%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW295+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:01:07 AM UTC 2026
% Result : Theorem 102.64s 20.80s
% Output : CNFRefutation 102.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 105
% Syntax : Number of formulae : 2318 (1711 unt; 0 typ; 0 def)
% Number of atoms : 10939 (6808 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 37141 (4120 ~;2604 |; 28 &;30088 @)
% ( 91 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 543 ( 540 usr; 60 con; 0-10 aty)
% Number of variables : 11028 ( 0 ^;11012 !; 16 ?;11028 :)
% 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__rec,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec: $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_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 > $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_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_DSequence_Oempty,type,
c_DSequence_Oempty: $i > $i ).
thf(tp_c_DSequence_Osingle,type,
c_DSequence_Osingle: $i > $i ).
thf(tp_c_DSequence_Ounion,type,
c_DSequence_Ounion: $i > $i ).
thf(tp_c_Divides_Oadjust,type,
c_Divides_Oadjust: $i > $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int__rel,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat__rel,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg__rel,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(tp_c_Divides_OnegateSnd,type,
c_Divides_OnegateSnd: $i ).
thf(tp_c_Divides_Opdivmod,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg__rel,type,
c_Divides_OposDivAlg__rel: $i ).
thf(tp_c_Enum_On__lists,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(tp_c_Enum_Osublists,type,
c_Enum_Osublists: $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequivp,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(tp_c_Finite__Set_Ofold,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__image,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofolding,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__idem,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple__idem,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one__idem,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm__idem,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_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_If,type,
c_If: $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_Obind,type,
c_Lazy__Sequence_Obind: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oempty,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__bind,type,
c_Lazy__Sequence_Ohb__bind: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__not__seq,type,
c_Lazy__Sequence_Ohb__not__seq: $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__single,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohit__bound,type,
c_Lazy__Sequence_Ohit__bound: $i > $i ).
thf(tp_c_Lazy__Sequence_Osingle,type,
c_Lazy__Sequence_Osingle: $i > $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_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_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__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_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_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_Oreturn__list,type,
c_List_Oreturn__list: $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i ).
thf(tp_c_List_Oset__Cons,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $i > $i ).
thf(tp_c_List_Otranspose,type,
c_List_Otranspose: $i > $i > $i ).
thf(tp_c_List_Otranspose__rel,type,
c_List_Otranspose__rel: $i > $i ).
thf(tp_c_List_Oupt,type,
c_List_Oupt: $i > $i > $i ).
thf(tp_c_List_Oupto,type,
c_List_Oupto: $i > $i > $i ).
thf(tp_c_List_Oupto__rel,type,
c_List_Oupto__rel: $i ).
thf(tp_c_List_Ozip,type,
c_List_Ozip: $i > $i > $i ).
thf(tp_c_Map_Odom,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(tp_c_Map_Omap__add,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(tp_c_Map_Omap__comp,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Map_Omap__of,type,
c_Map_Omap__of: $i > $i > $i > $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 > $i > $o ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(tp_c_Natural_Oupdate,type,
c_Natural_Oupdate: $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__bind,type,
c_New__DSequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__decr__bind,type,
c_New__DSequence_Oneg__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__single,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__bind,type,
c_New__DSequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__decr__bind,type,
c_New__DSequence_Opos__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__empty,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(tp_c_New__DSequence_Opos__not__seq,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(tp_c_New__DSequence_Opos__single,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__bind,type,
c_New__Random__Sequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__decr__bind,type,
c_New__Random__Sequence_Oneg__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__map,type,
c_New__Random__Sequence_Oneg__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__single,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__bind,type,
c_New__Random__Sequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__decr__bind,type,
c_New__Random__Sequence_Opos__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__empty,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__map,type,
c_New__Random__Sequence_Opos__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__not__random__dseq,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__single,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(tp_c_Nitpick_OAbs__Frac,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(tp_c_Nitpick_OFrac,type,
c_Nitpick_OFrac: $i ).
thf(tp_c_Nitpick_ORep__Frac,type,
c_Nitpick_ORep__Frac: $i > $i ).
thf(tp_c_Nitpick_Ocard_H,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(tp_c_Nitpick_Odenom,type,
c_Nitpick_Odenom: $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Ofrac,type,
c_Nitpick_Ofrac: $i > $i ).
thf(tp_c_Nitpick_Oint__gcd,type,
c_Nitpick_Oint__gcd: $i ).
thf(tp_c_Nitpick_Oint__lcm,type,
c_Nitpick_Oint__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Oinverse__frac,type,
c_Nitpick_Oinverse__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oless__eq__frac,type,
c_Nitpick_Oless__eq__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Oless__frac,type,
c_Nitpick_Oless__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd__rel,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(tp_c_Nitpick_Onat__lcm,type,
c_Nitpick_Onat__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac__rel,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(tp_c_Nitpick_Onum,type,
c_Nitpick_Onum: $i > $i ).
thf(tp_c_Nitpick_Onumber__of__frac,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oof__frac,type,
c_Nitpick_Oof__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oone__frac,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(tp_c_Nitpick_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_Oplus__frac,type,
c_Nitpick_Oplus__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oprod,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osetsum_H,type,
c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Otimes__frac,type,
c_Nitpick_Otimes__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ouminus__frac,type,
c_Nitpick_Ouminus__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Ounknown,type,
c_Nitpick_Ounknown: $i > $o ).
thf(tp_c_Nitpick_Owf_H,type,
c_Nitpick_Owf_H: $i > $i > $o ).
thf(tp_c_Nitpick_Ozero__frac,type,
c_Nitpick_Ozero__frac: $i > $i ).
thf(tp_c_Option_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_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_Omono,type,
c_Orderings_Oorder_Omono: $i > $i > $i > $i > $o ).
thf(tp_c_Orderings_Oorder_Ostrict__mono,type,
c_Orderings_Oorder_Ostrict__mono: $i > $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_Ocurry,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ofst,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(tp_c_Product__Type_Ointernal__split,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Omap__pair,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__case,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__size,type,
c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oscomp,type,
c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Osnd,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(tp_c_Quickcheck_Obeyond,type,
c_Quickcheck_Obeyond: $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_Random__Sequence_ORandom,type,
c_Random__Sequence_ORandom: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Obind,type,
c_Random__Sequence_Obind: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Oempty,type,
c_Random__Sequence_Oempty: $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Omap,type,
c_Random__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Osingle,type,
c_Random__Sequence_Osingle: $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_Odvd__class_Odvd,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
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_OInl,type,
c_Sum__Type_OInl: $i > $i > $i ).
thf(tp_c_Sum__Type_OInr,type,
c_Sum__Type_OInr: $i > $i > $i ).
thf(tp_c_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OProjl,type,
c_Sum__Type_OProjl: $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OProjr,type,
c_Sum__Type_OProjr: $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OSuml,type,
c_Sum__Type_OSuml: $i > $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OSumr,type,
c_Sum__Type_OSumr: $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_Sum__Type_Osum_Osum__rec,type,
c_Sum__Type_Osum_Osum__rec: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Sum__Type_Osum_Osum__size,type,
c_Sum__Type_Osum_Osum__size: $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_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_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,type,
class_Rings_Ocomm__ring: $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_Odvd,type,
class_Rings_Odvd: $i > $o ).
thf(tp_class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
thf(tp_class_Rings_Oinverse,type,
class_Rings_Oinverse: $i > $o ).
thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tp_class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(tp_class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(tp_class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
thf(tp_class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tp_class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(tp_class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
thf(tp_class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
thf(tp_class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
thf(tp_class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
thf(tp_class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(tp_class_Smallcheck_Osmall,type,
class_Smallcheck_Osmall: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK10_SY1395,type,
sK10_SY1395: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY1405,type,
sK11_SY1405: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SY2179,type,
sK13_SY2179: $i ).
thf(tp_sK14_SY2074,type,
sK14_SY2074: $i > $i > $i ).
thf(tp_sK15_SY2314,type,
sK15_SY2314: $i ).
thf(tp_sK16_SY2173,type,
sK16_SY2173: $i > $i > $i > $i ).
thf(tp_sK17_SY2375,type,
sK17_SY2375: $i > $i > $i > $i > $i > $i ).
thf(tp_sK18_SY2335,type,
sK18_SY2335: $i > $i > $i > $i > $i ).
thf(tp_sK19_SY2398,type,
sK19_SY2398: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY2208,type,
sK20_SY2208: $i > $i > $i > $i ).
thf(tp_sK21_SY2410,type,
sK21_SY2410: $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_SY2412,type,
sK22_SY2412: $i > $i > $i > $i > $i > $i ).
thf(tp_sK2_SY1138,type,
sK2_SY1138: $i ).
thf(tp_sK3_SY977,type,
sK3_SY977: $i > $i > $i ).
thf(tp_sK4_SY1288,type,
sK4_SY1288: $i ).
thf(tp_sK5_SY1209,type,
sK5_SY1209: $i > $i > $i > $i ).
thf(tp_sK6_SY1319,type,
sK6_SY1319: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY1401,type,
sK7_SY1401: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY1369,type,
sK8_SY1369: $i > $i > $i > $i > $i > $i ).
