY1622 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6108]) ).
thf(6220,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i,SV466: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1624 @ SY1623 @ SV466 @ SV425 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SY1623 @ SV466 @ SV176 ) @ SV55 ) )
| ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6109]) ).
thf(6221,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
| ( SV178 = SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6110]) ).
thf(6222,plain,
! [SV279: $i,SV57: $i,SV178: $i] :
( ( ( SV178 != SV57 )
| ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6111]) ).
thf(6223,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i,SV426: $i,SV467: $i] :
( ( ! [SY1626: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1626 @ SV467 @ SV426 @ SV362 ) @ SV280 )
!= SV179 )
| ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6112]) ).
thf(6224,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i] :
( ( ! [SY1627: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1627 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1627 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1627 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1627 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6113]) ).
thf(6225,plain,
! [SV60: $i,SV181: $i,SV282: $i,SV364: $i,SV428: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV428 @ SV364 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6114]) ).
thf(6226,plain,
! [SV61: $i,SV182: $i,SV283: $i,SV365: $i,SV429: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV429 @ SV365 ) @ SV283 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SV429 ) @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6115]) ).
thf(6227,plain,
! [SV62: $i,SV183: $i,SV284: $i,SV366: $i,SV430: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV430 @ SV366 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV430 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6116]) ).
thf(6228,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i,SV469: $i] :
( ( ! [SY1628: $i,SY1629: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1629 ) @ SY1628 ) @ SV469 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1589: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1629 ) @ SY1628 ) @ SY1589 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1589 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6117]) ).
thf(6229,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i,SV432: $i,SV470: $i] :
( ( ~ ( ( SV470 != SV432 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SV432 ) @ SV64 ) @ SV470 )
= ( hAPP @ SV185 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6118]) ).
thf(6230,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6231,plain,
! [SV66: $i,SV187: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
= $true )
| ( ( SV187 = SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6120]) ).
thf(6232,plain,
! [SV66: $i,SV187: $i] :
( ( ( SV187 != SV66 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6121]) ).
thf(6233,plain,
! [SV67: $i,SV188: $i,SV288: $i,SV370: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV188 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV67 ) )
| ( SV188 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6122]) ).
thf(6234,plain,
! [SV68: $i,SV189: $i,SV289: $i,SV371: $i,SV434: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV434 @ SV371 @ SV289 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6123]) ).
thf(6235,plain,
! [SV69: $i,SV190: $i,SV290: $i,SV372: $i,SV435: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV372 ) @ SV290 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SV435 ) @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6124]) ).
thf(6236,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) )
| ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6125]) ).
thf(6237,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ~ ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) )
| ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6126]) ).
thf(6238,plain,
! [SV72: $i,SV192: $i,SV292: $i,SV373: $i,SV436: $i,SV471: $i] :
( ( ( SV471 != SV436 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV471 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6127]) ).
thf(6239,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ~ ( ~ ( ( SV472 != SV437 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 ) )
| ~ ( ~ ( ( SV472 != SV437 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6128]) ).
thf(6240,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i,SY1634: $i,SY1635: $i] :
( ( ( hAPP @ SY1635 @ ( hAPP @ SY1634 @ SY1633 ) )
!= ( hAPP @ SY1632 @ ( hAPP @ SY1631 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1635 ) @ SY1634 ) @ SY1633 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SY1632 ) @ SY1631 ) @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6129]) ).
thf(6241,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
| ( SV295 = SV75 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6130]) ).
thf(6242,plain,
! [SV195: $i,SV376: $i,SV75: $i,SV295: $i] :
( ( ~ ( ( SV295 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6130]) ).
thf(6243,plain,
! [SV76: $i,SV196: $i,SV296: $i,SV377: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV196 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6131]) ).
thf(6244,plain,
! [SV77: $i,SV197: $i,SV297: $i,SV378: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV378 ) @ SV297 ) @ SV197 ) @ SV77 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV378 ) @ SV297 ) @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6132]) ).
thf(6245,plain,
! [SV78: $i,SV198: $i,SV298: $i,SV379: $i,SV439: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6133]) ).
thf(6246,plain,
! [SV79: $i,SV199: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
!= ( hAPP @ c_Nat_OSuc @ SV79 ) )
= $true )
| ( ( SV199 = SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6247,plain,
! [SV79: $i,SV199: $i] :
( ( ( SV199 != SV79 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6135]) ).
thf(6248,plain,
! [SV80: $i,SV200: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
!= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
= $true )
| ( ( SV200 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6136]) ).
thf(6249,plain,
! [SV80: $i,SV200: $i] :
( ( ( SV200 != SV80 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6137]) ).
thf(6250,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
| ~ ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6138]) ).
thf(6251,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6139]) ).
thf(6252,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ~ ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6139]) ).
thf(6253,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
| ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6140]) ).
thf(6254,plain,
! [SV301: $i,SV83: $i,SV203: $i] :
( ( ~ ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6141]) ).
thf(6255,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i,SV441: $i,SV474: $i] :
( ( ! [SY1636: $i] :
( ( SY1636 != SV474 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SY1636 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6142]) ).
thf(6256,plain,
! [SV85: $i,SV205: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
= $true )
| ( ( SV205 = SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6143]) ).
thf(6257,plain,
! [SV85: $i,SV205: $i] :
( ( ( SV205 != SV85 )
= $true )
| ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6144]) ).
thf(6258,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6145]) ).
thf(6259,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ~ ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6145]) ).
thf(6260,plain,
! [SV88: $i,SV208: $i,SV304: $i,SV384: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV384 @ SV304 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6261,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
| ( SV209 = SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6147]) ).
thf(6262,plain,
! [SV305: $i,SV385: $i,SV89: $i,SV209: $i] :
( ( ~ ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6147]) ).
thf(6263,plain,
! [SV90: $i,SV210: $i,SV306: $i,SV386: $i,SV442: $i,SV475: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV475 @ SV442 @ SV386 @ SV306 @ SV210 )
| ( ( hAPP @ SV306 @ ( hAPP @ SV386 @ SV90 ) )
= SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6148]) ).
thf(6264,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
| ~ ( ~ ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6149]) ).
thf(6265,plain,
! [SV92: $i,SV212: $i,SV308: $i,SV388: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false )
| ( ( ~ ! [SY1532: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ SY1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ SY1532 ) @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6150]) ).
thf(6266,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(6267,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ~ ( ~ ( ( SV476 != SV445 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 ) )
| ~ ( ~ ( ( SV476 != SV445 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6152]) ).
thf(6268,plain,
! [SV95: $i,SV215: $i,SV311: $i,SV391: $i] :
( ( ( SV391 = SV311 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6153]) ).
thf(6269,plain,
! [SV96: $i,SV216: $i,SV312: $i] :
( ( ( ! [SY1401: $i] :
~ ( hBOOL @ ( hAPP @ SV312 @ SY1401 ) ) )
= $true )
| ( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6154]) ).
thf(6270,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6155]) ).
thf(6271,plain,
! [SV313: $i,SV217: $i,SV97: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6156]) ).
thf(6272,plain,
! [SV98: $i,SV218: $i,SV314: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false )
| ( ( ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6157]) ).
thf(6273,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6158]) ).
thf(6274,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
| ~ ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6159]) ).
thf(6275,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i,SV448: $i,SV478: $i] :
( ( ~ ( ( SV478 != SV448 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV478 ) @ SV224 ) ) @ SV448 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV448 ) @ SV104 ) ) @ SV478 ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6161]) ).
thf(6276,plain,
! [SV105: $i,SV225: $i,SV318: $i,SV396: $i] :
( ( ( SV396 = SV318 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6162]) ).
thf(6277,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6163]) ).
thf(6278,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ~ ( ~ ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6163]) ).
thf(6279,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
| ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6164]) ).
thf(6280,plain,
! [SV398: $i,SV227: $i,SV107: $i,SV320: $i] :
( ( ~ ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6164]) ).
thf(6281,plain,
! [SV108: $i,SV228: $i,SV321: $i,SV399: $i] :
( ( ( SV399 = SV321 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6165]) ).
thf(6282,plain,
! [SV109: $i,SV479: $i,SV229: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV229 @ SV479 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6166]) ).
thf(6283,plain,
! [SV110: $i,SV230: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 ) )
= $true )
| ( ( ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6167]) ).
thf(6284,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6168]) ).
thf(6285,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i,SV449: $i,SV480: $i] :
( ( ! [SY1637: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1637 @ SV480 @ SV449 @ SV400 @ SV322 )
| ~ ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6169]) ).
thf(6286,plain,
! [SV112: $i,SV232: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
= $true )
| ( ( SV232 = SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6170]) ).
thf(6287,plain,
! [SV112: $i,SV232: $i] :
( ( ( SV232 != SV112 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6171]) ).
thf(6288,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i] :
( ( ! [SY1638: $i] :
~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SY1638 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SY1638 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6173]) ).
thf(6289,plain,
! [SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ ( sK2_SY906 @ SV115 ) ) )
= $true )
| ( ( SV115 = v_s_H )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6174]) ).
thf(6290,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6176]) ).
thf(6291,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ~ ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6176]) ).
thf(6292,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
| ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6177]) ).
thf(6293,plain,
! [SV326: $i,SV117: $i,SV236: $i] :
( ( ~ ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6178]) ).
thf(6294,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
!= SV118 )
| ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6179]) ).
thf(6295,plain,
! [SV118: $i,SV327: $i,SV237: $i] :
( ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
| ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6180]) ).
thf(6296,plain,
! [SV120: $i,SV239: $i,SV329: $i,SV403: $i,SV451: $i,SV482: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV403 )
!= SV329 )
| ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV403 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV329 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6182]) ).
thf(6297,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i,SV483: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1642 @ SY1641 ) @ SV483 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SY1642 @ SV452 @ SY1641 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6183]) ).
thf(6298,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6184]) ).
thf(6299,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6185]) ).
thf(6300,plain,
! [SV124: $i,SV243: $i,SV333: $i,SV405: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV453 ) @ SV405 ) @ SV333 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV453 @ SV243 ) ) @ SV405 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6187]) ).
thf(6301,plain,
! [SV125: $i,SV244: $i,SV334: $i,SV406: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV406 @ SV334 @ SV244 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV334 @ SV125 ) @ SV125 )
= SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6188]) ).
thf(6302,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
| ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6189]) ).
thf(6303,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ~ ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6190]) ).
thf(6304,plain,
! [SV9: $i,SV133: $i,SV252: $i,SV341: $i,SV410: $i,SV456: $i,SV484: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV484 @ SV456 @ SV410 @ SV341 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV484 @ SV410 @ SV133 ) @ SV9 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV252 @ SV456 @ SV410 @ ( hAPP @ ( c_Fun_Ocomp @ SV484 @ SV456 @ SV252 @ SV341 ) @ SV133 ) ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6193]) ).
thf(6305,plain,
! [SV14: $i,SV138: $i,SV254: $i,SV343: $i,SV412: $i,SV458: $i,SV485: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV458 @ SV412 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV343 @ SV458 ) @ SV254 ) @ SV138 ) ) @ SV14 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV485 @ SV343 @ SV412 ) @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV343 @ SV458 @ SV412 ) @ SV138 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6195]) ).
thf(6306,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ ( sK4_SY1283 @ SV37 @ SV159 @ SV263 ) ) @ SV37 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6201]) ).
thf(6307,plain,
! [SV160: $i,SV38: $i,SV264: $i,SV351: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV38 ) ) )
= $true )
| ( ( SV38 = SV160 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6202]) ).
thf(6308,plain,
! [SV39: $i,SV161: $i,SV265: $i,SV352: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6203]) ).
thf(6309,plain,
! [SV40: $i,SV162: $i,SV266: $i,SV353: $i,SV418: $i,SV462: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $true )
| ( ( ~ ( ( SV353 != SV162 )
| ( SV266 != SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6204]) ).
thf(6310,plain,
! [SV41: $i,SV463: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV463 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV163 @ ( c_Hilbert__Choice_OEps @ SV41 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6205]) ).
thf(6311,plain,
! [SV44: $i,SV165: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $false )
| ( ( SV165 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6206]) ).
thf(6312,plain,
! [SV44: $i,SV165: $i] :
( ( ( SV165 = SV44 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV165 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(6313,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6208]) ).
thf(6314,plain,
! [SV354: $i,SV419: $i,SV45: $i,SV166: $i,SV268: $i] :
( ( ~ ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6208]) ).
thf(6315,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
= $true )
| ( ( SV168 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6210]) ).
thf(6316,plain,
! [SV270: $i,SV47: $i,SV168: $i] :
( ( ( SV168 != SV47 )
= $true )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6211]) ).