thf(tp_sK9_SY1229,type,
sK9_SY1229: $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_Opname,type,
tc_Com_Opname: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $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_P,type,
v_P: $i > $i > $o ).
thf(tp_v_Q,type,
v_Q: $i > $i > $o ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_pn,type,
v_pn: $i ).
thf(16,axiom,
! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Qa_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(307,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(308,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(686,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/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(687,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(688,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(689,axiom,
! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(690,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/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(723,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/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(724,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/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(842,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/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(843,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/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(844,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1016,axiom,
! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1133,axiom,
! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1234,axiom,
! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1315,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(1519,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1537,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1538,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(1617,axiom,
! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(2173,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(2176,axiom,
! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(2179,axiom,
! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(2180,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(2181,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(2182,axiom,
! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(2183,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(2195,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(2321,axiom,
! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2322,axiom,
! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(2323,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2324,axiom,
! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
( ( V_a_2 != V_c_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(2325,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(2326,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(2327,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(2328,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(2329,axiom,
! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(2582,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(2583,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(2631,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(2669,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/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2794,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(2795,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(3223,axiom,
! [V_g_2: $i,V_f_2: $i,T_c: $i,T_d: $i,T_b: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(3253,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/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(3254,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/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(3438,axiom,
! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3440,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(3441,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/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(3522,axiom,
! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(3933,axiom,
! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(4887,axiom,
! [V_y: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
thf(4888,axiom,
! [V_a_H_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_2 )
= ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
thf(4889,axiom,
! [V_y: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
thf(4890,axiom,
! [V_b_H_2: $i,V_b_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_2 )
= ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_H_2 ) )
<=> ( V_b_2 = V_b_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I2_J) ).
thf(4929,axiom,
! [V_pname_H_2: $i,V_fun_2: $i,V_vname_2: $i] :
( ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
thf(4930,axiom,
! [V_fun_2: $i,V_vname_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
thf(5002,axiom,
! [V_com_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
thf(5003,axiom,
! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
thf(5045,axiom,
! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i,V_loc_2: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(5046,axiom,
! [V_com_2: $i,V_fun_2: $i,V_loc_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(5062,axiom,
! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(5096,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_x ) )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
thf(5107,axiom,
! [V_pname_2: $i,V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(5108,axiom,
! [V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i,V_pname_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_2 )
!= ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(5129,axiom,
! [V_com2_2: $i,V_com1_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
thf(5130,axiom,
! [V_pname_H_2: $i,V_com2_2: $i,V_com1_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
thf(5159,axiom,
! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nat__rec__Suc) ).
thf(5160,axiom,
! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(5162,axiom,
! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
thf(5163,axiom,
! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
thf(5165,axiom,
! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(5166,axiom,
! [V_pname_H: $i,V_com2: $i,V_com1: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
thf(5167,axiom,
! [V_com2: $i,V_com1: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
thf(5169,axiom,
! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(5177,axiom,
! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__rec @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I7_J) ).
thf(5178,axiom,
! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(5180,axiom,
! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(5181,axiom,
! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(5182,axiom,
! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(5185,axiom,
! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I70_J) ).
thf(5186,axiom,
! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(5187,axiom,
! [V_t: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c @ V_s @ B_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(5189,axiom,
! [V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ V_a3_2 )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(5190,axiom,
! [V_t_2: $i,V_s_2: $i,V_c_2: $i] :
( ( c_Natural_Oevalc @ V_c_2 @ V_s_2 @ V_t_2 )
<=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c_2 @ V_s_2 @ B_n @ V_t_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(5191,axiom,
! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t )
=> ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(5193,axiom,
! [V_s1: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(5194,axiom,
! [V_s1: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(5195,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/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5196,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/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5197,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5198,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5199,axiom,
! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname_2 )
= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(5200,axiom,
! [V_s1: $i,V_n: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 )
=> ~ ! [B_n: $i] :
( ( V_n
= ( hAPP @ c_Nat_OSuc @ B_n ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ B_n @ V_s1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(5201,axiom,
! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(5202,axiom,
! [V_a4_2: $i,V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ ( hAPP @ c_Nat_OSuc @ V_a3_2 ) @ V_a4_2 )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 @ V_a4_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(5203,axiom,
! [V_s1: $i,V_n: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(5204,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/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(5205,conjecture,
( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
<=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(5206,negated_conjecture,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
<=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5205]) ).
thf(5207,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
<=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5206]) ).
thf(5208,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5209,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Qa_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5210,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5211,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(5212,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5213,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(5214,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(5215,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)],[309]) ).
thf(5216,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)],[686]) ).
thf(5217,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(5218,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(5219,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(5220,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)],[690]) ).
thf(5221,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)],[723]) ).
thf(5222,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)],[724]) ).
thf(5223,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)],[842]) ).
thf(5224,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)],[843]) ).
thf(5225,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[844]) ).
thf(5226,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1016]) ).
thf(5227,plain,
( ( ! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1133]) ).
thf(5228,plain,
( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1234]) ).
thf(5229,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1315]) ).
thf(5230,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1519]) ).
thf(5231,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1537]) ).
thf(5232,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)],[1538]) ).
thf(5233,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1617]) ).
thf(5234,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2173]) ).
thf(5235,plain,
( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2176]) ).
thf(5236,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2179]) ).
thf(5237,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2180]) ).
thf(5238,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2181]) ).
thf(5239,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2182]) ).
thf(5240,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2183]) ).
thf(5241,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2195]) ).
thf(5242,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2321]) ).
thf(5243,plain,
( ( ! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2322]) ).
thf(5244,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2323]) ).
thf(5245,plain,
( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
( ( V_a_2 != V_c_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2324]) ).
thf(5246,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2325]) ).
thf(5247,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[2326]) ).
thf(5248,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2327]) ).
thf(5249,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2328]) ).
thf(5250,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[2329]) ).
thf(5251,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2582]) ).
thf(5252,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2583]) ).
thf(5253,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2631]) ).
thf(5254,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)],[2669]) ).
thf(5255,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2794]) ).
thf(5256,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2795]) ).
thf(5257,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_d: $i,T_b: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3223]) ).
thf(5258,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)],[3253]) ).
thf(5259,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)],[3254]) ).
thf(5260,plain,
( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3438]) ).
thf(5261,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3440]) ).
thf(5262,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)],[3441]) ).
thf(5263,plain,
( ( ! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3522]) ).
thf(5264,plain,
( ( ! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3933]) ).
thf(5265,plain,
( ( ! [V_y: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4887]) ).
thf(5266,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_2 )
= ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4888]) ).
thf(5267,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4889]) ).
thf(5268,plain,
( ( ! [V_b_H_2: $i,V_b_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_2 )
= ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_H_2 ) )
<=> ( V_b_2 = V_b_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4890]) ).
thf(5269,plain,
( ( ! [V_pname_H_2: $i,V_fun_2: $i,V_vname_2: $i] :
( ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4929]) ).
thf(5270,plain,
( ( ! [V_fun_2: $i,V_vname_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4930]) ).
thf(5271,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5002]) ).
thf(5272,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5003]) ).
thf(5273,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i,V_loc_2: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5045]) ).
thf(5274,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_loc_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5046]) ).
thf(5275,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5062]) ).
thf(5276,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_x ) )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[5096]) ).
thf(5277,plain,
( ( ! [V_pname_2: $i,V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5107]) ).
thf(5278,plain,
( ( ! [V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i,V_pname_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_2 )
!= ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5108]) ).
thf(5279,plain,
( ( ! [V_com2_2: $i,V_com1_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5129]) ).
thf(5280,plain,
( ( ! [V_pname_H_2: $i,V_com2_2: $i,V_com1_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5130]) ).
thf(5281,plain,
( ( ! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5159]) ).
thf(5282,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5160]) ).
thf(5283,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[5162]) ).
thf(5284,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5163]) ).
thf(5285,plain,
( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5165]) ).
thf(5286,plain,
( ( ! [V_pname_H: $i,V_com2: $i,V_com1: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5166]) ).
thf(5287,plain,
( ( ! [V_com2: $i,V_com1: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5167]) ).
thf(5288,plain,
( ( ! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5169]) ).
thf(5289,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__rec @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5177]) ).
thf(5290,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5178]) ).
thf(5291,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5180]) ).
thf(5292,plain,
( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[5181]) ).
thf(5293,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5182]) ).
thf(5294,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5185]) ).
thf(5295,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5186]) ).
thf(5296,plain,
( ( ! [V_t: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c @ V_s @ B_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5187]) ).
thf(5297,plain,
( ( ! [V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ V_a3_2 )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5189]) ).
thf(5298,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_c_2: $i] :
( ( c_Natural_Oevalc @ V_c_2 @ V_s_2 @ V_t_2 )
<=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c_2 @ V_s_2 @ B_n @ V_t_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5190]) ).
thf(5299,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t )
=> ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5191]) ).
thf(5300,plain,
( ( ! [V_s1: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5193]) ).
thf(5301,plain,
( ( ! [V_s1: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5194]) ).
thf(5302,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)],[5195]) ).
thf(5303,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)],[5196]) ).
thf(5304,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[5197]) ).
thf(5305,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5198]) ).
thf(5306,plain,
( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname_2 )
= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5199]) ).
thf(5307,plain,
( ( ! [V_s1: $i,V_n: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 )
=> ~ ! [B_n: $i] :
( ( V_n
= ( hAPP @ c_Nat_OSuc @ B_n ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ B_n @ V_s1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5200]) ).
thf(5308,plain,
( ( ! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5201]) ).
thf(5309,plain,
( ( ! [V_a4_2: $i,V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ ( hAPP @ c_Nat_OSuc @ V_a3_2 ) @ V_a4_2 )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 @ V_a4_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5202]) ).
thf(5310,plain,
( ( ! [V_s1: $i,V_n: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5203]) ).
thf(5311,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)],[5204]) ).
thf(5312,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5207]) ).
thf(5313,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5207]) ).
thf(5314,plain,
( ( ~ ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5312]) ).
thf(5315,plain,
( ( ~ ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5313]) ).
thf(5316,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)],[5311]) ).
thf(5317,plain,
( ( ! [V_s1: $i,V_n: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5310]) ).
thf(5318,plain,
( ( ! [V_a4_2: $i,V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ ( hAPP @ c_Nat_OSuc @ V_a3_2 ) @ V_a4_2 )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 @ V_a4_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5309]) ).
thf(5319,plain,
( ( ! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[5308]) ).
thf(5320,plain,
( ( ! [V_s1: $i,V_n: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 )
=> ~ ! [B_n: $i] :
( ( V_n
= ( hAPP @ c_Nat_OSuc @ B_n ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ B_n @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(5321,plain,
( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname_2 )
= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5306]) ).
thf(5322,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5305]) ).
thf(5323,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5304]) ).
thf(5324,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)],[5303]) ).
thf(5325,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)],[5302]) ).
thf(5326,plain,
( ( ! [V_s1: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5301]) ).
thf(5327,plain,
( ( ! [V_s1: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5300]) ).
thf(5328,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t )
=> ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(5329,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_c_2: $i] :
( ( c_Natural_Oevalc @ V_c_2 @ V_s_2 @ V_t_2 )
<=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c_2 @ V_s_2 @ B_n @ V_t_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5298]) ).
thf(5330,plain,
( ( ! [V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ V_a3_2 )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(5331,plain,
( ( ! [V_t: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c @ V_s @ B_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[5296]) ).
thf(5332,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5333,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(5334,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[5293]) ).
thf(5335,plain,
( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[5292]) ).
thf(5336,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5291]) ).
thf(5337,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5290]) ).
thf(5338,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__rec @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5339,plain,
( ( ! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5340,plain,
( ( ! [V_com2: $i,V_com1: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5341,plain,
( ( ! [V_pname_H: $i,V_com2: $i,V_com1: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5342,plain,
( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(5343,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(5344,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(5345,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5282]) ).
thf(5346,plain,
( ( ! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(5347,plain,
( ( ! [V_pname_H_2: $i,V_com2_2: $i,V_com1_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5280]) ).
thf(5348,plain,
( ( ! [V_com2_2: $i,V_com1_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(5349,plain,
( ( ! [V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i,V_pname_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_2 )
!= ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(5350,plain,
( ( ! [V_pname_2: $i,V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(5351,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_x ) )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(5352,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(5353,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_loc_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5274]) ).
thf(5354,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i,V_loc_2: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5273]) ).
thf(5355,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5272]) ).
thf(5356,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5271]) ).
thf(5357,plain,
( ( ! [V_fun_2: $i,V_vname_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5270]) ).
thf(5358,plain,
( ( ! [V_pname_H_2: $i,V_fun_2: $i,V_vname_2: $i] :
( ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5269]) ).
thf(5359,plain,
( ( ! [V_b_H_2: $i,V_b_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_2 )
= ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_H_2 ) )
<=> ( V_b_2 = V_b_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5268]) ).
thf(5360,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5267]) ).
thf(5361,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_2 )
= ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(5362,plain,
( ( ! [V_y: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5265]) ).
thf(5363,plain,
( ( ! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5264]) ).
thf(5364,plain,
( ( ! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5263]) ).
thf(5365,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)],[5262]) ).
thf(5366,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5261]) ).
thf(5367,plain,
( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5260]) ).
thf(5368,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)],[5259]) ).
thf(5369,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)],[5258]) ).
thf(5370,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_d: $i,T_b: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(5371,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5256]) ).
thf(5372,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5255]) ).
thf(5373,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)],[5254]) ).
thf(5374,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(5375,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5252]) ).
thf(5376,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(5377,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(copy,[status(thm)],[5250]) ).
thf(5378,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(5379,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5248]) ).
thf(5380,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(copy,[status(thm)],[5247]) ).
thf(5381,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5246]) ).
thf(5382,plain,
( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
( ( V_a_2 != V_c_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(5383,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(5384,plain,
( ( ! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(5385,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(5386,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(5387,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(5388,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(5389,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(5390,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(5391,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(5392,plain,
( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(5393,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(5394,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ) )
= $true ),
inference(copy,[status(thm)],[5233]) ).
thf(5395,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)],[5232]) ).
thf(5396,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5231]) ).
thf(5397,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5230]) ).
thf(5398,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5229]) ).
thf(5399,plain,
( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(copy,[status(thm)],[5228]) ).
thf(5400,plain,
( ( ! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5227]) ).
thf(5401,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5226]) ).
thf(5402,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5225]) ).
thf(5403,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)],[5224]) ).
thf(5404,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)],[5223]) ).
thf(5405,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)],[5222]) ).
thf(5406,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)],[5221]) ).
thf(5407,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)],[5220]) ).
thf(5408,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5219]) ).
thf(5409,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5218]) ).
thf(5410,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5217]) ).
thf(5411,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)],[5216]) ).
thf(5412,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)],[5215]) ).
thf(5413,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5214]) ).
thf(5414,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5213]) ).
thf(5415,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5212]) ).
thf(5416,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)],[5211]) ).
thf(5417,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5210]) ).
thf(5418,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Qa_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5209]) ).
thf(5419,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5208]) ).
thf(5420,plain,
( ( ~ ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5314]) ).
thf(5421,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5345]) ).
thf(5422,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5330]) ).
thf(5423,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)],[5385]) ).
thf(5424,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)],[5393]) ).
thf(5425,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)],[5365]) ).
thf(5426,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)],[5373]) ).
thf(5427,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5420]) ).
thf(5428,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)],[5389]) ).
thf(5429,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OCond @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5347]) ).
thf(5430,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)],[5410]) ).
thf(5431,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5322]) ).
thf(5432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5404]) ).
thf(5433,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)],[5411]) ).
thf(5434,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)],[5409]) ).
thf(5435,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ ( hAPP @ SX4 @ SX0 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5401]) ).
thf(5436,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)],[5392]) ).
thf(5437,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)],[5369]) ).
thf(5438,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)],[5324]) ).
thf(5439,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)],[5370]) ).
thf(5440,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)],[5386]) ).
thf(5441,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)],[5405]) ).
thf(5442,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)],[5378]) ).
thf(5443,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5326]) ).
thf(5444,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5317]) ).
thf(5445,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SX2 @ SX1 @ SX0 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5334]) ).
thf(5446,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)],[5388]) ).
thf(5447,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Com_Ocom_OBODY @ SX1 )
= ( c_Com_Ocom_OBODY @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5321]) ).
thf(5448,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5359]) ).
thf(5449,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5403]) ).
thf(5450,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5325]) ).
thf(5451,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)],[5402]) ).
thf(5452,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)],[5413]) ).
thf(5453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OCond @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5348]) ).
thf(5454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OAss @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5358]) ).
thf(5455,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5316]) ).
thf(5456,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)],[5384]) ).
thf(5457,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX4: $i] :
( ( SX1
!= ( hAPP @ c_Nat_OSuc @ SX4 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX4 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5320]) ).
thf(5458,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)],[5352]) ).
thf(5459,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ SX3 @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5328]) ).
thf(5460,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)],[5408]) ).
thf(5461,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)],[5375]) ).
thf(5462,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OSemi @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5341]) ).
thf(5463,plain,
( ( ! [SX0: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5343]) ).
thf(5464,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)],[5382]) ).
thf(5465,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5318]) ).
thf(5466,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5360]) ).
thf(5467,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)],[5366]) ).
thf(5468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SX4 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SX3 @ SX2 @ SX1 ) @ SX5 ) )
| ( ( hAPP @ SX4 @ ( hAPP @ c_Nat_OSuc @ SX0 ) )
= ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ ( hAPP @ SX4 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5346]) ).
thf(5469,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OWhile @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5355]) ).
thf(5470,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)],[5414]) ).
thf(5471,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OAss @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5357]) ).
thf(5472,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5331]) ).
thf(5473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5361]) ).
thf(5474,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)],[5381]) ).
thf(5475,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)],[5364]) ).
thf(5476,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)],[5367]) ).
thf(5477,plain,
( ( ! [SX0: $i] :
( ( c_Com_Ocom_OBODY @ SX0 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[5344]) ).
thf(5478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( c_Natural_Oevaln @ SX1 @ SX2 @ SX3 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX5 @ SX1 ) @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5337]) ).