thf(6317,plain,
! [SV48: $i,SV169: $i,SV271: $i,SV355: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6212]) ).
thf(6318,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i,SV486: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1644 @ SY1643 @ SV486 @ SV464 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SY1643 @ SV486 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6213]) ).
thf(6319,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6214]) ).
thf(6320,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6214]) ).
thf(6321,plain,
! [SV358: $i,SV51: $i,SV274: $i,SV172: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV358 ) @ SV51 ) )
= $true )
| ( ( SV358 = SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6215]) ).
thf(6322,plain,
! [SV52: $i,SV173: $i,SV275: $i,SV359: $i,SV423: $i] :
( ( ( ( hAPP @ SV423 @ SV359 )
= SV275 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV173 @ SV52 ) @ SV423 ) @ SV359 ) @ SV275 )
= SV423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6323,plain,
! [SV53: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $false )
| ( ( ~ ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6217]) ).
thf(6324,plain,
! [SV53: $i,SV174: $i] :
( ( ( ~ ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6218]) ).
thf(6325,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i,SV465: $i,SV487: $i] :
( ( ~ ( ( SV487 != SV465 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV487 ) @ SV175 ) ) @ SV465 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV465 ) @ SV54 ) ) @ SV487 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6219]) ).
thf(6326,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i,SV466: $i,SV488: $i] :
( ( ! [SY1645: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1645 @ SV488 @ SV466 @ SV425 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV488 @ SV466 @ SV176 ) @ SV55 ) )
| ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6220]) ).
thf(6327,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
!= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
= $true )
| ( ( SV178 = SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6221]) ).
thf(6328,plain,
! [SV279: $i,SV57: $i,SV178: $i] :
( ( ( SV178 != SV57 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6222]) ).
thf(6329,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i,SV426: $i,SV467: $i,SV489: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV467 @ SV426 @ SV362 ) @ SV280 )
!= SV179 )
| ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6223]) ).
thf(6330,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6224]) ).
thf(6331,plain,
! [SV60: $i,SV181: $i,SV282: $i,SV364: $i,SV428: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV428 @ SV364 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6225]) ).
thf(6332,plain,
! [SV61: $i,SV182: $i,SV283: $i,SV365: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV429 @ SV365 ) @ SV283 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV182 @ SV61 @ SV429 ) @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6226]) ).
thf(6333,plain,
! [SV62: $i,SV183: $i,SV284: $i,SV366: $i,SV430: $i] :
( ( ( hBOOL @ ( hAPP @ SV430 @ SV366 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV430 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6227]) ).
thf(6334,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i,SV469: $i,SV491: $i] :
( ( ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1647 ) @ SV491 ) @ SV469 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1648: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SY1647 ) @ SV491 ) @ SY1648 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1648 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6228]) ).
thf(6335,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i,SV432: $i,SV470: $i] :
( ( ( ~ ( ( SV470 != SV432 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SV432 ) @ SV64 ) @ SV470 )
= ( hAPP @ SV185 @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6229]) ).
thf(6336,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6230]) ).
thf(6337,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ~ ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6230]) ).
thf(6338,plain,
! [SV66: $i,SV187: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
= $false )
| ( ( SV187 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6231]) ).
thf(6339,plain,
! [SV66: $i,SV187: $i] :
( ( ( SV187 = SV66 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV187 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6232]) ).
thf(6340,plain,
! [SV188: $i,SV67: $i,SV288: $i,SV370: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV67 ) ) )
= $true )
| ( ( SV188 = SV67 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6233]) ).
thf(6341,plain,
! [SV68: $i,SV189: $i,SV289: $i,SV371: $i,SV434: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV434 @ SV371 @ SV289 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ SV289 @ SV189 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6234]) ).
thf(6342,plain,
! [SV69: $i,SV190: $i,SV290: $i,SV372: $i,SV435: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV435 @ SV372 ) @ SV290 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV190 @ SV69 @ SV435 ) @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6235]) ).
thf(6343,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( ~ ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) ) )
= $true )
| ( ( ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6236]) ).
thf(6344,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( ~ ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) ) )
= $true )
| ( ( ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6237]) ).
thf(6345,plain,
! [SV72: $i,SV192: $i,SV292: $i,SV373: $i,SV436: $i,SV471: $i] :
( ( ( SV471 != SV436 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV471 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6238]) ).
thf(6346,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ~ ( ( SV472 != SV437 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 ) )
| ~ ( ~ ( ( SV472 != SV437 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6239]) ).
thf(6347,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i] :
( ( ! [SY1649: $i,SY1650: $i,SY1651: $i,SY1652: $i] :
( ( ( hAPP @ SY1652 @ ( hAPP @ SY1651 @ SY1650 ) )
!= ( hAPP @ SY1649 @ ( hAPP @ SV492 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1652 ) @ SY1651 ) @ SY1650 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SY1649 ) @ SV492 ) @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6240]) ).
thf(6348,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
| ( SV295 = SV75 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6241]) ).
thf(6349,plain,
! [SV195: $i,SV376: $i,SV75: $i,SV295: $i] :
( ( ( SV295 != SV75 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6242]) ).
thf(6350,plain,
! [SV377: $i,SV196: $i,SV76: $i,SV296: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV76 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6243]) ).
thf(6351,plain,
! [SV78: $i,SV198: $i,SV298: $i,SV379: $i,SV439: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6245]) ).
thf(6352,plain,
! [SV79: $i,SV199: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) )
= $false )
| ( ( SV199 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(6353,plain,
! [SV79: $i,SV199: $i] :
( ( ( SV199 = SV79 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV199 )
= ( hAPP @ c_Nat_OSuc @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6247]) ).
thf(6354,plain,
! [SV80: $i,SV200: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
= $false )
| ( ( SV200 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(6355,plain,
! [SV80: $i,SV200: $i] :
( ( ( SV200 = SV80 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV200 )
= ( hAPP @ c_Int_ORep__Integ @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6249]) ).
thf(6356,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6250]) ).
thf(6357,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ~ ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6250]) ).
thf(6358,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
| ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6251]) ).
thf(6359,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6252]) ).
thf(6360,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) ) )
= $true )
| ( ( ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6253]) ).
thf(6361,plain,
! [SV301: $i,SV83: $i,SV203: $i] :
( ( ( ~ ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6254]) ).
thf(6362,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i,SV441: $i,SV474: $i,SV493: $i] :
( ( ( SV493 != SV474 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV493 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6255]) ).
thf(6363,plain,
! [SV85: $i,SV205: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
= $false )
| ( ( SV205 = SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6256]) ).
thf(6364,plain,
! [SV85: $i,SV205: $i] :
( ( ( SV205 = SV85 )
= $false )
| ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV205 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6365,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
| ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6258]) ).
thf(6366,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6259]) ).
thf(6367,plain,
! [SV384: $i,SV88: $i,SV208: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV384 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6260]) ).
thf(6368,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
| ( SV209 = SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6261]) ).
thf(6369,plain,
! [SV305: $i,SV385: $i,SV89: $i,SV209: $i] :
( ( ( SV209 != SV89 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6262]) ).
thf(6370,plain,
! [SV90: $i,SV210: $i,SV306: $i,SV386: $i,SV442: $i,SV475: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV475 @ SV442 @ SV386 @ SV306 @ SV210 ) )
= $true )
| ( ( ( hAPP @ SV306 @ ( hAPP @ SV386 @ SV90 ) )
= SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6263]) ).
thf(6371,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6264]) ).
thf(6372,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ~ ( ~ ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6264]) ).
thf(6373,plain,
! [SV92: $i,SV308: $i,SV212: $i,SV388: $i] :
( ( ( ! [SY1532: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ SY1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ SY1532 ) @ SV92 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(6374,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6266]) ).
thf(6375,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6266]) ).
thf(6376,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ~ ( ( SV476 != SV445 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 ) )
| ~ ( ~ ( ( SV476 != SV445 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6267]) ).
thf(6377,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6268]) ).
thf(6378,plain,
! [SV96: $i,SV216: $i,SV494: $i,SV312: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV312 @ SV494 ) ) )
= $true )
| ( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6269]) ).
thf(6379,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6270]) ).
thf(6380,plain,
! [SV313: $i,SV217: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6271]) ).
thf(6381,plain,
! [SV314: $i,SV392: $i,SV218: $i,SV98: $i] :
( ( ( ~ ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6272]) ).
thf(6382,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6273]) ).
thf(6383,plain,
! [SV393: $i,SV446: $i,SV99: $i,SV315: $i,SV219: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6273]) ).
thf(6384,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
| ~ ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6274]) ).
thf(6385,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i,SV448: $i,SV478: $i] :
( ( ( ~ ( ( SV478 != SV448 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV478 ) @ SV224 ) ) @ SV448 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV448 ) @ SV104 ) ) @ SV478 ) @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6275]) ).
thf(6386,plain,
! [SV318: $i,SV396: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) ) )
= $false )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6276]) ).
thf(6387,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
| ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6277]) ).
thf(6388,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ~ ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6278]) ).
thf(6389,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
| ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6279]) ).
thf(6390,plain,
! [SV398: $i,SV227: $i,SV107: $i,SV320: $i] :
( ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6280]) ).
thf(6391,plain,
! [SV321: $i,SV108: $i,SV399: $i,SV228: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) ) )
= $false )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6392,plain,
! [SV109: $i,SV479: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ SV479 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( c_Hilbert__Choice_OEps @ SV109 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6393,plain,
! [SV110: $i,SV230: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false )
| ( ( ! [SY885: $i,SY886: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) )
| ( ( hAPP @ SV110 @ SY885 )
= ( hAPP @ SV110 @ SY886 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY885 )
!= ( hAPP @ SV110 @ SY886 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY885 ) @ SY886 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6283]) ).
thf(6394,plain,
! [SV230: $i,SV110: $i] :
( ( ( ! [SY887: $i,SY888: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) )
| ( ( hAPP @ SV110 @ SY887 )
= ( hAPP @ SV110 @ SY888 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY887 )
!= ( hAPP @ SV110 @ SY888 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY887 ) @ SY888 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6284]) ).
thf(6395,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i,SV449: $i,SV480: $i,SV495: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
| ~ ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6285]) ).
thf(6396,plain,
! [SV112: $i,SV232: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
= $false )
| ( ( SV232 = SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6286]) ).
thf(6397,plain,
! [SV112: $i,SV232: $i] :
( ( ( SV232 = SV112 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV232 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(6398,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ~ ( ~ ( ~ ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6288]) ).
thf(6399,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
| ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6290]) ).
thf(6400,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6291]) ).
thf(6401,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6292]) ).
thf(6402,plain,
! [SV326: $i,SV117: $i,SV236: $i] :
( ( ( ~ ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6293]) ).
thf(6403,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
!= SV118 )
= $true )
| ( ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6294]) ).
thf(6404,plain,
! [SV118: $i,SV327: $i,SV237: $i] :
( ( ( SV237
!= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6295]) ).
thf(6405,plain,
! [SV120: $i,SV239: $i,SV329: $i,SV403: $i,SV451: $i,SV482: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV403 )
!= SV329 )
= $true )
| ( ( ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV403 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV329 ) @ SV120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6296]) ).
thf(6406,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i,SV483: $i,SV497: $i] :
( ( ! [SY1655: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1655 @ SV497 ) @ SV483 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SY1655 @ SV452 @ SV497 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6297]) ).
thf(6407,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6298]) ).
thf(6408,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6299]) ).
thf(6409,plain,
! [SV124: $i,SV243: $i,SV333: $i,SV405: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV453 ) @ SV405 ) @ SV333 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV453 @ SV243 ) ) @ SV405 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6300]) ).
thf(6410,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) ) )
= $true )
| ( ( ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6302]) ).
thf(6411,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ~ ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6303]) ).
thf(6412,plain,
! [SV37: $i,SV159: $i,SV263: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV263 ) @ SV159 ) @ ( sK4_SY1283 @ SV37 @ SV159 @ SV263 ) ) @ SV37 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV263 ) @ SV159 ) @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6306]) ).
thf(6413,plain,
! [SV160: $i,SV38: $i,SV264: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV38 ) )
= $false )
| ( ( SV38 = SV160 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV351 ) @ SV264 ) @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6307]) ).
thf(6414,plain,
! [SV39: $i,SV417: $i,SV161: $i,SV352: $i,SV265: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6308]) ).
thf(6415,plain,
! [SV40: $i,SV162: $i,SV266: $i,SV353: $i,SV418: $i,SV462: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false )
| ( ( ~ ( ( SV353 != SV162 )
| ( SV266 != SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(6416,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
| ( ( hAPP @ SV268 @ SV166 )
= SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6313]) ).
thf(6417,plain,
! [SV354: $i,SV419: $i,SV45: $i,SV166: $i,SV268: $i] :
( ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6314]) ).
thf(6418,plain,
! [SV47: $i,SV168: $i,SV270: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
= $false )
| ( ( SV168 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(6419,plain,
! [SV270: $i,SV47: $i,SV168: $i] :
( ( ( SV168 = SV47 )
= $false )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV168 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV270 ) @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6316]) ).
thf(6420,plain,
! [SV271: $i,SV48: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6317]) ).
thf(6421,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i,SV486: $i,SV498: $i] :
( ( ! [SY1656: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1656 @ SV498 @ SV486 @ SV464 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SV498 @ SV486 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6318]) ).
thf(6422,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6319]) ).
thf(6423,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6320]) ).
thf(6424,plain,
! [SV358: $i,SV51: $i,SV274: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV274 ) @ SV51 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV172 ) @ SV358 ) @ SV51 ) )
= $true )
| ( ( SV358 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6321]) ).
thf(6425,plain,
! [SV53: $i,SV174: $i] :
( ( ( ! [SY1037: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1037 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6323]) ).
thf(6426,plain,
! [SV53: $i,SV174: $i] :
( ( ( ! [SY1038: $i] :
~ ( hBOOL @ ( hAPP @ SV174 @ SY1038 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6324]) ).
thf(6427,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i,SV465: $i,SV487: $i] :
( ( ( ~ ( ( SV487 != SV465 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV487 ) @ SV175 ) ) @ SV465 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV465 ) @ SV54 ) ) @ SV487 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6325]) ).
thf(6428,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i,SV466: $i,SV488: $i,SV499: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV499 @ SV488 @ SV466 @ SV425 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV488 @ SV466 @ SV176 ) @ SV55 ) )
| ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6326]) ).
thf(6429,plain,
! [SV57: $i,SV178: $i,SV279: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
= $false )
| ( ( SV178 = SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6327]) ).
thf(6430,plain,
! [SV279: $i,SV57: $i,SV178: $i] :
( ( ( SV178 = SV57 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV279 ) @ SV178 )
= ( hAPP @ ( c_List_Orev @ SV279 ) @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6328]) ).
thf(6431,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i,SV426: $i,SV467: $i,SV489: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV467 @ SV426 @ SV362 ) @ SV280 )
!= SV179 )
= $true )
| ( ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6329]) ).
thf(6432,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6330]) ).
thf(6433,plain,
! [SV60: $i,SV181: $i,SV282: $i,SV364: $i,SV428: $i] :
( ( ( hBOOL @ ( hAPP @ SV428 @ SV364 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6331]) ).
thf(6434,plain,
! [SV62: $i,SV430: $i,SV183: $i,SV366: $i,SV284: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV430 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV430 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6333]) ).
thf(6435,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6334]) ).
thf(6436,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i,SV432: $i,SV470: $i] :
( ( ( SV470 != SV432 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SV432 ) @ SV64 ) @ SV470 )
= ( hAPP @ SV185 @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6335]) ).
thf(6437,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6336]) ).
thf(6438,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6337]) ).
thf(6439,plain,
! [SV188: $i,SV67: $i,SV288: $i,SV370: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV67 ) )
= $false )
| ( ( SV188 = SV67 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV370 @ SV288 ) @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6340]) ).
thf(6440,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( ! [SY1345: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1345 ) ) )
= $false )
| ( ( ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6343]) ).
thf(6441,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( ! [SY1348: $i,SY1349: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1348 ) @ SY1349 ) ) ) )
= $false )
| ( ( ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(6442,plain,
! [SV72: $i,SV192: $i,SV292: $i,SV373: $i,SV436: $i,SV471: $i] :
( ( ( SV471 = SV436 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV471 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV373 @ SV292 @ SV192 ) @ SV72 ) @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6345]) ).
thf(6443,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ~ ( ( SV472 != SV437 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6346]) ).
thf(6444,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ~ ( ~ ( ( SV472 != SV437 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6346]) ).
thf(6445,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i] :
( ( ! [SY1659: $i,SY1660: $i,SY1661: $i] :
( ( ( hAPP @ SY1661 @ ( hAPP @ SY1660 @ SY1659 ) )
!= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1661 ) @ SY1660 ) @ SY1659 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6347]) ).
thf(6446,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
= $true )
| ( ( SV295 = SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6348]) ).
thf(6447,plain,
! [SV195: $i,SV376: $i,SV75: $i,SV295: $i] :
( ( ( SV295 != SV75 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6349]) ).
thf(6448,plain,
! [SV377: $i,SV196: $i,SV76: $i,SV296: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV296 @ SV76 ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV76 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV377 @ SV296 ) @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6350]) ).
thf(6449,plain,
! [SV439: $i,SV78: $i,SV198: $i,SV298: $i,SV379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6351]) ).
thf(6450,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
| ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6356]) ).
thf(6451,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6357]) ).
thf(6452,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) ) )
= $true )
| ( ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6358]) ).
thf(6453,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ~ ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6359]) ).
thf(6454,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $false )
| ( ( ! [SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1375 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1375 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6360]) ).
thf(6455,plain,
! [SV301: $i,SV83: $i,SV203: $i] :
( ( ( ! [SY1376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SY1376 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SY1376 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6361]) ).
thf(6456,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i,SV441: $i,SV474: $i,SV493: $i] :
( ( ( SV493 != SV474 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV493 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6457,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) ) )
= $true )
| ( ( ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6365]) ).
thf(6458,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ( ~ ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6366]) ).
thf(6459,plain,
! [SV384: $i,SV88: $i,SV208: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV208 ) @ SV88 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV304 @ SV88 ) @ SV208 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV384 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6367]) ).
thf(6460,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
= $true )
| ( ( SV209 = SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6368]) ).
thf(6461,plain,
! [SV305: $i,SV385: $i,SV89: $i,SV209: $i] :
( ( ( SV209 != SV89 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6369]) ).
thf(6462,plain,
! [SV90: $i,SV210: $i,SV306: $i,SV386: $i,SV442: $i,SV475: $i] :
( ( ( c_Typedef_Otype__definition @ SV475 @ SV442 @ SV386 @ SV306 @ SV210 )
= $false )
| ( ( ( hAPP @ SV306 @ ( hAPP @ SV386 @ SV90 ) )
= SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6370]) ).
thf(6463,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
| ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6371]) ).
thf(6464,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ~ ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6372]) ).
thf(6465,plain,
! [SV308: $i,SV92: $i,SV212: $i,SV388: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) @ SV92 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6373]) ).
thf(6466,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6374]) ).
thf(6467,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6375]) ).
thf(6468,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ~ ( ( SV476 != SV445 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6376]) ).
thf(6469,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ~ ( ~ ( ( SV476 != SV445 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6376]) ).
thf(6470,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6377]) ).
thf(6471,plain,
! [SV96: $i,SV216: $i,SV494: $i,SV312: $i] :
( ( ( hBOOL @ ( hAPP @ SV312 @ SV494 ) )
= $false )
| ( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
| ( hBOOL @ ( hAPP @ SV312 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6378]) ).
thf(6472,plain,
! [SV97: $i,SV217: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6379]) ).
thf(6473,plain,
! [SV313: $i,SV217: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ SV217 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV313 ) @ SV217 ) @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6380]) ).
thf(6474,plain,
! [SV314: $i,SV392: $i,SV218: $i,SV98: $i] :
( ( ( ( SV98 != SV218 )
| ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6381]) ).
thf(6475,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
| ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6382]) ).
thf(6476,plain,
! [SV393: $i,SV446: $i,SV99: $i,SV315: $i,SV219: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6383]) ).
thf(6477,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6384]) ).
thf(6478,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ~ ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6384]) ).
thf(6479,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i,SV448: $i,SV478: $i] :
( ( ( SV478 != SV448 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV478 ) @ SV224 ) ) @ SV448 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV448 ) @ SV104 ) ) @ SV478 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6385]) ).
thf(6480,plain,
! [SV318: $i,SV396: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) ) )
= $false )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6386]) ).
thf(6481,plain,
! [SV396: $i,SV318: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) ) )
= $false )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6386]) ).
thf(6482,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) ) )
= $true )
| ( ( ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6387]) ).
thf(6483,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ( ~ ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6388]) ).
thf(6484,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) ) )
= $true )
| ( ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6389]) ).
thf(6485,plain,
! [SV398: $i,SV227: $i,SV107: $i,SV320: $i] :
( ( ( ~ ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6390]) ).
thf(6486,plain,
! [SV321: $i,SV108: $i,SV399: $i,SV228: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) ) )
= $false )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6391]) ).
thf(6487,plain,
! [SV399: $i,SV108: $i,SV321: $i,SV228: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) ) )
= $false )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6391]) ).
thf(6488,plain,
! [SV230: $i,SV502: $i,SV110: $i] :
( ( ( ! [SY1662: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SY1662 ) )
| ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SY1662 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SY1662 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SY1662 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6393]) ).
thf(6489,plain,
! [SV230: $i,SV110: $i] :
( ( ( ! [SY1663: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ SY1663 ) )
| ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ SY1663 ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ SY1663 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ SY1663 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6394]) ).
thf(6490,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i,SV449: $i,SV480: $i,SV495: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6395]) ).
thf(6491,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ~ ( ~ ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
| ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6398]) ).
thf(6492,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) ) )
= $true )
| ( ( ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6399]) ).
thf(6493,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ( ~ ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6400]) ).
thf(6494,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $false )
| ( ( ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1431 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1431 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6401]) ).
thf(6495,plain,
! [SV326: $i,SV117: $i,SV236: $i] :
( ( ( ! [SY1432: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SY1432 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SY1432 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6402]) ).
thf(6496,plain,
! [SV118: $i,SV237: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 )
= $false )
| ( ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6403]) ).
thf(6497,plain,
! [SV118: $i,SV327: $i,SV237: $i] :
( ( ( SV237
= ( hAPP @ ( c_List_Orev @ SV327 ) @ SV118 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV327 ) @ SV237 )
= SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6404]) ).
thf(6498,plain,
! [SV120: $i,SV239: $i,SV329: $i,SV403: $i,SV451: $i,SV482: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV403 )
= SV329 )
= $false )
| ( ( ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV403 ) @ SV120 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV329 ) @ SV120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6405]) ).
thf(6499,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i,SV483: $i,SV497: $i,SV503: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV503 @ SV497 ) @ SV483 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SV503 @ SV452 @ SV497 @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6406]) ).
thf(6500,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6407]) ).
thf(6501,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6408]) ).
thf(6502,plain,
! [SV405: $i,SV453: $i,SV124: $i,SV333: $i,SV243: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV453 @ SV243 ) ) @ SV405 ) @ SV124 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV453 ) @ SV405 ) @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6409]) ).
thf(6503,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $false )
| ( ( ~ ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6410]) ).
thf(6504,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ~ ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6411]) ).
thf(6505,plain,
! [SV39: $i,SV417: $i,SV161: $i,SV352: $i,SV265: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6414]) ).
thf(6506,plain,
! [SV418: $i,SV462: $i,SV40: $i,SV266: $i,SV162: $i,SV353: $i] :
( ( ( ( SV353 != SV162 )
| ( SV266 != SV40 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6415]) ).
thf(6507,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
!= SV268 )
= $true )
| ( ( ( hAPP @ SV268 @ SV166 )
= SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6416]) ).
thf(6508,plain,
! [SV354: $i,SV419: $i,SV45: $i,SV166: $i,SV268: $i] :
( ( ( ( hAPP @ SV268 @ SV166 )
!= SV45 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6417]) ).
thf(6509,plain,
! [SV271: $i,SV48: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6420]) ).
thf(6510,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i,SV486: $i,SV498: $i,SV504: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV504 @ SV498 @ SV486 @ SV464 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SV498 @ SV486 @ SV272 ) @ SV170 ) )
| ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6421]) ).
thf(6511,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6422]) ).
thf(6512,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6423]) ).
thf(6513,plain,
! [SV53: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV174 @ ( sK7_SY1037 @ SV53 @ SV174 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6425]) ).
thf(6514,plain,
! [SV53: $i,SV505: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV174 @ SV505 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6426]) ).
thf(6515,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i,SV465: $i,SV487: $i] :
( ( ( SV487 != SV465 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV487 ) @ SV175 ) ) @ SV465 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV465 ) @ SV54 ) ) @ SV487 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6427]) ).