thf(5479,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OSemi @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5340]) ).
thf(5480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5339]) ).
thf(5481,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)],[5374]) ).
thf(5482,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OWhile @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5356]) ).
thf(5483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OCall @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5349]) ).
thf(5484,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ SX3 @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ SX3 @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5319]) ).
thf(5485,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5323]) ).
thf(5486,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5362]) ).
thf(5487,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 )
| ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5329]) ).
thf(5488,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OLocal @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5354]) ).
thf(5489,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)],[5376]) ).
thf(5490,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5327]) ).
thf(5491,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OLocal @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5353]) ).
thf(5492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OCall @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5350]) ).
thf(5493,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)],[5368]) ).
thf(5494,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)],[5383]) ).
thf(5495,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SX5 @ SX4 @ SX3 )
| ( ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
= ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5398]) ).
thf(5496,plain,
! [SV1: $i] :
( ( ! [SY462: $i,SY463: $i,SY464: $i] :
( ( c_Nat_Onat_Onat__case @ SY464 @ SY463 @ SY462 @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ SY462 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5332]) ).
thf(5497,plain,
! [SV2: $i] :
( ( ! [SY465: $i,SY466: $i,SY467: $i,SY468: $i,SY469: $i,SY470: $i,SY471: $i,SY472: $i,SY473: $i] :
( ( c_Com_Ocom_Ocom__case @ SY473 @ SY472 @ SY471 @ SY470 @ SY469 @ SY468 @ SY467 @ SY466 @ SY465 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SY466 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5333]) ).
thf(5498,plain,
! [SV3: $i] :
( ( ! [SY474: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY474 @ SV3 @ SY474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5335]) ).
thf(5499,plain,
! [SV4: $i] :
( ( ! [SY475: $i,SY476: $i,SY477: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY477 @ SY476 @ SY475 ) @ ( hAPP @ c_Nat_OSuc @ SV4 ) )
= ( hAPP @ ( hAPP @ SY475 @ SV4 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY477 @ SY476 @ SY475 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5336]) ).
thf(5500,plain,
! [SV5: $i] :
( ( ! [SY478: $i,SY479: $i,SY480: $i,SY481: $i,SY482: $i,SY483: $i,SY484: $i,SY485: $i,SY486: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY486 @ SY485 @ SY484 @ SY483 @ SY482 @ SY481 @ SY480 @ SY479 @ SY478 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SY479 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5338]) ).
thf(5501,plain,
! [SV6: $i] :
( ( ! [SY487: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY487 @ SV6 @ SY487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5342]) ).
thf(5502,plain,
! [SV7: $i] :
( ( ! [SY488: $i] :
( ( hAPP @ ( c_Option_Othe @ SY488 ) @ ( hAPP @ ( c_Option_Ooption_OSome @ SY488 ) @ SV7 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5351]) ).
thf(5503,plain,
! [SV8: $i] :
( ( ! [SY489: $i,SY490: $i,SY491: $i,SY492: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY492 @ SY491 @ SY490 ) @ SY489 ) @ ( hAPP @ c_Nat_OSuc @ SV8 ) )
= ( hAPP @ ( hAPP @ SY490 @ SY489 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY492 @ SY491 @ SY490 ) @ SY489 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5504,plain,
! [SV9: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY494 ) @ SY493 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY494 ) @ SY493 ) @ SV9 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY494 ) @ SY493 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5371]) ).
thf(5505,plain,
! [SV10: $i] :
( ( ! [SY495: $i,SY496: $i,SY497: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY497 ) @ SY496 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY497 ) @ SY495 ) @ SV10 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY497 ) @ SY495 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY497 ) @ SY496 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5372]) ).
thf(5506,plain,
! [SV11: $i] :
( ( ! [SY498: $i,SY499: $i,SY500: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY500 @ SY499 ) @ SY498 ) @ SV11 ) @ ( hAPP @ SY498 @ SV11 ) )
= SY498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(5507,plain,
! [SV12: $i] :
( ( ! [SY501: $i,SY502: $i,SY503: $i,SY504: $i,SY505: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY505 @ SY504 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY505 @ SY504 ) @ SY503 ) @ SY502 ) @ SY501 ) ) @ SY502 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY505 @ SY504 ) @ SY503 ) @ SY502 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5379]) ).
thf(5508,plain,
! [SV13: $i] :
( ( ! [SY506: $i,SY507: $i,SY508: $i,SY509: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY509 @ SY508 ) @ SY507 ) @ SY506 ) @ SV13 ) @ SY506 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5380]) ).
thf(5509,plain,
! [SV14: $i] :
( ( ! [SY510: $i,SY511: $i,SY512: $i,SY513: $i,SY514: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY514 @ SY513 @ SY512 @ SY511 ) @ SY510 ) @ SV14 )
= ( hAPP @ SY511 @ ( hAPP @ SY510 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5387]) ).
thf(5510,plain,
! [SV15: $i] :
( ( ! [SY515: $i,SY516: $i,SY517: $i,SY518: $i,SY519: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY519 @ SY518 @ SY517 @ SY516 ) @ SY515 ) @ SV15 )
= ( hAPP @ SY516 @ ( hAPP @ SY515 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5390]) ).
thf(5511,plain,
! [SV16: $i] :
( ( ! [SY520: $i,SY521: $i,SY522: $i,SY523: $i,SY524: $i,SY525: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY525 @ SY524 @ SY523 @ SY522 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY521 @ SY525 @ SY523 @ SY520 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY521 @ SY524 @ SY523 @ ( hAPP @ ( c_Fun_Ocomp @ SY525 @ SY524 @ SY521 @ SY522 ) @ SY520 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5391]) ).
thf(5512,plain,
! [SV17: $i] :
( ( ! [SY526: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY526 ) @ SV17 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5394]) ).
thf(5513,plain,
! [SV18: $i] :
( ( ! [SY527: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY527 ) @ SV18 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5395]) ).
thf(5514,plain,
! [SV19: $i] :
( ( ! [SY528: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY528 ) @ SV19 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5396]) ).
thf(5515,plain,
! [SV20: $i] :
( ( ! [SY529: $i,SY530: $i,SY531: $i,SY532: $i,SY533: $i,SY534: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY534 @ SY533 @ SY532 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY534 @ SY531 @ SY533 ) @ SY530 ) @ SY529 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY534 @ SY531 @ SY532 ) @ SY530 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY531 @ SY533 @ SY532 ) @ SY529 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(5516,plain,
! [SV21: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY536 @ SY535 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY535 @ SY536 ) @ SV21 ) )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(5517,plain,
! [SV22: $i] :
( ( ! [SY537: $i,SY538: $i,SY539: $i] :
( ( hAPP @ SY539 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY538 @ SY538 ) @ SY537 ) @ SY539 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY538 @ SY538 ) @ SY537 ) @ SY539 ) @ ( hAPP @ SY539 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5400]) ).
thf(5518,plain,
! [SV23: $i] :
( ( ! [SY540: $i,SY541: $i,SY542: $i,SY543: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY543 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY543 @ SY542 ) @ SY541 ) @ SY540 ) ) @ SY541 ) @ SV23 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY543 @ SY542 ) @ SY541 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5406]) ).
thf(5519,plain,
! [SV24: $i] :
( ( ! [SY544: $i,SY545: $i,SY546: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY546 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY546 ) @ SY545 ) @ SY544 ) ) @ SV24 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY546 ) @ SY545 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY546 ) @ SY544 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5407]) ).
thf(5520,plain,
! [SV25: $i] :
( ( ! [SY547: $i] :
( ( hAPP @ ( c_List_Orev @ SY547 ) @ ( hAPP @ ( c_List_Orev @ SY547 ) @ SV25 ) )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(5521,plain,
! [SV26: $i] :
( ( ! [SY548: $i] :
( ( hAPP @ ( c_COMBI @ SY548 ) @ SV26 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5415]) ).
thf(5522,plain,
! [SV27: $i] :
( ( ! [SY549: $i,SY550: $i,SY551: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY551 @ SY550 ) @ SY549 ) @ SV27 )
= SY549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5416]) ).
thf(5523,plain,
! [SV28: $i] :
( ( ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i,SY556: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY556 @ SY555 @ SY554 ) @ SY553 ) @ SY552 ) @ SV28 )
= ( hAPP @ SY553 @ ( hAPP @ SY552 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5417]) ).
thf(5524,plain,
! [SV29: $i] :
( ( ! [SY557: $i,SY558: $i,SY559: $i,SY560: $i,SY561: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY561 @ SY560 @ SY559 ) @ SY558 ) @ SY557 ) @ SV29 )
= ( hAPP @ ( hAPP @ SY558 @ SV29 ) @ SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5418]) ).
thf(5525,plain,
! [SV30: $i] :
( ( ! [SY562: $i,SY563: $i,SY564: $i,SY565: $i,SY566: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY566 @ SY565 @ SY564 ) @ SY563 ) @ SY562 ) @ SV30 )
= ( hAPP @ ( hAPP @ SY563 @ SV30 ) @ ( hAPP @ SY562 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5419]) ).