thf(6516,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i,SV466: $i,SV488: $i,SV499: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV499 @ SV488 @ SV466 @ SV425 ) @ SV361 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV488 @ SV466 @ SV176 ) @ SV55 ) )
= $true )
| ( ( ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6428]) ).
thf(6517,plain,
! [SV58: $i,SV179: $i,SV280: $i,SV362: $i,SV426: $i,SV467: $i,SV489: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV489 @ SV467 @ SV426 @ SV362 ) @ SV280 )
= SV179 )
= $false )
| ( ( ( hAPP @ SV362 @ ( hAPP @ SV280 @ SV58 ) )
= ( hAPP @ SV179 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(6518,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6432]) ).
thf(6519,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6432]) ).
thf(6520,plain,
! [SV60: $i,SV428: $i,SV181: $i,SV364: $i,SV282: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV428 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6433]) ).
thf(6521,plain,
! [SV62: $i,SV430: $i,SV183: $i,SV366: $i,SV284: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV284 ) @ SV366 ) @ SV183 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV430 @ SV284 @ SV62 ) ) @ SV366 ) @ SV183 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV430 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(6522,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6435]) ).
thf(6523,plain,
! [SV64: $i,SV185: $i,SV286: $i,SV368: $i,SV432: $i,SV470: $i] :
( ( ( SV470 = SV432 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV368 @ SV286 ) @ SV185 ) @ SV432 ) @ SV64 ) @ SV470 )
= ( hAPP @ SV185 @ SV470 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6436]) ).
thf(6524,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6437]) ).
thf(6525,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6438]) ).
thf(6526,plain,
! [SV191: $i,SV70: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ ( sK8_SY1345 @ SV70 @ SV191 @ SV291 ) ) )
= $false )
| ( ( ! [SY1346: $i,SY1347: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SY1346 ) @ SY1347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6440]) ).
thf(6527,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( ! [SY1664: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ ( sK9_SY1348 @ SV70 @ SV191 @ SV291 ) ) @ SY1664 ) ) ) )
= $false )
| ( ( ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6441]) ).
thf(6528,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( SV472 != SV437 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6443]) ).
thf(6529,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ~ ( ( SV472 != SV437 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6444]) ).
thf(6530,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i,SV506: $i] :
( ( ! [SY1665: $i,SY1666: $i] :
( ( ( hAPP @ SY1666 @ ( hAPP @ SY1665 @ SV506 ) )
!= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1666 ) @ SY1665 ) @ SV506 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6445]) ).
thf(6531,plain,
! [SV75: $i,SV195: $i,SV295: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
= $false )
| ( ( SV295 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6446]) ).
thf(6532,plain,
! [SV195: $i,SV376: $i,SV75: $i,SV295: $i] :
( ( ( SV295 = SV75 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV295 ) @ SV195 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV376 ) @ SV75 ) @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6447]) ).
thf(6533,plain,
! [SV439: $i,SV78: $i,SV198: $i,SV298: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6449]) ).
thf(6534,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true )
| ( ( ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6450]) ).
thf(6535,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( ~ ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6451]) ).
thf(6536,plain,
! [SV82: $i,SV202: $i,SV300: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false )
| ( ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6452]) ).
thf(6537,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6453]) ).
thf(6538,plain,
! [SV301: $i,SV83: $i,SV507: $i,SV203: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV507 ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV507 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6454]) ).
thf(6539,plain,
! [SV83: $i,SV301: $i,SV203: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ ( sK10_SY1376 @ SV301 @ SV83 @ SV203 ) ) @ SV83 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ ( sK10_SY1376 @ SV301 @ SV83 @ SV203 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6455]) ).
thf(6540,plain,
! [SV84: $i,SV204: $i,SV302: $i,SV382: $i,SV441: $i,SV474: $i,SV493: $i] :
( ( ( SV493 = SV474 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV493 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV441 @ SV382 @ SV302 @ SV204 @ SV84 ) @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6456]) ).
thf(6541,plain,
! [SV86: $i,SV206: $i,SV303: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $false )
| ( ( ~ ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6457]) ).
thf(6542,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ( ~ ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6458]) ).
thf(6543,plain,
! [SV89: $i,SV209: $i,SV305: $i,SV385: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
= $false )
| ( ( SV209 = SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(6544,plain,
! [SV305: $i,SV385: $i,SV89: $i,SV209: $i] :
( ( ( SV209 = SV89 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV209 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV385 ) @ SV305 ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6461]) ).
thf(6545,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true )
| ( ( ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6463]) ).
thf(6546,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6464]) ).
thf(6547,plain,
! [SV308: $i,SV92: $i,SV212: $i,SV388: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6465]) ).
thf(6548,plain,
! [SV388: $i,SV212: $i,SV92: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) @ SV92 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6465]) ).
thf(6549,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6466]) ).
thf(6550,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6467]) ).
thf(6551,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( SV476 != SV445 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6468]) ).
thf(6552,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ~ ( ( SV476 != SV445 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6469]) ).
thf(6553,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6470]) ).
thf(6554,plain,
! [SV391: $i,SV311: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6470]) ).
thf(6555,plain,
! [SV494: $i,SV312: $i,SV96: $i,SV216: $i] :
( ( ( SV216
!= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV312 @ SV216 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV312 @ SV494 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6471]) ).
thf(6556,plain,
! [SV314: $i,SV392: $i,SV218: $i,SV98: $i] :
( ( ( SV98 != SV218 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6474]) ).
thf(6557,plain,
! [SV98: $i,SV314: $i,SV218: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6474]) ).
thf(6558,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6475]) ).
thf(6559,plain,
! [SV393: $i,SV446: $i,SV99: $i,SV315: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6476]) ).
thf(6560,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
| ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6477]) ).
thf(6561,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6478]) ).
thf(6562,plain,
! [SV104: $i,SV224: $i,SV317: $i,SV395: $i,SV448: $i,SV478: $i] :
( ( ( SV478 = SV448 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV478 ) @ SV224 ) ) @ SV448 ) @ SV104 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV395 @ SV317 ) @ SV448 ) @ SV104 ) ) @ SV478 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6479]) ).
thf(6563,plain,
! [SV318: $i,SV396: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6480]) ).
thf(6564,plain,
! [SV396: $i,SV318: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6481]) ).
thf(6565,plain,
! [SV106: $i,SV226: $i,SV319: $i,SV397: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false )
| ( ( ~ ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6482]) ).
thf(6566,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ( ~ ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6483]) ).
thf(6567,plain,
! [SV107: $i,SV227: $i,SV320: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $false )
| ( ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6484]) ).
thf(6568,plain,
! [SV398: $i,SV227: $i,SV107: $i,SV320: $i] :
( ( ( ( SV320 = SV107 )
| ( hBOOL @ ( hAPP @ SV227 @ SV107 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6485]) ).
thf(6569,plain,
! [SV321: $i,SV108: $i,SV399: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6486]) ).
thf(6570,plain,
! [SV399: $i,SV108: $i,SV321: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6487]) ).
thf(6571,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
| ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SV508 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6488]) ).
thf(6572,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6489]) ).
thf(6573,plain,
! [SV111: $i,SV231: $i,SV322: $i,SV400: $i,SV449: $i,SV480: $i,SV495: $i] :
( ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6490]) ).
thf(6574,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ~ ( ~ ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6491]) ).
thf(6575,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ~ ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6491]) ).
thf(6576,plain,
! [SV116: $i,SV235: $i,SV325: $i,SV402: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $false )
| ( ( ~ ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6492]) ).
thf(6577,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ( ~ ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(6578,plain,
! [SV326: $i,SV117: $i,SV509: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV509 ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV509 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6494]) ).
thf(6579,plain,
! [SV117: $i,SV326: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ ( sK12_SY1432 @ SV326 @ SV117 @ SV236 ) ) @ SV117 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ ( sK12_SY1432 @ SV326 @ SV117 @ SV236 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6495]) ).
thf(6580,plain,
! [SV329: $i,SV451: $i,SV120: $i,SV403: $i,SV482: $i,SV239: $i] :
( ( ( SV239
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV403 ) @ SV120 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV329 ) @ SV120 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV403 )
= SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6498]) ).
thf(6581,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i,SV483: $i,SV497: $i,SV503: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV503 @ SV497 ) @ SV483 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SV503 @ SV452 @ SV497 @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6499]) ).
thf(6582,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) ) )
= $true )
| ( ( ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6500]) ).
thf(6583,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV122 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6501]) ).
thf(6584,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6501]) ).
thf(6585,plain,
! [SV405: $i,SV453: $i,SV124: $i,SV333: $i,SV243: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV243 ) @ SV333 ) @ SV124 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV453 @ SV243 ) ) @ SV405 ) @ SV124 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV453 ) @ SV405 ) @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(6586,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ! [SY1446: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1446 ) @ SV126 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(6587,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ! [SY1447: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SY1447 ) @ SV126 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6504]) ).
thf(6588,plain,
! [SV352: $i,SV39: $i,SV161: $i,SV265: $i,SV417: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6505]) ).
thf(6589,plain,
! [SV40: $i,SV266: $i,SV418: $i,SV462: $i,SV162: $i,SV353: $i] :
( ( ( SV353 != SV162 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6506]) ).
thf(6590,plain,
! [SV162: $i,SV353: $i,SV418: $i,SV462: $i,SV40: $i,SV266: $i] :
( ( ( SV266 != SV40 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6506]) ).
thf(6591,plain,
! [SV45: $i,SV166: $i,SV268: $i,SV354: $i,SV419: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 )
= $false )
| ( ( ( hAPP @ SV268 @ SV166 )
= SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6507]) ).
thf(6592,plain,
! [SV354: $i,SV419: $i,SV45: $i,SV166: $i,SV268: $i] :
( ( ( ( hAPP @ SV268 @ SV166 )
= SV45 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV419 @ SV354 ) @ SV268 ) @ SV166 ) @ SV45 )
= SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(6593,plain,
! [SV355: $i,SV48: $i,SV271: $i,SV169: $i,SV420: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6509]) ).
thf(6594,plain,
! [SV271: $i,SV420: $i,SV48: $i,SV169: $i,SV355: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6509]) ).
thf(6595,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i,SV486: $i,SV498: $i,SV504: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV504 @ SV498 @ SV486 @ SV464 ) @ SV421 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SV498 @ SV486 @ SV272 ) @ SV170 ) )
= $true )
| ( ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6510]) ).
thf(6596,plain,
! [SV50: $i,SV171: $i,SV273: $i,SV357: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6511]) ).
thf(6597,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6512]) ).
thf(6598,plain,
! [SV53: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ SV174 @ ( sK7_SY1037 @ SV53 @ SV174 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6513]) ).
thf(6599,plain,
! [SV53: $i,SV505: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ SV174 @ SV505 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV174 @ ( c_Hilbert__Choice_OEps @ SV53 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6514]) ).
thf(6600,plain,
! [SV54: $i,SV175: $i,SV276: $i,SV360: $i,SV424: $i,SV465: $i,SV487: $i] :
( ( ( SV487 = SV465 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV487 ) @ SV175 ) ) @ SV465 ) @ SV54 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV424 @ SV360 ) @ SV276 ) @ SV465 ) @ SV54 ) ) @ SV487 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6515]) ).
thf(6601,plain,
! [SV55: $i,SV176: $i,SV277: $i,SV361: $i,SV425: $i,SV466: $i,SV488: $i,SV499: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV499 @ SV488 @ SV466 @ SV425 ) @ SV361 )
= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV488 @ SV466 @ SV176 ) @ SV55 ) )
= $false )
| ( ( ! [SY1581: $i] :
( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SY1581 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SY1581 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(6602,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
| ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6518]) ).
thf(6603,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6519]) ).
thf(6604,plain,
! [SV60: $i,SV428: $i,SV181: $i,SV364: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV282 ) @ SV364 ) @ SV181 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV428 @ SV60 @ SV282 ) ) @ SV364 ) @ SV181 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV428 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6520]) ).
thf(6605,plain,
! [SV63: $i,SV184: $i,SV285: $i,SV367: $i,SV431: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
| ~ ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6522]) ).
thf(6606,plain,
! [SV65: $i,SV186: $i,SV287: $i,SV369: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6524]) ).
thf(6607,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(6608,plain,
! [SV510: $i,SV70: $i,SV191: $i,SV291: $i] :
( ( ( ! [SY1667: $i] : ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SV510 ) @ SY1667 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ ( sK8_SY1345 @ SV70 @ SV191 @ SV291 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6526]) ).
thf(6609,plain,
! [SV70: $i,SV191: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ ( sK9_SY1348 @ SV70 @ SV191 @ SV291 ) ) @ ( sK13_SY1664 @ SV70 @ SV191 @ SV291 ) ) ) )
= $false )
| ( ( ! [SY1350: $i] : ( hBOOL @ ( hAPP @ SV291 @ SY1350 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6527]) ).
thf(6610,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( SV472 != SV437 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6528]) ).
thf(6611,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( ~ ( ( SV472 != SV437 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6529]) ).
thf(6612,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i,SV506: $i,SV511: $i] :
( ( ! [SY1668: $i] :
( ( ( hAPP @ SY1668 @ ( hAPP @ SV511 @ SV506 ) )
!= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SY1668 ) @ SV511 ) @ SV506 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6530]) ).
thf(6613,plain,
! [SV439: $i,SV298: $i,SV78: $i,SV198: $i,SV379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6533]) ).
thf(6614,plain,
! [SV81: $i,SV201: $i,SV299: $i,SV380: $i,SV440: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false )
| ( ( ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6534]) ).
thf(6615,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( ~ ( ( SV380 != SV201 )
| ( SV299 != SV81 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6535]) ).
thf(6616,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6536]) ).
thf(6617,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ~ ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6537]) ).
thf(6618,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6537]) ).
thf(6619,plain,
! [SV301: $i,SV83: $i,SV507: $i,SV203: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV507 ) @ SV83 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV507 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6538]) ).
thf(6620,plain,
! [SV83: $i,SV301: $i,SV203: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ ( sK10_SY1376 @ SV301 @ SV83 @ SV203 ) ) @ SV83 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6539]) ).
thf(6621,plain,
! [SV83: $i,SV203: $i,SV301: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ ( sK10_SY1376 @ SV301 @ SV83 @ SV203 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6539]) ).
thf(6622,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ( ! [SY1144: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1144 ) @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6541]) ).
thf(6623,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV206: $i] :
( ( ( ! [SY1145: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SY1145 ) @ SV86 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6542]) ).
thf(6624,plain,
! [SV91: $i,SV211: $i,SV307: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false )
| ( ( ~ ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6545]) ).
thf(6625,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6546]) ).
thf(6626,plain,
! [SV308: $i,SV92: $i,SV212: $i,SV388: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV388 ) @ SV212 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6547]) ).
thf(6627,plain,
! [SV388: $i,SV212: $i,SV92: $i,SV308: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV308 ) @ ( sK5_SY1532 @ SV92 @ SV308 @ SV212 @ SV388 ) ) @ SV92 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV388 @ SV308 ) ) @ SV212 ) @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6548]) ).
thf(6628,plain,
! [SV93: $i,SV213: $i,SV309: $i,SV389: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6549]) ).
thf(6629,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6550]) ).
thf(6630,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( SV476 != SV445 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6551]) ).
thf(6631,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( ~ ( ( SV476 != SV445 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6552]) ).
thf(6632,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6553]) ).
thf(6633,plain,
! [SV391: $i,SV311: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6554]) ).
thf(6634,plain,
! [SV494: $i,SV312: $i,SV96: $i,SV216: $i] :
( ( ( SV216
= ( c_Hilbert__Choice_OEps @ SV96 @ SV312 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV312 @ SV216 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV312 @ SV494 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6555]) ).
thf(6635,plain,
! [SV314: $i,SV392: $i,SV218: $i,SV98: $i] :
( ( ( SV98 = SV218 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6556]) ).
thf(6636,plain,
! [SV98: $i,SV314: $i,SV218: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(6637,plain,
! [SV99: $i,SV219: $i,SV315: $i,SV393: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6558]) ).
thf(6638,plain,
! [SV393: $i,SV446: $i,SV99: $i,SV315: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ SV219 @ ( hAPP @ SV315 @ SV99 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV446 @ SV393 @ SV315 ) @ SV219 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6559]) ).
thf(6639,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true )
| ( ( ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6560]) ).
thf(6640,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( ~ ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6561]) ).
thf(6641,plain,
! [SV318: $i,SV396: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6563]) ).
thf(6642,plain,
! [SV396: $i,SV318: $i,SV105: $i,SV225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6564]) ).
thf(6643,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ( ! [SY1542: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1542 ) @ SV106 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(6644,plain,
! [SV106: $i,SV319: $i,SV226: $i,SV397: $i] :
( ( ( ! [SY1543: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SY1543 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SY1543 ) @ SV106 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6566]) ).
thf(6645,plain,
! [SV398: $i,SV227: $i,SV107: $i,SV320: $i] :
( ( ( SV320 = SV107 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV227 @ SV107 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6567]) ).
thf(6646,plain,
! [SV227: $i,SV398: $i,SV107: $i,SV320: $i] :
( ( ( SV320 = SV107 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6568]) ).
thf(6647,plain,
! [SV320: $i,SV398: $i,SV107: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ SV227 @ SV107 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV398 ) @ SV320 ) @ SV227 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6568]) ).
thf(6648,plain,
! [SV321: $i,SV108: $i,SV399: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6569]) ).
thf(6649,plain,
! [SV399: $i,SV108: $i,SV321: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6570]) ).
thf(6650,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
| ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SV508 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6571]) ).
thf(6651,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6572]) ).
thf(6652,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV111: $i,SV231: $i,SV449: $i] :
( ( ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
| ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6573]) ).
thf(6653,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ~ ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
| ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6574]) ).
thf(6654,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) )
| ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6575]) ).
thf(6655,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ( ! [SY1219: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1219 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6576]) ).
thf(6656,plain,
! [SV325: $i,SV402: $i,SV116: $i,SV235: $i] :
( ( ( ! [SY1220: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SY1220 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6577]) ).
thf(6657,plain,
! [SV326: $i,SV117: $i,SV509: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV509 ) @ SV117 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV509 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6578]) ).
thf(6658,plain,
! [SV117: $i,SV326: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ ( sK12_SY1432 @ SV326 @ SV117 @ SV236 ) ) @ SV117 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6579]) ).
thf(6659,plain,
! [SV117: $i,SV236: $i,SV326: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ ( sK12_SY1432 @ SV326 @ SV117 @ SV236 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6579]) ).
thf(6660,plain,
! [SV329: $i,SV451: $i,SV120: $i,SV403: $i,SV482: $i,SV239: $i] :
( ( ( SV239
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV403 ) @ SV120 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV239 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV329 ) @ SV120 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV482 ) @ SV451 ) @ SV403 )
= SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6580]) ).
thf(6661,plain,
! [SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV452: $i,SV483: $i,SV497: $i,SV503: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV503 @ SV497 ) @ SV483 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
| ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SV503 @ SV452 @ SV497 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6581]) ).
thf(6662,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( ~ ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6582]) ).
thf(6663,plain,
! [SV241: $i,SV122: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6583]) ).
thf(6664,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1442 ) @ SV122 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6584]) ).
thf(6665,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ ( sK14_SY1446 @ SV126 @ SV245 @ SV335 ) ) @ SV126 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6586]) ).
thf(6666,plain,
! [SV126: $i,SV512: $i,SV245: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SV512 ) @ SV126 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6587]) ).
thf(6667,plain,
! [SV352: $i,SV39: $i,SV161: $i,SV265: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV161 ) @ SV39 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV417 @ SV265 ) ) @ SV352 ) @ SV39 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV265 ) @ SV352 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV352 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6588]) ).
thf(6668,plain,
! [SV40: $i,SV266: $i,SV418: $i,SV462: $i,SV162: $i,SV353: $i] :
( ( ( SV353 = SV162 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6589]) ).
thf(6669,plain,
! [SV162: $i,SV353: $i,SV418: $i,SV462: $i,SV40: $i,SV266: $i] :
( ( ( SV266 = SV40 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV353 ) @ SV266 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV462 @ SV418 ) @ SV162 ) @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6590]) ).
thf(6670,plain,
! [SV355: $i,SV48: $i,SV271: $i,SV169: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6593]) ).
thf(6671,plain,
! [SV271: $i,SV420: $i,SV48: $i,SV169: $i,SV355: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6594]) ).
thf(6672,plain,
! [SV49: $i,SV170: $i,SV272: $i,SV356: $i,SV421: $i,SV464: $i,SV486: $i,SV498: $i,SV504: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV504 @ SV498 @ SV486 @ SV464 ) @ SV421 )
= ( hAPP @ ( c_Fun_Ocomp @ SV356 @ SV498 @ SV486 @ SV272 ) @ SV170 ) )
= $false )
| ( ( ( hAPP @ SV464 @ ( hAPP @ SV421 @ SV49 ) )
= ( hAPP @ SV272 @ ( hAPP @ SV170 @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6595]) ).
thf(6673,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6596]) ).
thf(6674,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6597]) ).
thf(6675,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6597]) ).
thf(6676,plain,
! [SV277: $i,SV466: $i,SV488: $i,SV499: $i,SV55: $i,SV176: $i,SV513: $i,SV361: $i,SV425: $i] :
( ( ( ( hAPP @ SV425 @ ( hAPP @ SV361 @ SV513 ) )
= ( hAPP @ SV176 @ ( hAPP @ SV55 @ SV513 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV499 @ SV488 @ SV466 @ SV425 ) @ SV361 )
= ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV488 @ SV466 @ SV176 ) @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6601]) ).
thf(6677,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6602]) ).
thf(6678,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6603]) ).
thf(6679,plain,
! [SV469: $i,SV431: $i,SV491: $i,SV500: $i,SV63: $i,SV184: $i,SV285: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) ) )
= $true )
| ( ( ~ ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6605]) ).
thf(6680,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6606]) ).
thf(6681,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6607]) ).
thf(6682,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6607]) ).
thf(6683,plain,
! [SV514: $i,SV510: $i,SV70: $i,SV191: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ SV510 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ ( sK8_SY1345 @ SV70 @ SV191 @ SV291 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6608]) ).
thf(6684,plain,
! [SV70: $i,SV191: $i,SV515: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ SV515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV191 @ SV70 ) @ ( sK9_SY1348 @ SV70 @ SV191 @ SV291 ) ) @ ( sK13_SY1664 @ SV70 @ SV191 @ SV291 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6609]) ).
thf(6685,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( SV472 = SV437 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6610]) ).
thf(6686,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( SV472 != SV437 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6611]) ).
thf(6687,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i,SV506: $i,SV511: $i,SV516: $i] :
( ( ( ( hAPP @ SV516 @ ( hAPP @ SV511 @ SV506 ) )
!= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SV516 ) @ SV511 ) @ SV506 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6612]) ).
thf(6688,plain,
! [SV439: $i,SV298: $i,SV78: $i,SV198: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV198 ) @ SV78 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV78 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV379 @ SV298 ) @ SV198 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV439 @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6613]) ).
thf(6689,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6614]) ).
thf(6690,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( ( SV380 != SV201 )
| ( SV299 != SV81 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6615]) ).
thf(6691,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6616]) ).
thf(6692,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( ( SV82 != SV202 )
| ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6617]) ).
thf(6693,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6618]) ).
thf(6694,plain,
! [SV301: $i,SV83: $i,SV507: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ SV507 ) @ SV83 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV507 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6619]) ).
thf(6695,plain,
! [SV83: $i,SV301: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV203 @ ( sK10_SY1376 @ SV301 @ SV83 @ SV203 ) ) @ SV83 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV301 @ SV203 ) @ SV83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6620]) ).
thf(6696,plain,
! [SV86: $i,SV383: $i,SV303: $i,SV206: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ ( sK15_SY1144 @ SV303 @ SV383 @ SV86 @ SV206 ) ) @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6622]) ).
thf(6697,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV517: $i,SV206: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SV517 ) @ SV86 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6623]) ).
thf(6698,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ! [SY1602: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1602 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1602 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1602 ) @ SV91 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6624]) ).
thf(6699,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ! [SY1603: $i] :
~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SY1603 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SY1603 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SY1603 ) @ SV91 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6625]) ).
thf(6700,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6628]) ).
thf(6701,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
| ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6629]) ).
thf(6702,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( SV476 = SV445 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6630]) ).
thf(6703,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( SV476 != SV445 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(6704,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6632]) ).
thf(6705,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6633]) ).
thf(6706,plain,
! [SV98: $i,SV314: $i,SV218: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
| ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6635]) ).
thf(6707,plain,
! [SV98: $i,SV314: $i,SV218: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6636]) ).
thf(6708,plain,
! [SV98: $i,SV392: $i,SV218: $i,SV314: $i] :
( ( ( ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6636]) ).
thf(6709,plain,
! [SV100: $i,SV220: $i,SV316: $i,SV394: $i,SV447: $i,SV477: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false )
| ( ( ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6639]) ).
thf(6710,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( ~ ( ( SV394 != SV220 )
| ( SV316 != SV100 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6640]) ).