thf(5526,plain,
! [SV31: $i] :
( ( ! [SY567: $i,SY568: $i,SY569: $i,SY570: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY570 @ SY569 ) @ SY568 @ SY567 @ SV31 )
| ~ ! [SY571: $i] :
( ~ ( c_Natural_Oevaln @ SY570 @ SY568 @ SY567 @ SY571 )
| ~ ( c_Natural_Oevaln @ SY569 @ SY571 @ SY567 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5421]) ).
thf(5527,plain,
! [SV32: $i] :
( ( ! [SY572: $i,SY573: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY573 ) @ SY572 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY573 ) ) @ SY572 @ SV32 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY573 ) ) @ SY572 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY573 ) @ SY572 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5422]) ).
thf(5528,plain,
! [SV33: $i] :
( ( ! [SY574: $i,SY575: $i,SY576: $i,SY577: $i,SY578: $i] :
~ ( ~ ( ( SY578 != SY577 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY576 @ SY575 ) @ SY574 ) @ SY577 ) @ SV33 ) @ SY578 )
= SV33 ) )
| ~ ( ~ ( ( SY578 != SY577 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY576 @ SY575 ) @ SY574 ) @ SY577 ) @ SV33 ) @ SY578 )
= ( hAPP @ SY574 @ SY578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5423]) ).
thf(5529,plain,
! [SV34: $i] :
( ( ! [SY579: $i,SY580: $i,SY581: $i,SY582: $i,SY583: $i,SY584: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY584 @ SY583 @ SY582 @ SY581 ) @ SY580 )
!= SY579 )
| ( ( hAPP @ SY581 @ ( hAPP @ SY580 @ SV34 ) )
= ( hAPP @ SY579 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5530,plain,
! [SV35: $i] :
( ( ! [SY585: $i,SY586: $i,SY587: $i,SY588: $i,SY589: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY589 @ SY588 ) @ SY587 ) @ SY586 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY589 @ SY588 ) @ SY585 ) @ SV35 ) )
| ~ ( ( SY587 != SY585 )
| ( SY586 != SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5531,plain,
! [SV36: $i] :
( ( ! [SY590: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY590 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
| ( SY590 = SV36 ) )
| ~ ( ( SY590 != SV36 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY590 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(5532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5533,plain,
! [SV37: $i] :
( ( ! [SY591: $i,SY592: $i,SY593: $i,SY594: $i,SY595: $i,SY596: $i,SY597: $i,SY598: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY598 @ SY597 @ SY596 @ SY595 ) @ SY594 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY593 @ SY597 @ SY596 @ SY592 ) @ SY591 ) )
| ( ( hAPP @ SY595 @ ( hAPP @ SY594 @ SV37 ) )
= ( hAPP @ SY592 @ ( hAPP @ SY591 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5428]) ).
thf(5534,plain,
! [SV38: $i] :
( ( ! [SY599: $i,SY600: $i,SY601: $i] :
( ( c_Com_Ocom_OCond @ SY601 @ SY600 @ SY599 )
!= ( c_Com_Ocom_OBODY @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5429]) ).
thf(5535,plain,
! [SV39: $i] :
( ( ! [SY602: $i,SY603: $i,SY604: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY604 ) @ SY603 ) @ SY602 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY604 ) @ SV39 ) @ SY602 ) )
| ( SY603 = SV39 ) )
| ~ ( ( SY603 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY604 ) @ SY603 ) @ SY602 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY604 ) @ SV39 ) @ SY602 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5430]) ).
thf(5536,plain,
! [SV40: $i] :
( ( SV40
!= ( hAPP @ c_Nat_OSuc @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(5537,plain,
! [SV41: $i] :
( ( ! [SY605: $i,SY606: $i] :
( SY606
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY605 ) @ SV41 ) @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5432]) ).
thf(5538,plain,
! [SV42: $i] :
( ( ! [SY607: $i,SY608: $i,SY609: $i,SY610: $i,SY611: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY611 ) @ SY610 ) @ SY609 )
!= SY608 )
| ( SY607
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY611 ) @ SY609 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY611 ) @ SY610 ) @ SY607 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY611 ) @ SY608 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5433]) ).
thf(5539,plain,
! [SV43: $i] :
( ( ! [SY612: $i,SY613: $i,SY614: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY614 ) @ SY613 ) @ SY612 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY614 ) @ SY613 ) @ SV43 ) )
| ( SY612 = SV43 ) )
| ~ ( ( SY612 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY614 ) @ SY613 ) @ SY612 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY614 ) @ SY613 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5434]) ).
thf(5540,plain,
! [SV44: $i] :
( ( ! [SY615: $i,SY616: $i,SY617: $i,SY618: $i,SY619: $i,SY620: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY620 @ SY619 @ SY618 @ SY617 @ SY616 @ SY615 )
| ( ( hAPP @ ( hAPP @ SY618 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5435]) ).
thf(5541,plain,
! [SV45: $i] :
( ( ! [SY621: $i,SY622: $i,SY623: $i,SY624: $i,SY625: $i,SY626: $i,SY627: $i,SY628: $i,SY629: $i,SY630: $i] :
( ( ( hAPP @ SY630 @ ( hAPP @ SY629 @ SY628 ) )
!= ( hAPP @ SY627 @ ( hAPP @ SY626 @ SY625 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY624 @ SY623 @ SY622 @ SY630 ) @ SY629 ) @ SY628 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY621 @ SY623 @ SV45 @ SY627 ) @ SY626 ) @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5436]) ).
thf(5542,plain,
! [SV46: $i] :
( ( ! [SY631: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY631 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
| ( SY631 = SV46 ) )
| ~ ( ( SY631 != SV46 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY631 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5437]) ).
thf(5543,plain,
! [SV47: $i] :
( ( ! [SY632: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY632 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
| ( SY632 = SV47 ) )
| ~ ( ( SY632 != SV47 )
| ( ( hAPP @ c_Nat_OSuc @ SY632 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5438]) ).
thf(5544,plain,
! [SV48: $i] :
( ( ! [SY633: $i,SY634: $i,SY635: $i,SY636: $i,SY637: $i,SY638: $i] :
( ( SY638 != SY637 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY636 @ SY635 @ SY634 @ SY633 @ SV48 ) @ SY638 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY636 @ SY635 @ SY634 @ SY633 @ SV48 ) @ SY637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5439]) ).
thf(5545,plain,
! [SV49: $i] :
( ( ! [SY639: $i,SY640: $i,SY641: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY641 @ SY640 @ SY639 )
| ( ( hAPP @ ( hAPP @ SY640 @ SV49 ) @ SV49 )
= SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(5546,plain,
! [SV50: $i] :
( ( ! [SY642: $i,SY643: $i,SY644: $i,SY645: $i,SY646: $i] :
( ~ ( ( SY646 != SY645 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY644 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY644 @ SY643 ) @ SY646 ) @ SY642 ) ) @ SY645 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY644 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY644 @ SY643 ) @ SY645 ) @ SV50 ) ) @ SY646 ) @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(5547,plain,
! [SV51: $i] :
( ( ! [SY647: $i,SY648: $i,SY649: $i,SY650: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY650 @ SY649 ) @ SY648 ) @ SY647 ) @ SV51 )
!= SY648 )
| ( ( hAPP @ SY648 @ SY647 )
= SV51 ) )
| ~ ( ( ( hAPP @ SY648 @ SY647 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY650 @ SY649 ) @ SY648 ) @ SY647 ) @ SV51 )
= SY648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5442]) ).
thf(5548,plain,
! [SV52: $i] :
( ( ! [SY651: $i,SY652: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY652 ) @ SY651 @ SV52 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY652 ) ) @ SY651 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5443]) ).
thf(5549,plain,
! [SV53: $i] :
( ( ! [SY653: $i,SY654: $i,SY655: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY655 ) ) @ SY654 @ SY653 @ SV53 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY655 ) @ SY654 @ ( hAPP @ c_Nat_OSuc @ SY653 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5444]) ).
thf(5550,plain,
! [SV54: $i] :
( ( ! [SY656: $i,SY657: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY657 @ SY656 @ SV54 )
| ( SV54 = SY657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5445]) ).
thf(5551,plain,
! [SV55: $i] :
( ( ! [SY658: $i,SY659: $i,SY660: $i,SY661: $i,SY662: $i,SY663: $i,SY664: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY664 @ SY663 @ SY662 @ SY661 ) @ SY660 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY659 @ SY663 @ SY662 @ SY658 ) @ SV55 ) )
| ! [SY665: $i] :
( ( hAPP @ SY661 @ ( hAPP @ SY660 @ SY665 ) )
= ( hAPP @ SY658 @ ( hAPP @ SV55 @ SY665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5446]) ).
thf(5552,plain,
! [SV56: $i] :
( ( ! [SY666: $i] :
~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SY666 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
| ( SY666 = SV56 ) )
| ~ ( ( SY666 != SV56 )
| ( ( c_Com_Ocom_OBODY @ SY666 )
= ( c_Com_Ocom_OBODY @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5447]) ).