thf(6711,plain,
! [SV318: $i,SV396: $i,SV105: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6641]) ).
thf(6712,plain,
! [SV396: $i,SV318: $i,SV105: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV318 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV225 ) @ SV105 ) @ SV396 ) )
= $true )
| ( ( SV396 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6642]) ).
thf(6713,plain,
! [SV319: $i,SV106: $i,SV226: $i,SV397: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) @ SV106 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6643]) ).
thf(6714,plain,
! [SV106: $i,SV319: $i,SV518: $i,SV226: $i,SV397: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6644]) ).
thf(6715,plain,
! [SV321: $i,SV108: $i,SV399: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6648]) ).
thf(6716,plain,
! [SV399: $i,SV108: $i,SV321: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV321 ) @ SV108 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV228 ) @ SV399 ) @ SV108 ) )
= $true )
| ( ( SV399 = SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6649]) ).
thf(6717,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
| ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6650]) ).
thf(6718,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SV508 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6650]) ).
thf(6719,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6651]) ).
thf(6720,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV111: $i,SV231: $i,SV449: $i] :
( ( ( ~ ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6652]) ).
thf(6721,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV449: $i,SV111: $i,SV231: $i] :
( ( ( ~ ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6652]) ).
thf(6722,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ( ~ ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 ) )
= $true )
| ( ( ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6653]) ).
thf(6723,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ( ~ ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6654]) ).
thf(6724,plain,
! [SV402: $i,SV325: $i,SV116: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ ( sK17_SY1219 @ SV325 @ SV402 @ SV116 @ SV235 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6655]) ).
thf(6725,plain,
! [SV325: $i,SV402: $i,SV519: $i,SV116: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SV519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6656]) ).
thf(6726,plain,
! [SV326: $i,SV117: $i,SV509: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ SV509 ) @ SV117 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV509 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6657]) ).
thf(6727,plain,
! [SV117: $i,SV326: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV236 @ ( sK12_SY1432 @ SV326 @ SV117 @ SV236 ) ) @ SV117 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV326 @ SV236 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6658]) ).
thf(6728,plain,
! [SV497: $i,SV503: $i,SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV483: $i,SV452: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SV503 @ SV452 @ SV497 @ SV404 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV503 @ SV497 ) @ SV483 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6661]) ).
thf(6729,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ! [SY1441: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SY1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SY1441 ) @ SV122 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6662]) ).
thf(6730,plain,
! [SV331: $i,SV520: $i,SV122: $i,SV241: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6664]) ).
thf(6731,plain,
! [SV126: $i,SV245: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ ( sK14_SY1446 @ SV126 @ SV245 @ SV335 ) ) @ SV126 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6665]) ).
thf(6732,plain,
! [SV126: $i,SV512: $i,SV245: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV335 ) @ SV245 ) @ SV512 ) @ SV126 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV335 ) @ SV245 ) @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6666]) ).
thf(6733,plain,
! [SV355: $i,SV48: $i,SV271: $i,SV169: $i,SV420: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6670]) ).
thf(6734,plain,
! [SV355: $i,SV48: $i,SV271: $i,SV169: $i,SV420: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6671]) ).
thf(6735,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6673]) ).
thf(6736,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6674]) ).
thf(6737,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6675]) ).
thf(6738,plain,
! [SV59: $i,SV180: $i,SV281: $i,SV363: $i,SV427: $i,SV468: $i,SV490: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6677]) ).
thf(6739,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6678]) ).
thf(6740,plain,
! [SV469: $i,SV431: $i,SV491: $i,SV500: $i,SV63: $i,SV184: $i,SV285: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( ~ ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6679]) ).
thf(6741,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(6742,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6681]) ).
thf(6743,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6682]) ).
thf(6744,plain,
! [SV73: $i,SV193: $i,SV293: $i,SV374: $i,SV437: $i,SV472: $i] :
( ( ( SV472 = SV437 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV374 @ SV293 ) @ SV193 ) @ SV437 ) @ SV73 ) @ SV472 )
= ( hAPP @ SV193 @ SV472 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6686]) ).
thf(6745,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i,SV506: $i,SV511: $i,SV516: $i] :
( ( ( ( hAPP @ SV516 @ ( hAPP @ SV511 @ SV506 ) )
!= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SV516 ) @ SV511 ) @ SV506 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6687]) ).
thf(6746,plain,
! [SV81: $i,SV299: $i,SV440: $i,SV201: $i,SV380: $i] :
( ( ( SV380 != SV201 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6689]) ).
thf(6747,plain,
! [SV201: $i,SV380: $i,SV440: $i,SV81: $i,SV299: $i] :
( ( ( SV299 != SV81 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6689]) ).
thf(6748,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( SV380 != SV201 )
= $true )
| ( ( SV299 != SV81 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6690]) ).
thf(6749,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( SV82 != SV202 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6691]) ).
thf(6750,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6691]) ).
thf(6751,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( SV82 != SV202 )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6692]) ).
thf(6752,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $true )
| ( ( ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6693]) ).
thf(6753,plain,
! [SV86: $i,SV383: $i,SV303: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ ( sK15_SY1144 @ SV303 @ SV383 @ SV86 @ SV206 ) ) @ SV86 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6696]) ).
thf(6754,plain,
! [SV303: $i,SV383: $i,SV86: $i,SV517: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV206 @ SV517 ) @ SV86 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV383 @ SV303 @ SV206 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6697]) ).
thf(6755,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6698]) ).
thf(6756,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6699]) ).
thf(6757,plain,
! [SV309: $i,SV444: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6700]) ).
thf(6758,plain,
! [SV213: $i,SV389: $i,SV444: $i,SV93: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6700]) ).
thf(6759,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6701]) ).
thf(6760,plain,
! [SV94: $i,SV214: $i,SV310: $i,SV390: $i,SV445: $i,SV476: $i] :
( ( ( SV476 = SV445 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV390 @ SV310 ) @ SV214 ) @ SV445 ) @ SV94 ) @ SV476 )
= ( hAPP @ SV214 @ SV476 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6703]) ).
thf(6761,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6704]) ).
thf(6762,plain,
! [SV391: $i,SV311: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6704]) ).
thf(6763,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6705]) ).
thf(6764,plain,
! [SV391: $i,SV311: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6705]) ).
thf(6765,plain,
! [SV314: $i,SV98: $i,SV218: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV218 ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6706]) ).
thf(6766,plain,
! [SV98: $i,SV392: $i,SV218: $i,SV314: $i] :
( ( ( ! [SY1536: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SY1536 ) @ SV98 ) ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6706]) ).
thf(6767,plain,
! [SV98: $i,SV314: $i,SV218: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6707]) ).
thf(6768,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6708]) ).
thf(6769,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6709]) ).
thf(6770,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( ( SV394 != SV220 )
| ( SV316 != SV100 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6710]) ).
thf(6771,plain,
! [SV319: $i,SV106: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) @ SV106 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6713]) ).
thf(6772,plain,
! [SV106: $i,SV319: $i,SV518: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6714]) ).
thf(6773,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
| ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6717]) ).
thf(6774,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SV508 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6718]) ).
thf(6775,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6719]) ).
thf(6776,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV111: $i,SV231: $i,SV449: $i] :
( ( ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
| ( SV231 = SV111 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6720]) ).
thf(6777,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV449: $i,SV111: $i,SV231: $i] :
( ( ( ( SV231 != SV111 )
| ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6721]) ).
thf(6778,plain,
! [SV114: $i,SV234: $i,SV324: $i,SV401: $i,SV450: $i,SV481: $i,SV496: $i] :
( ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false )
| ( ( ~ ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6722]) ).
thf(6779,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ( ~ ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6723]) ).
thf(6780,plain,
! [SV402: $i,SV325: $i,SV116: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ ( sK17_SY1219 @ SV325 @ SV402 @ SV116 @ SV235 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6724]) ).
thf(6781,plain,
! [SV325: $i,SV402: $i,SV519: $i,SV116: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV116 ) @ SV519 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV402 @ SV325 @ SV235 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6725]) ).
thf(6782,plain,
! [SV497: $i,SV503: $i,SV121: $i,SV240: $i,SV330: $i,SV404: $i,SV483: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV452 @ SV483 ) @ SV404 ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV330 @ SV240 @ SV121 @ SV503 @ SV452 @ SV497 @ SV404 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV503 @ SV497 ) @ SV483 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6728]) ).
thf(6783,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) @ SV122 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6729]) ).
thf(6784,plain,
! [SV331: $i,SV520: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6730]) ).
thf(6785,plain,
! [SV48: $i,SV271: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6733]) ).
thf(6786,plain,
! [SV355: $i,SV420: $i,SV48: $i,SV169: $i,SV271: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6733]) ).
thf(6787,plain,
! [SV271: $i,SV48: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6734]) ).
thf(6788,plain,
! [SV420: $i,SV355: $i,SV48: $i,SV169: $i,SV271: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6734]) ).
thf(6789,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6735]) ).
thf(6790,plain,
! [SV273: $i,SV422: $i,SV50: $i,SV171: $i,SV357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6735]) ).
thf(6791,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6736]) ).
thf(6792,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6737]) ).
thf(6793,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6738]) ).
thf(6794,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
| ( SV363 != SV59 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6739]) ).
thf(6795,plain,
! [SV469: $i,SV184: $i,SV63: $i,SV285: $i,SV367: $i,SV431: $i,SV491: $i,SV500: $i] :
( ( ( ! [SY1658: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SY1658 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SY1658 ) @ SV63 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6740]) ).
thf(6796,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6741]) ).
thf(6797,plain,
! [SV287: $i,SV433: $i,SV65: $i,SV186: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6741]) ).
thf(6798,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6742]) ).
thf(6799,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6743]) ).
thf(6800,plain,
! [SV74: $i,SV194: $i,SV294: $i,SV375: $i,SV438: $i,SV473: $i,SV492: $i,SV501: $i,SV506: $i,SV511: $i,SV516: $i] :
( ( ( ( hAPP @ SV516 @ ( hAPP @ SV511 @ SV506 ) )
= ( hAPP @ SV501 @ ( hAPP @ SV492 @ SV473 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV438 @ SV375 @ SV294 @ SV516 ) @ SV511 ) @ SV506 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV194 @ SV375 @ SV74 @ SV501 ) @ SV492 ) @ SV473 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6745]) ).
thf(6801,plain,
! [SV81: $i,SV299: $i,SV440: $i,SV201: $i,SV380: $i] :
( ( ( SV380 = SV201 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6746]) ).
thf(6802,plain,
! [SV201: $i,SV380: $i,SV440: $i,SV81: $i,SV299: $i] :
( ( ( SV299 = SV81 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6747]) ).
thf(6803,plain,
! [SV440: $i,SV81: $i,SV299: $i,SV201: $i,SV380: $i] :
( ( ( SV380 = SV201 )
= $false )
| ( ( SV299 != SV81 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6748]) ).
thf(6804,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( SV82 = SV202 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6749]) ).
thf(6805,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6750]) ).
thf(6806,plain,
! [SV300: $i,SV381: $i,SV202: $i,SV82: $i] :
( ( ( SV82 = SV202 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6751]) ).
thf(6807,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( ~ ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6752]) ).
thf(6808,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6755]) ).
thf(6809,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6756]) ).
thf(6810,plain,
! [SV309: $i,SV444: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6757]) ).
thf(6811,plain,
! [SV213: $i,SV389: $i,SV444: $i,SV93: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ SV93 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6758]) ).
thf(6812,plain,
! [SV444: $i,SV309: $i,SV93: $i,SV213: $i,SV389: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ SV93 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6759]) ).
thf(6813,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6761]) ).
thf(6814,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6763]) ).
thf(6815,plain,
! [SV314: $i,SV98: $i,SV218: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $true )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6765]) ).
thf(6816,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6766]) ).
thf(6817,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6768]) ).
thf(6818,plain,
! [SV218: $i,SV98: $i,SV314: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6768]) ).
thf(6819,plain,
! [SV100: $i,SV316: $i,SV447: $i,SV477: $i,SV220: $i,SV394: $i] :
( ( ( SV394 != SV220 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6769]) ).
thf(6820,plain,
! [SV220: $i,SV394: $i,SV447: $i,SV477: $i,SV100: $i,SV316: $i] :
( ( ( SV316 != SV100 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6769]) ).
thf(6821,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( SV394 != SV220 )
= $true )
| ( ( SV316 != SV100 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6770]) ).
thf(6822,plain,
! [SV319: $i,SV106: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) @ SV106 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6771]) ).
thf(6823,plain,
! [SV106: $i,SV319: $i,SV518: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6772]) ).
thf(6824,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) ) )
= $true )
| ( ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6773]) ).
thf(6825,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV502 )
!= ( hAPP @ SV110 @ SV508 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6774]) ).
thf(6826,plain,
! [SV230: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6775]) ).
thf(6827,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6775]) ).
thf(6828,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV111: $i,SV231: $i,SV449: $i] :
( ( ( ( hAPP @ SV449 @ SV231 )
!= ( hAPP @ SV449 @ SV111 ) )
= $true )
| ( ( SV231 = SV111 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6776]) ).
thf(6829,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV449: $i,SV111: $i,SV231: $i] :
( ( ( SV231 != SV111 )
= $true )
| ( ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6777]) ).
thf(6830,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ( ! [SY1550: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1550 ) @ SV114 ) ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6778]) ).
thf(6831,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV234: $i,SV401: $i] :
( ( ( ! [SY1551: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SY1551 ) @ SV114 ) ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6779]) ).
thf(6832,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) @ SV122 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6783]) ).
thf(6833,plain,
! [SV331: $i,SV520: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6784]) ).
thf(6834,plain,
! [SV48: $i,SV271: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6785]) ).
thf(6835,plain,
! [SV355: $i,SV420: $i,SV48: $i,SV169: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6786]) ).
thf(6836,plain,
! [SV271: $i,SV48: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV420 @ SV169 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6787]) ).
thf(6837,plain,
! [SV420: $i,SV355: $i,SV48: $i,SV169: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV271 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6788]) ).
thf(6838,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6789]) ).
thf(6839,plain,
! [SV273: $i,SV422: $i,SV50: $i,SV171: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6790]) ).
thf(6840,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6791]) ).
thf(6841,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6792]) ).
thf(6842,plain,
! [SV59: $i,SV363: $i,SV490: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6793]) ).
thf(6843,plain,
! [SV180: $i,SV281: $i,SV427: $i,SV468: $i,SV490: $i,SV59: $i,SV363: $i] :
( ( ( SV363 != SV59 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6793]) ).
thf(6844,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) ) )
= $true )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6794]) ).
thf(6845,plain,
! [SV431: $i,SV367: $i,SV285: $i,SV63: $i,SV184: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV63 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6795]) ).
thf(6846,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6796]) ).
thf(6847,plain,
! [SV287: $i,SV433: $i,SV65: $i,SV186: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6797]) ).
thf(6848,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6798]) ).
thf(6849,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6799]) ).
thf(6850,plain,
! [SV440: $i,SV201: $i,SV380: $i,SV81: $i,SV299: $i] :
( ( ( SV299 = SV81 )
= $false )
| ( ( SV380 = SV201 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV380 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV440 ) @ SV201 ) @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6803]) ).
thf(6851,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6804]) ).
thf(6852,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6805]) ).
thf(6853,plain,
! [SV300: $i,SV82: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $false )
| ( ( SV82 = SV202 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6806]) ).
thf(6854,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ~ ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6807]) ).
thf(6855,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
!= SV91 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6808]) ).
thf(6856,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ~ ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6809]) ).
thf(6857,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV521: $i,SV387: $i,SV443: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6809]) ).
thf(6858,plain,
! [SV444: $i,SV213: $i,SV389: $i,SV93: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ SV93 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV389 @ SV213 ) @ SV93 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ SV444 @ SV389 @ SV309 ) @ SV213 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6812]) ).
thf(6859,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6813]) ).
thf(6860,plain,
! [SV311: $i,SV391: $i,SV95: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV215 ) @ SV95 ) @ SV311 ) )
= $true )
| ( ( SV391 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6814]) ).
thf(6861,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6816]) ).
thf(6862,plain,
! [SV218: $i,SV98: $i,SV314: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) ) )
= $false )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6816]) ).
thf(6863,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6817]) ).
thf(6864,plain,
! [SV218: $i,SV98: $i,SV314: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK19_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV392 @ SV218 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6818]) ).
thf(6865,plain,
! [SV100: $i,SV316: $i,SV447: $i,SV477: $i,SV220: $i,SV394: $i] :
( ( ( SV394 = SV220 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6819]) ).
thf(6866,plain,
! [SV220: $i,SV394: $i,SV447: $i,SV477: $i,SV100: $i,SV316: $i] :
( ( ( SV316 = SV100 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6820]) ).
thf(6867,plain,
! [SV447: $i,SV477: $i,SV100: $i,SV316: $i,SV220: $i,SV394: $i] :
( ( ( SV394 = SV220 )
= $false )
| ( ( SV316 != SV100 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6821]) ).
thf(6868,plain,
! [SV319: $i,SV106: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6822]) ).
thf(6869,plain,
! [SV397: $i,SV226: $i,SV106: $i,SV319: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) @ SV106 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6822]) ).
thf(6870,plain,
! [SV106: $i,SV319: $i,SV518: $i,SV226: $i,SV397: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6823]) ).
thf(6871,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
= $false )
| ( ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6824]) ).
thf(6872,plain,
! [SV230: $i,SV508: $i,SV502: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV502 )
= ( hAPP @ SV110 @ SV508 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV502 ) @ SV508 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6825]) ).
thf(6873,plain,
! [SV230: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6826]) ).
thf(6874,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6827]) ).
thf(6875,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV111: $i,SV231: $i,SV449: $i] :
( ( ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) )
= $false )
| ( ( SV231 = SV111 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6828]) ).
thf(6876,plain,
! [SV322: $i,SV400: $i,SV480: $i,SV495: $i,SV449: $i,SV111: $i,SV231: $i] :
( ( ( SV231 = SV111 )
= $false )
| ( ( ( hAPP @ SV449 @ SV231 )
= ( hAPP @ SV449 @ SV111 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV495 @ SV480 @ SV449 @ SV400 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6829]) ).
thf(6877,plain,
! [SV324: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV234: $i,SV401: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) @ SV114 ) ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6830]) ).
thf(6878,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV522: $i,SV234: $i,SV401: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6831]) ).
thf(6879,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) @ SV122 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6832]) ).
thf(6880,plain,
! [SV331: $i,SV520: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6833]) ).
thf(6881,plain,
! [SV48: $i,SV271: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6834]) ).
thf(6882,plain,
! [SV271: $i,SV48: $i,SV355: $i,SV169: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV169 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV355 ) @ SV169 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV420 @ SV355 @ SV271 ) ) @ SV169 ) @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6836]) ).
thf(6883,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6838]) ).
thf(6884,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6839]) ).
thf(6885,plain,
! [SV273: $i,SV422: $i,SV50: $i,SV171: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6840]) ).
thf(6886,plain,
! [SV357: $i,SV50: $i,SV273: $i,SV171: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6841]) ).
thf(6887,plain,
! [SV59: $i,SV363: $i,SV490: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6842]) ).
thf(6888,plain,
! [SV180: $i,SV281: $i,SV427: $i,SV468: $i,SV490: $i,SV59: $i,SV363: $i] :
( ( ( SV363 = SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6843]) ).
thf(6889,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ~ ( ( SV468 != SV281 )
| ( SV427 != SV180 ) ) )
= $false )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(6890,plain,
! [SV431: $i,SV367: $i,SV285: $i,SV63: $i,SV184: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV63 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6845]) ).
thf(6891,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6846]) ).
thf(6892,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(6893,plain,
! [SV287: $i,SV433: $i,SV65: $i,SV186: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6848]) ).
thf(6894,plain,
! [SV369: $i,SV65: $i,SV287: $i,SV186: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6849]) ).
thf(6895,plain,
! [SV300: $i,SV82: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6851]) ).
thf(6896,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6851]) ).
thf(6897,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
| ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6898,plain,
! [SV300: $i,SV82: $i,SV202: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $true )
| ( ( SV82 = SV202 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6853]) ).
thf(6899,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ! [SY1521: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1521 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6854]) ).
thf(6900,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
!= SV91 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6855]) ).
thf(6901,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6856]) ).
thf(6902,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV521: $i,SV387: $i,SV443: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6857]) ).
thf(6903,plain,
! [SV392: $i,SV98: $i,SV218: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV314 ) @ SV218 ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) )
= $true )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6861]) ).
thf(6904,plain,
! [SV218: $i,SV98: $i,SV314: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ ( sK21_SY1536 @ SV98 @ SV392 @ SV218 @ SV314 ) ) @ SV98 ) )
= $true )
| ( ( SV98 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV392 @ SV314 ) ) @ SV218 ) @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6862]) ).
thf(6905,plain,
! [SV447: $i,SV477: $i,SV220: $i,SV394: $i,SV100: $i,SV316: $i] :
( ( ( SV316 = SV100 )
= $false )
| ( ( SV394 = SV220 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV394 ) @ SV316 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV477 @ SV447 ) @ SV220 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6867]) ).
thf(6906,plain,
! [SV319: $i,SV106: $i,SV226: $i,SV397: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6868]) ).
thf(6907,plain,
! [SV397: $i,SV226: $i,SV106: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ ( sK16_SY1542 @ SV106 @ SV319 @ SV226 @ SV397 ) ) @ SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6869]) ).
thf(6908,plain,
! [SV106: $i,SV319: $i,SV518: $i,SV226: $i,SV397: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6870]) ).
thf(6909,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6873]) ).
thf(6910,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6874]) ).
thf(6911,plain,
! [SV230: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6874]) ).
thf(6912,plain,
! [SV324: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) @ SV114 ) ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6877]) ).
thf(6913,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV522: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6878]) ).
thf(6914,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6879]) ).
thf(6915,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) @ SV122 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6879]) ).
thf(6916,plain,
! [SV331: $i,SV520: $i,SV122: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(6917,plain,
! [SV50: $i,SV273: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6883]) ).
thf(6918,plain,
! [SV357: $i,SV422: $i,SV50: $i,SV171: $i,SV273: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6883]) ).
thf(6919,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6884]) ).
thf(6920,plain,
! [SV422: $i,SV357: $i,SV50: $i,SV171: $i,SV273: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6884]) ).
thf(6921,plain,
! [SV357: $i,SV422: $i,SV50: $i,SV171: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6886]) ).
thf(6922,plain,
! [SV59: $i,SV363: $i,SV490: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6887]) ).
thf(6923,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( ( SV468 != SV281 )
| ( SV427 != SV180 ) )
= $true )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6889]) ).
thf(6924,plain,
! [SV431: $i,SV367: $i,SV285: $i,SV63: $i,SV184: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV63 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6890]) ).
thf(6925,plain,
! [SV65: $i,SV287: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6891]) ).
thf(6926,plain,
! [SV369: $i,SV433: $i,SV65: $i,SV186: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6891]) ).
thf(6927,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6892]) ).
thf(6928,plain,
! [SV433: $i,SV369: $i,SV65: $i,SV186: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6892]) ).
thf(6929,plain,
! [SV369: $i,SV433: $i,SV65: $i,SV186: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6894]) ).
thf(6930,plain,
! [SV300: $i,SV82: $i,SV202: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $true )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6895]) ).
thf(6931,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $true )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6896]) ).
thf(6932,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV381 @ SV202 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6897]) ).
thf(6933,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ~ ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6897]) ).
thf(6934,plain,
! [SV82: $i,SV381: $i,SV523: $i,SV202: $i,SV300: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6899]) ).
thf(6935,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6900]) ).
thf(6936,plain,
! [SV387: $i,SV211: $i,SV307: $i,SV91: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
!= SV91 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6900]) ).
thf(6937,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( SV387
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6901]) ).
thf(6938,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV521: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
!= SV211 )
= $true )
| ( ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6902]) ).
thf(6939,plain,
! [SV226: $i,SV397: $i,SV106: $i,SV518: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV319 ) @ SV518 ) @ SV106 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV397 ) @ SV226 ) @ SV518 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV397 @ SV319 ) ) @ SV226 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6908]) ).
thf(6940,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6909]) ).
thf(6941,plain,
! [SV230: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6909]) ).
thf(6942,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6910]) ).
thf(6943,plain,
! [SV324: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) @ SV114 ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6912]) ).
thf(6944,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV522: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6913]) ).
thf(6945,plain,
! [SV331: $i,SV122: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6914]) ).
thf(6946,plain,
! [SV122: $i,SV241: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ ( sK20_SY1441 @ SV331 @ SV122 @ SV241 ) ) @ SV122 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV331 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6915]) ).
thf(6947,plain,
! [SV122: $i,SV520: $i,SV241: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV520 ) @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV241 ) @ SV122 ) @ SV520 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV331 @ SV241 ) ) @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6916]) ).
thf(6948,plain,
! [SV50: $i,SV273: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6917]) ).