thf(5553,plain,
! [SV57: $i] :
( ( ! [SY667: $i,SY668: $i,SY669: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY669 @ SY668 ) @ SY667 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY669 @ SY668 ) @ SV57 ) )
| ( SY667 = SV57 ) )
| ~ ( ( SY667 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY669 @ SY668 ) @ SY667 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY669 @ SY668 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5448]) ).
thf(5554,plain,
! [SV58: $i] :
( ( ! [SY670: $i,SY671: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY671 ) @ SY670 ) @ SV58 )
!= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5449]) ).
thf(5555,plain,
! [SV59: $i] :
( ( ! [SY672: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY672 )
!= ( hAPP @ c_Nat_OSuc @ SV59 ) )
| ( SY672 = SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5450]) ).
thf(5556,plain,
! [SV60: $i] :
( ( ! [SY673: $i,SY674: $i,SY675: $i,SY676: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY676 ) @ SY675 ) @ SY674 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY676 ) @ SY673 ) @ SV60 ) )
| ~ ( ( SY675 != SY673 )
| ( SY674 != SV60 ) ) )
| ~ ( ~ ~ ( ( SY675 != SY673 )
| ( SY674 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY676 ) @ SY675 ) @ SY674 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY676 ) @ SY673 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5451]) ).
thf(5557,plain,
! [SV61: $i] :
( ( ! [SY677: $i,SY678: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY678 ) @ SY677 )
!= SV61 )
| ( SY677
= ( hAPP @ ( c_List_Orev @ SY678 ) @ SV61 ) ) )
| ~ ( ( SY677
!= ( hAPP @ ( c_List_Orev @ SY678 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SY678 ) @ SY677 )
= SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5452]) ).
thf(5558,plain,
! [SV62: $i] :
( ( ! [SY679: $i,SY680: $i,SY681: $i] :
( ( c_Com_Ocom_OBODY @ SY681 )
!= ( c_Com_Ocom_OCond @ SY680 @ SY679 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5453]) ).
thf(5559,plain,
! [SV63: $i] :
( ( ! [SY682: $i,SY683: $i] :
( ( c_Com_Ocom_OAss @ SY683 @ SY682 )
!= ( c_Com_Ocom_OBODY @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5454]) ).
thf(5560,plain,
! [SV64: $i] :
( ( ! [SY684: $i] :
( ~ ! [SY685: $i] :
( ( hAPP @ SY684 @ SY685 )
= ( hAPP @ SV64 @ SY685 ) )
| ( SY684 = SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5455]) ).
thf(5561,plain,
! [SV65: $i] :
( ( ! [SY686: $i,SY687: $i,SY688: $i,SY689: $i] :
( ( ( hAPP @ SY689 @ SY688 )
!= SY687 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY686 @ SV65 ) @ SY689 ) @ SY688 ) @ SY687 )
= SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5456]) ).
thf(5562,plain,
! [SV66: $i] :
( ( ! [SY690: $i,SY691: $i,SY692: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY692 ) @ SY691 @ SY690 @ SV66 )
| ~ ! [SY693: $i] :
( ( SY690
!= ( hAPP @ c_Nat_OSuc @ SY693 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY692 ) ) @ SY691 @ SY693 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5457]) ).
thf(5563,plain,
! [SV67: $i] :
( ( ! [SY694: $i,SY695: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY695 ) @ SY694 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY695 ) @ SV67 ) )
| ( SY694 = SV67 ) )
| ~ ( ( SY694 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY695 ) @ SY694 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY695 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5458]) ).
thf(5564,plain,
! [SV68: $i] :
( ( ! [SY696: $i,SY697: $i,SY698: $i] :
( ~ ( c_Natural_Oevaln @ SY698 @ SY697 @ SY696 @ SV68 )
| ( c_Natural_Oevalc @ SY698 @ SY697 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5459]) ).
thf(5565,plain,
! [SV69: $i] :
( ( ! [SY699: $i,SY700: $i,SY701: $i,SY702: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY701 ) @ SY700 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY699 ) @ SV69 ) )
| ~ ! [SY703: $i] :
~ ( ~ ( ( SY701
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY699 ) @ SY703 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY703 ) @ SY700 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY701 ) @ SY703 )
!= SY699 )
| ( SY700
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY703 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY704: $i] :
~ ( ~ ( ( SY701
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY699 ) @ SY704 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY704 ) @ SY700 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY701 ) @ SY704 )
!= SY699 )
| ( SY700
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY704 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY701 ) @ SY700 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY702 ) @ SY699 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5460]) ).
thf(5566,plain,
! [SV70: $i] :
( ( ! [SY705: $i,SY706: $i,SY707: $i,SY708: $i,SY709: $i] :
( ~ ( c_Typedef_Otype__definition @ SY709 @ SY708 @ SY707 @ SY706 @ SY705 )
| ( ( hAPP @ SY706 @ ( hAPP @ SY707 @ SV70 ) )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5461]) ).
thf(5567,plain,
! [SV71: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ( c_Com_Ocom_OSemi @ SY711 @ SY710 )
!= ( c_Com_Ocom_OBODY @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5462]) ).
thf(5568,plain,
! [SV72: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5569,plain,
! [SV73: $i] :
( ( ! [SY712: $i,SY713: $i,SY714: $i,SY715: $i,SY716: $i,SY717: $i] :
( ~ ( ( SY717 != SY716 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY715 @ SY714 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY715 @ SY714 ) @ SY713 ) @ SY717 ) @ SY712 ) ) @ SY716 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY715 @ SY714 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY715 @ SY714 ) @ SY713 ) @ SY716 ) @ SV73 ) ) @ SY717 ) @ SY712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5464]) ).
thf(5570,plain,
! [SV74: $i] :
( ( ! [SY718: $i,SY719: $i,SY720: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY720 ) @ SY719 @ ( hAPP @ c_Nat_OSuc @ SY718 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY720 ) ) @ SY719 @ SY718 @ SV74 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY720 ) ) @ SY719 @ SY718 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY720 ) @ SY719 @ ( hAPP @ c_Nat_OSuc @ SY718 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5465]) ).
thf(5571,plain,
! [SV75: $i] :
( ( ! [SY721: $i,SY722: $i,SY723: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY723 @ SY722 ) @ SY721 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY723 @ SY722 ) @ SV75 ) )
| ( SY721 = SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5466]) ).
thf(5572,plain,
! [SV76: $i] :
( ( ! [SY724: $i,SY725: $i,SY726: $i,SY727: $i,SY728: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY728 @ SY727 ) @ SY726 ) @ SY725 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY728 @ SY727 ) @ SY724 ) @ SV76 ) )
| ~ ( ( SY726 != SY724 )
| ( SY725 != SV76 ) ) )
| ~ ( ~ ~ ( ( SY726 != SY724 )
| ( SY725 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY728 @ SY727 ) @ SY726 ) @ SY725 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY728 @ SY727 ) @ SY724 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5467]) ).
thf(5573,plain,
! [SV77: $i] :
( ( ! [SY729: $i,SY730: $i,SY731: $i,SY732: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SY732 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY731 @ SY730 @ SY729 ) @ SX5 ) )
| ( ( hAPP @ SY732 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SY729 @ SV77 ) @ ( hAPP @ SY732 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5468]) ).
thf(5574,plain,
! [SV78: $i] :
( ( ! [SY734: $i,SY735: $i] :
( ( c_Com_Ocom_OWhile @ SY735 @ SY734 )
!= ( c_Com_Ocom_OBODY @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(5575,plain,
! [SV79: $i] :
( ( ! [SY736: $i,SY737: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY737 ) @ SY736 )
!= ( hAPP @ ( c_List_Orev @ SY737 ) @ SV79 ) )
| ( SY736 = SV79 ) )
| ~ ( ( SY736 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SY737 ) @ SY736 )
= ( hAPP @ ( c_List_Orev @ SY737 ) @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(5576,plain,
! [SV80: $i] :
( ( ! [SY738: $i,SY739: $i] :
( ( c_Com_Ocom_OBODY @ SY739 )
!= ( c_Com_Ocom_OAss @ SY738 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5471]) ).
thf(5577,plain,
! [SV81: $i] :
( ( ! [SY740: $i,SY741: $i] :
( ~ ( c_Natural_Oevalc @ SY741 @ SY740 @ SV81 )
| ~ ! [SY742: $i] :
~ ( c_Natural_Oevaln @ SY741 @ SY740 @ SY742 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5472]) ).
thf(5578,plain,
! [SV82: $i] :
( ( ! [SY743: $i,SY744: $i,SY745: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY745 @ SY744 ) @ SY743 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY745 @ SY744 ) @ SV82 ) )
| ( SY743 = SV82 ) )
| ~ ( ( SY743 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY745 @ SY744 ) @ SY743 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY745 @ SY744 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5473]) ).