thf(6949,plain,
! [SV357: $i,SV422: $i,SV50: $i,SV171: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6918]) ).
thf(6950,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV422 @ SV171 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6919]) ).
thf(6951,plain,
! [SV422: $i,SV357: $i,SV50: $i,SV171: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV273 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6920]) ).
thf(6952,plain,
! [SV59: $i,SV180: $i,SV363: $i,SV427: $i,SV490: $i,SV281: $i,SV468: $i] :
( ( ( SV468 != SV281 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6922]) ).
thf(6953,plain,
! [SV59: $i,SV281: $i,SV363: $i,SV468: $i,SV490: $i,SV180: $i,SV427: $i] :
( ( ( SV427 != SV180 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6922]) ).
thf(6954,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( SV468 != SV281 )
= $true )
| ( ( SV427 != SV180 )
= $true )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6923]) ).
thf(6955,plain,
! [SV431: $i,SV367: $i,SV285: $i,SV63: $i,SV184: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV431 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6924]) ).
thf(6956,plain,
! [SV500: $i,SV491: $i,SV431: $i,SV63: $i,SV184: $i,SV469: $i,SV285: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV63 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6924]) ).
thf(6957,plain,
! [SV65: $i,SV287: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6925]) ).
thf(6958,plain,
! [SV369: $i,SV433: $i,SV65: $i,SV186: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6926]) ).
thf(6959,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV433 @ SV186 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6927]) ).
thf(6960,plain,
! [SV433: $i,SV369: $i,SV65: $i,SV186: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV287 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6928]) ).
thf(6961,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6931]) ).
thf(6962,plain,
! [SV82: $i,SV300: $i,SV202: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6932]) ).
thf(6963,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ~ ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6933]) ).
thf(6964,plain,
! [SV82: $i,SV381: $i,SV523: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6934]) ).
thf(6965,plain,
! [SV307: $i,SV91: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6935]) ).
thf(6966,plain,
! [SV387: $i,SV211: $i,SV307: $i,SV91: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6936]) ).
thf(6967,plain,
! [SV91: $i,SV307: $i,SV521: $i,SV211: $i,SV443: $i,SV387: $i] :
( ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
!= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6937]) ).
thf(6968,plain,
! [SV91: $i,SV307: $i,SV211: $i,SV521: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
= SV211 )
= $false )
| ( ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6938]) ).
thf(6969,plain,
! [SV230: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK6_SY887 @ SV230 @ SV110 ) ) @ ( sK11_SY1663 @ SV230 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV230 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6940]) ).
thf(6970,plain,
! [SV324: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6943]) ).
thf(6971,plain,
! [SV401: $i,SV234: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) @ SV114 ) ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6943]) ).
thf(6972,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV522: $i,SV234: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6944]) ).
thf(6973,plain,
! [SV50: $i,SV273: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6948]) ).
thf(6974,plain,
! [SV273: $i,SV50: $i,SV357: $i,SV171: $i,SV422: $i] :
( ( ( hBOOL @ ( hAPP @ SV422 @ SV171 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV357 ) @ SV171 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV422 @ SV357 @ SV273 ) ) @ SV171 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6950]) ).
thf(6975,plain,
! [SV59: $i,SV180: $i,SV363: $i,SV427: $i,SV490: $i,SV281: $i,SV468: $i] :
( ( ( SV468 = SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6952]) ).
thf(6976,plain,
! [SV59: $i,SV281: $i,SV363: $i,SV468: $i,SV490: $i,SV180: $i,SV427: $i] :
( ( ( SV427 = SV180 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6953]) ).
thf(6977,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i] :
( ( ( SV468 = SV281 )
= $false )
| ( ( SV427 != SV180 )
= $true )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6954]) ).
thf(6978,plain,
! [SV431: $i,SV367: $i,SV285: $i,SV63: $i,SV184: $i,SV469: $i,SV491: $i,SV500: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV431 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6955]) ).
thf(6979,plain,
! [SV500: $i,SV491: $i,SV431: $i,SV63: $i,SV184: $i,SV469: $i,SV285: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ ( sK22_SY1658 @ SV469 @ SV184 @ SV63 @ SV285 @ SV367 @ SV431 @ SV491 @ SV500 ) ) @ SV63 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV367 ) @ SV285 ) @ SV184 ) @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ SV500 ) @ SV491 ) @ SV469 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6956]) ).
thf(6980,plain,
! [SV65: $i,SV287: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6957]) ).
thf(6981,plain,
! [SV287: $i,SV65: $i,SV369: $i,SV186: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV186 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV369 ) @ SV186 ) @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV433 @ SV369 @ SV287 ) ) @ SV186 ) @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6959]) ).
thf(6982,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6961]) ).
thf(6983,plain,
! [SV82: $i,SV381: $i,SV202: $i,SV300: $i] :
( ( ( ! [SY1520: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SY1520 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SY1520 ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6963]) ).
thf(6984,plain,
! [SV82: $i,SV381: $i,SV523: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6964]) ).
thf(6985,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) )
= $false )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6965]) ).
thf(6986,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
| ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6966]) ).
thf(6987,plain,
! [SV211: $i,SV387: $i,SV91: $i,SV307: $i,SV521: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV307 )
= SV91 )
= $false )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV521 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6967]) ).
thf(6988,plain,
! [SV211: $i,SV387: $i,SV91: $i,SV521: $i,SV443: $i,SV307: $i] :
( ( ( SV307
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV521 ) @ SV91 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV521 )
= SV211 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6968]) ).
thf(6989,plain,
! [SV324: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV234: $i,SV401: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6970]) ).
thf(6990,plain,
! [SV401: $i,SV234: $i,SV114: $i,SV496: $i,SV481: $i,SV450: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ ( sK23_SY1550 @ SV450 @ SV481 @ SV496 @ SV114 @ SV324 @ SV234 @ SV401 ) ) @ SV114 ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6971]) ).
thf(6991,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV114: $i,SV324: $i,SV522: $i,SV234: $i,SV401: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) ) )
= $true )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6972]) ).
thf(6992,plain,
! [SV490: $i,SV59: $i,SV363: $i,SV281: $i,SV468: $i,SV180: $i,SV427: $i] :
( ( ( SV427 = SV180 )
= $false )
| ( ( SV468 = SV281 )
= $false )
| ( ( SV363 != SV59 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6977]) ).
thf(6993,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) ) )
= $true )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6982]) ).
thf(6994,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6983]) ).
thf(6995,plain,
! [SV82: $i,SV381: $i,SV523: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6984]) ).
thf(6996,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
= $false )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6985]) ).
thf(6997,plain,
! [SV387: $i,SV211: $i,SV91: $i,SV443: $i,SV307: $i] :
( ( ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) )
= $false )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6985]) ).
thf(6998,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
!= SV211 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6986]) ).
thf(6999,plain,
! [SV387: $i,SV211: $i,SV91: $i,SV443: $i,SV307: $i] :
( ( ( SV307
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6986]) ).
thf(7000,plain,
! [SV450: $i,SV481: $i,SV496: $i,SV234: $i,SV401: $i,SV114: $i,SV522: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV324 @ SV522 ) @ SV114 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV401 @ SV234 ) @ SV522 ) )
= $false )
| ( ( c_Predicate_Opred__comp @ SV496 @ SV481 @ SV450 @ SV401 @ SV324 @ SV234 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6991]) ).
thf(7001,plain,
! [SV490: $i,SV180: $i,SV427: $i,SV281: $i,SV468: $i,SV59: $i,SV363: $i] :
( ( ( SV363 = SV59 )
= $false )
| ( ( SV468 = SV281 )
= $false )
| ( ( SV427 = SV180 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV468 ) @ SV427 ) @ SV363 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV490 ) @ SV281 ) @ SV180 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6992]) ).
thf(7002,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6993]) ).
thf(7003,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6994]) ).
thf(7004,plain,
! [SV82: $i,SV381: $i,SV523: $i,SV202: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6995]) ).
thf(7005,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
= SV211 )
= $true )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6996]) ).
thf(7006,plain,
! [SV387: $i,SV211: $i,SV91: $i,SV443: $i,SV307: $i] :
( ( ( SV307
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) )
= $true )
| ( ( SV387
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6997]) ).
thf(7007,plain,
! [SV211: $i,SV307: $i,SV91: $i,SV387: $i,SV443: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) )
= SV211 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6998]) ).
thf(7008,plain,
! [SV387: $i,SV211: $i,SV91: $i,SV443: $i,SV307: $i] :
( ( ( SV307
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV91 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ ( sK18_SY1602 @ SV91 @ SV307 @ SV211 @ SV443 @ SV387 ) ) @ SV307 )
= SV91 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV387 ) @ SV307 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV443 ) @ SV211 ) @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6999]) ).
thf(7009,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7002]) ).
thf(7010,plain,
! [SV202: $i,SV82: $i,SV300: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) )
= $false )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7002]) ).
thf(7011,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7003]) ).
thf(7012,plain,
! [SV202: $i,SV82: $i,SV523: $i,SV300: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV523 ) @ SV82 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ SV523 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7004]) ).
thf(7013,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
= $true )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7009]) ).
thf(7014,plain,
! [SV202: $i,SV82: $i,SV300: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK24_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) )
= $true )
| ( ( SV82 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7010]) ).
thf(7015,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7011]) ).
thf(7016,plain,
! [SV202: $i,SV82: $i,SV300: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7011]) ).
thf(7017,plain,
! [SV381: $i,SV82: $i,SV202: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV300 ) @ SV202 ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7015]) ).
thf(7018,plain,
! [SV202: $i,SV82: $i,SV300: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ ( sK25_SY1520 @ SV82 @ SV381 @ SV202 @ SV300 ) ) @ SV82 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV381 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV381 @ SV300 ) ) @ SV202 ) @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7016]) ).
thf(7019,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5479,7018,7017,7014,7013,7012,7008,7007,7006,7005,7001,7000,6990,6989,6988,6987,6981,6980,6979,6978,6976,6975,6974,6973,6969,6962,6960,6958,6951,6949,6947,6946,6945,6942,6941,6939,6930,6929,6921,6911,6907,6906,6905,6904,6903,6898,6893,6888,6885,6882,6881,6876,6875,6872,6871,6866,6865,6864,6863,6860,6859,6858,6850,6837,6835,6815,6811,6810,6802,6801,6800,6782,6781,6780,6767,6764,6762,6760,6754,6753,6744,6732,6731,6727,6726,6716,6715,6712,6711,6702,6695,6694,6688,6685,6684,6683,6676,6672,6669,6668,6667,6663,6660,6659,6647,6646,6645,6638,6637,6634,6627,6626,6621,6604,6600,6599,6598,6592,6591,6585,6562,6544,6543,6540,6532,6531,6523,6521,6517,6497,6496,6473,6472,6462,6459,6448,6442,6439,6430,6429,6424,6419,6418,6413,6412,6397,6396,6392,6364,6363,6355,6354,6353,6352,6342,6341,6339,6338,6332,6322,6312,6311,6310,6305,6304,6301,6289,6244,6209,6200,6199,6198,6197,6196,6194,6192,6191,6186,6181,6175,6172,6160,6088,6083,6079,6051,6050,6035,6001,5986,5979,5977,5976,5975,5974,5972,5971,5970,5966,5965,5964,5957,5955,5925,5863,5848,5837,5780,5751,5729,5726,5722,5721,5720,5620,5608,5584,5583]) ).
thf(7020,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[7019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW350+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
% 0.08/0.21 % Computer : n014.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Oct 6 16:54:26 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 113.09/22.93 ....................................
% 113.09/22.93
% 113.09/22.93 No.of.Axioms: 129
% 113.09/22.93
% 113.09/22.93 Length.of.Defs: 0
% 113.09/22.93
% 113.09/22.93 Contains.Choice.Funs: false
% 113.09/22.93 ......................................................................................................................................
% 113.09/22.93
% 113.09/22.93 ********************************
% 113.09/22.93 * All subproblems solved! *
% 113.09/22.93 ********************************
% 113.09/22.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:129,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:292,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7019,loop_count:0,foatp_calls:1,translation:fof_full)
% 113.09/22.93
% 113.09/22.93 %**** Beginning of derivation protocol ****
% 113.09/22.93 % SZS output start CNFRefutation
% See solution above
% 113.09/22.95
% 113.09/22.95 %**** End of derivation protocol ****
% 113.09/22.95 %**** no. of clauses in derivation: 1921 ****
% 113.09/22.95 %**** clause counter: 7019 ****
% 113.09/22.95
% 113.09/22.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:129,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:292,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7019,loop_count:0,foatp_calls:1,translation:fof_full)
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