thf(5579,plain,
! [SV83: $i] :
( ( ! [SY746: $i,SY747: $i,SY748: $i,SY749: $i,SY750: $i] :
~ ( ~ ( ( SY750 != SY749 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY748 @ SY747 ) @ SY746 ) @ SY749 ) @ SV83 ) @ SY750 )
= SV83 ) )
| ~ ( ~ ( ( SY750 != SY749 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY748 @ SY747 ) @ SY746 ) @ SY749 ) @ SV83 ) @ SY750 )
= ( hAPP @ SY746 @ SY750 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(5580,plain,
! [SV84: $i] :
( ( ! [SY751: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY751 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
| ( SY751 = SV84 ) )
| ~ ( ( SY751 != SV84 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY751 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5475]) ).
thf(5581,plain,
! [SV85: $i] :
( ( ! [SY752: $i,SY753: $i,SY754: $i,SY755: $i,SY756: $i] :
( ( SY756 != SY755 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY754 @ SY753 @ SY752 ) @ SV85 ) @ SY756 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY754 @ SY753 @ SY752 ) @ SV85 ) @ SY755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(5582,plain,
! [SV86: $i] :
( ( ( c_Com_Ocom_OBODY @ SV86 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(5583,plain,
! [SV87: $i] :
( ( ! [SY757: $i,SY758: $i,SY759: $i,SY760: $i,SY761: $i] :
( ~ ( c_Natural_Oevaln @ SY761 @ SY760 @ SY759 @ SY758 )
| ~ ( c_Natural_Oevaln @ SY757 @ SY758 @ SY759 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY761 @ SY757 ) @ SY760 @ SY759 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5478]) ).
thf(5584,plain,
! [SV88: $i] :
( ( ! [SY762: $i,SY763: $i] :
( ( c_Com_Ocom_OBODY @ SY763 )
!= ( c_Com_Ocom_OSemi @ SY762 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5479]) ).
thf(5585,plain,
! [SV89: $i] :
( ( ! [SY764: $i,SY765: $i,SY766: $i,SY767: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY767 @ SY766 ) @ SY765 @ SY764 @ SV89 )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY767 @ SY765 @ SY764 @ SY768 )
| ~ ( c_Natural_Oevaln @ SY766 @ SY768 @ SY764 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY769: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY767 @ SY765 @ SY764 @ SY769 )
| ~ ( c_Natural_Oevaln @ SY766 @ SY769 @ SY764 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY767 @ SY766 ) @ SY765 @ SY764 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5480]) ).
thf(5586,plain,
! [SV90: $i] :
( ( ! [SY770: $i,SY771: $i,SY772: $i,SY773: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY773 @ SY772 @ SY771 )
| ( ( hAPP @ ( hAPP @ SY771 @ SY770 ) @ ( hAPP @ ( hAPP @ SY771 @ SY770 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SY771 @ SY770 ) @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5481]) ).
thf(5587,plain,
! [SV91: $i] :
( ( ! [SY774: $i,SY775: $i] :
( ( c_Com_Ocom_OBODY @ SY775 )
!= ( c_Com_Ocom_OWhile @ SY774 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5482]) ).
thf(5588,plain,
! [SV92: $i] :
( ( ! [SY776: $i,SY777: $i,SY778: $i] :
( ( c_Com_Ocom_OBODY @ SY778 )
!= ( c_Com_Ocom_OCall @ SY777 @ SY776 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5483]) ).
thf(5589,plain,
! [SV93: $i] :
( ( ! [SY779: $i,SY780: $i,SY781: $i] :
( ~ ( c_Natural_Oevaln @ SY781 @ SY780 @ SY779 @ SV93 )
| ( c_Natural_Oevaln @ SY781 @ SY780 @ ( hAPP @ c_Nat_OSuc @ SY779 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5484]) ).
thf(5590,plain,
! [SV94: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV94 )
!= SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5485]) ).
thf(5591,plain,
! [SV95: $i] :
( ( ! [SY782: $i,SY783: $i,SY784: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY784 @ SY783 ) @ SY782 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY784 @ SY783 ) @ SV95 ) )
| ( SY782 = SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(5592,plain,
! [SV96: $i] :
( ( ! [SY785: $i,SY786: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SY786 @ SY785 @ SV96 )
| ~ ! [SY787: $i] :
~ ( c_Natural_Oevaln @ SY786 @ SY785 @ SY787 @ SV96 ) )
| ~ ( ~ ~ ! [SY788: $i] :
~ ( c_Natural_Oevaln @ SY786 @ SY785 @ SY788 @ SV96 )
| ( c_Natural_Oevalc @ SY786 @ SY785 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(5593,plain,
! [SV97: $i] :
( ( ! [SY789: $i,SY790: $i,SY791: $i] :
( ( c_Com_Ocom_OLocal @ SY791 @ SY790 @ SY789 )
!= ( c_Com_Ocom_OBODY @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5488]) ).
thf(5594,plain,
! [SV98: $i] :
( ( ! [SY792: $i,SY793: $i,SY794: $i,SY795: $i,SY796: $i,SY797: $i] :
( ~ ( c_Typedef_Otype__definition @ SY797 @ SY796 @ SY795 @ SY794 @ SY793 )
| ~ ( ~ ( ( ( hAPP @ SY795 @ SY792 )
!= ( hAPP @ SY795 @ SV98 ) )
| ( SY792 = SV98 ) )
| ~ ( ( SY792 != SV98 )
| ( ( hAPP @ SY795 @ SY792 )
= ( hAPP @ SY795 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5489]) ).
thf(5595,plain,
! [SV99: $i] :
( ( ! [SY798: $i,SY799: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY799 ) ) @ SY798 @ SV99 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY799 ) @ SY798 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5490]) ).
thf(5596,plain,
! [SV100: $i] :
( ( ! [SY800: $i,SY801: $i,SY802: $i] :
( ( c_Com_Ocom_OBODY @ SY802 )
!= ( c_Com_Ocom_OLocal @ SY801 @ SY800 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5491]) ).
thf(5597,plain,
! [SV101: $i] :
( ( ! [SY803: $i,SY804: $i,SY805: $i] :
( ( c_Com_Ocom_OCall @ SY805 @ SY804 @ SY803 )
!= ( c_Com_Ocom_OBODY @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5598,plain,
! [SV102: $i] :
( ( ! [SY806: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY806 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
| ( SY806 = SV102 ) )
| ~ ( ( SY806 != SV102 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY806 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(5599,plain,
! [SV103: $i] :
( ( ! [SY807: $i,SY808: $i,SY809: $i,SY810: $i,SY811: $i] :
( ~ ( ( SY811 != SY810 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY809 @ SY808 ) @ SY807 ) @ SY810 ) @ SV103 ) @ SY811 )
= ( hAPP @ SY807 @ SY811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(5600,plain,
! [SV104: $i] :
( ( ! [SY812: $i,SY813: $i,SY814: $i,SY815: $i,SY816: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY816 @ SY815 @ SY814 )
| ( ( hAPP @ ( hAPP @ SY814 @ SY813 ) @ ( hAPP @ ( hAPP @ SY814 @ SY812 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SY814 @ SY812 ) @ ( hAPP @ ( hAPP @ SY814 @ SY813 ) @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5495]) ).
thf(5601,plain,
! [SV1: $i,SV105: $i] :
( ( ! [SY817: $i,SY818: $i] :
( ( c_Nat_Onat_Onat__case @ SY818 @ SY817 @ SV105 @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ SV105 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5496]) ).
thf(5602,plain,
! [SV2: $i,SV106: $i] :
( ( ! [SY819: $i,SY820: $i,SY821: $i,SY822: $i,SY823: $i,SY824: $i,SY825: $i,SY826: $i] :
( ( c_Com_Ocom_Ocom__case @ SY826 @ SY825 @ SY824 @ SY823 @ SY822 @ SY821 @ SY820 @ SY819 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SY819 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5497]) ).
thf(5603,plain,
! [SV3: $i,SV107: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV107 @ SV3 @ SV107 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5498]) ).
thf(5604,plain,
! [SV4: $i,SV108: $i] :
( ( ! [SY827: $i,SY828: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY828 @ SY827 @ SV108 ) @ ( hAPP @ c_Nat_OSuc @ SV4 ) )
= ( hAPP @ ( hAPP @ SV108 @ SV4 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY828 @ SY827 @ SV108 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(5605,plain,
! [SV5: $i,SV109: $i] :
( ( ! [SY829: $i,SY830: $i,SY831: $i,SY832: $i,SY833: $i,SY834: $i,SY835: $i,SY836: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY836 @ SY835 @ SY834 @ SY833 @ SY832 @ SY831 @ SY830 @ SY829 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SY829 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(5606,plain,
! [SV6: $i,SV110: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV110 @ SV6 @ SV110 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(5607,plain,
! [SV7: $i,SV111: $i] :
( ( ( hAPP @ ( c_Option_Othe @ SV111 ) @ ( hAPP @ ( c_Option_Ooption_OSome @ SV111 ) @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(5608,plain,
! [SV8: $i,SV112: $i] :
( ( ! [SY837: $i,SY838: $i,SY839: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY839 @ SY838 @ SY837 ) @ SV112 ) @ ( hAPP @ c_Nat_OSuc @ SV8 ) )
= ( hAPP @ ( hAPP @ SY837 @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY839 @ SY838 @ SY837 ) @ SV112 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5609,plain,
! [SV9: $i,SV113: $i] :
( ( ! [SY840: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SV113 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SV113 ) @ SV9 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY840 ) @ SV113 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5504]) ).
thf(5610,plain,
! [SV10: $i,SV114: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY842 ) @ SY841 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY842 ) @ SV114 ) @ SV10 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY842 ) @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY842 ) @ SY841 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5505]) ).
thf(5611,plain,
! [SV11: $i,SV115: $i] :
( ( ! [SY843: $i,SY844: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY844 @ SY843 ) @ SV115 ) @ SV11 ) @ ( hAPP @ SV115 @ SV11 ) )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5612,plain,
! [SV12: $i,SV116: $i] :
( ( ! [SY845: $i,SY846: $i,SY847: $i,SY848: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY848 @ SY847 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY848 @ SY847 ) @ SY846 ) @ SY845 ) @ SV116 ) ) @ SY845 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY848 @ SY847 ) @ SY846 ) @ SY845 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5507]) ).
thf(5613,plain,
! [SV13: $i,SV117: $i] :
( ( ! [SY849: $i,SY850: $i,SY851: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY851 @ SY850 ) @ SY849 ) @ SV117 ) @ SV13 ) @ SV117 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5508]) ).
thf(5614,plain,
! [SV14: $i,SV118: $i] :
( ( ! [SY852: $i,SY853: $i,SY854: $i,SY855: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY855 @ SY854 @ SY853 @ SY852 ) @ SV118 ) @ SV14 )
= ( hAPP @ SY852 @ ( hAPP @ SV118 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5509]) ).
thf(5615,plain,
! [SV15: $i,SV119: $i] :
( ( ! [SY856: $i,SY857: $i,SY858: $i,SY859: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY859 @ SY858 @ SY857 @ SY856 ) @ SV119 ) @ SV15 )
= ( hAPP @ SY856 @ ( hAPP @ SV119 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5510]) ).
thf(5616,plain,
! [SV16: $i,SV120: $i] :
( ( ! [SY860: $i,SY861: $i,SY862: $i,SY863: $i,SY864: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY864 @ SY863 @ SY862 @ SY861 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY860 @ SY864 @ SY862 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY860 @ SY863 @ SY862 @ ( hAPP @ ( c_Fun_Ocomp @ SY864 @ SY863 @ SY860 @ SY861 ) @ SV120 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5617,plain,
! [SV17: $i,SV121: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV121 ) @ SV17 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5512]) ).
thf(5618,plain,
! [SV18: $i,SV122: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV122 ) @ SV18 )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(5619,plain,
! [SV19: $i,SV123: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV123 ) @ SV19 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(5620,plain,
! [SV20: $i,SV124: $i] :
( ( ! [SY865: $i,SY866: $i,SY867: $i,SY868: $i,SY869: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY869 @ SY868 @ SY867 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY869 @ SY866 @ SY868 ) @ SY865 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY869 @ SY866 @ SY867 ) @ SY865 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY866 @ SY868 @ SY867 ) @ SV124 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5515]) ).
thf(5621,plain,
! [SV21: $i,SV125: $i] :
( ( ! [SY870: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY870 @ SV125 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV125 @ SY870 ) @ SV21 ) )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5516]) ).
thf(5622,plain,
! [SV22: $i,SV126: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ( hAPP @ SY872 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY871 @ SY871 ) @ SV126 ) @ SY872 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY871 @ SY871 ) @ SV126 ) @ SY872 ) @ ( hAPP @ SY872 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(5623,plain,
! [SV23: $i,SV127: $i] :
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY875 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY875 @ SY874 ) @ SY873 ) @ SV127 ) ) @ SY873 ) @ SV23 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY875 @ SY874 ) @ SY873 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5518]) ).
thf(5624,plain,
! [SV24: $i,SV128: $i] :
( ( ! [SY876: $i,SY877: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY877 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY877 ) @ SY876 ) @ SV128 ) ) @ SV24 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY877 ) @ SY876 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY877 ) @ SV128 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5519]) ).
thf(5625,plain,
! [SV25: $i,SV129: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV129 ) @ ( hAPP @ ( c_List_Orev @ SV129 ) @ SV25 ) )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5520]) ).
thf(5626,plain,
! [SV26: $i,SV130: $i] :
( ( ( hAPP @ ( c_COMBI @ SV130 ) @ SV26 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(5627,plain,
! [SV27: $i,SV131: $i] :
( ( ! [SY878: $i,SY879: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY879 @ SY878 ) @ SV131 ) @ SV27 )
= SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5522]) ).
thf(5628,plain,
! [SV28: $i,SV132: $i] :
( ( ! [SY880: $i,SY881: $i,SY882: $i,SY883: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY883 @ SY882 @ SY881 ) @ SY880 ) @ SV132 ) @ SV28 )
= ( hAPP @ SY880 @ ( hAPP @ SV132 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5629,plain,
! [SV29: $i,SV133: $i] :
( ( ! [SY884: $i,SY885: $i,SY886: $i,SY887: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY887 @ SY886 @ SY885 ) @ SY884 ) @ SV133 ) @ SV29 )
= ( hAPP @ ( hAPP @ SY884 @ SV29 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5630,plain,
! [SV30: $i,SV134: $i] :
( ( ! [SY888: $i,SY889: $i,SY890: $i,SY891: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY891 @ SY890 @ SY889 ) @ SY888 ) @ SV134 ) @ SV30 )
= ( hAPP @ ( hAPP @ SY888 @ SV30 ) @ ( hAPP @ SV134 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5631,plain,
! [SV31: $i,SV135: $i] :
( ( ! [SY892: $i,SY893: $i,SY894: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY894 @ SY893 ) @ SY892 @ SV135 @ SV31 )
| ~ ! [SY895: $i] :
( ~ ( c_Natural_Oevaln @ SY894 @ SY892 @ SV135 @ SY895 )
| ~ ( c_Natural_Oevaln @ SY893 @ SY895 @ SV135 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5526]) ).
thf(5632,plain,
! [SV32: $i,SV136: $i] :
( ( ! [SY896: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY896 ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY896 ) ) @ SV136 @ SV32 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY896 ) ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY896 ) @ SV136 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(5633,plain,
! [SV33: $i,SV137: $i] :
( ( ! [SY897: $i,SY898: $i,SY899: $i,SY900: $i] :
~ ( ~ ( ( SY900 != SY899 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY898 @ SY897 ) @ SV137 ) @ SY899 ) @ SV33 ) @ SY900 )
= SV33 ) )
| ~ ( ~ ( ( SY900 != SY899 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY898 @ SY897 ) @ SV137 ) @ SY899 ) @ SV33 ) @ SY900 )
= ( hAPP @ SV137 @ SY900 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(5634,plain,
! [SV34: $i,SV138: $i] :
( ( ! [SY901: $i,SY902: $i,SY903: $i,SY904: $i,SY905: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY905 @ SY904 @ SY903 @ SY902 ) @ SY901 )
!= SV138 )
| ( ( hAPP @ SY902 @ ( hAPP @ SY901 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5635,plain,
! [SV35: $i,SV139: $i] :
( ( ! [SY906: $i,SY907: $i,SY908: $i,SY909: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY909 @ SY908 ) @ SY907 ) @ SY906 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY909 @ SY908 ) @ SV139 ) @ SV35 ) )
| ~ ( ( SY907 != SV139 )
| ( SY906 != SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(5636,plain,
! [SV36: $i,SV140: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
| ( SV140 = SV36 ) )
| ~ ( ( SV140 != SV36 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(5637,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5638,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5639,plain,
! [SV37: $i,SV141: $i] :
( ( ! [SY910: $i,SY911: $i,SY912: $i,SY913: $i,SY914: $i,SY915: $i,SY916: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY916 @ SY915 @ SY914 @ SY913 ) @ SY912 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY911 @ SY915 @ SY914 @ SY910 ) @ SV141 ) )
| ( ( hAPP @ SY913 @ ( hAPP @ SY912 @ SV37 ) )
= ( hAPP @ SY910 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5640,plain,
! [SV38: $i,SV142: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ( c_Com_Ocom_OCond @ SY918 @ SY917 @ SV142 )
!= ( c_Com_Ocom_OBODY @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5534]) ).
thf(5641,plain,
! [SV39: $i,SV143: $i] :
( ( ! [SY919: $i,SY920: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY920 ) @ SY919 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY920 ) @ SV39 ) @ SV143 ) )
| ( SY919 = SV39 ) )
| ~ ( ( SY919 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY920 ) @ SY919 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY920 ) @ SV39 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5642,plain,
! [SV40: $i] :
( ( SV40
= ( hAPP @ c_Nat_OSuc @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5643,plain,
! [SV41: $i,SV144: $i] :
( ( ! [SY921: $i] :
( SY921
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV144 ) @ SV41 ) @ SY921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5644,plain,
! [SV42: $i,SV145: $i] :
( ( ! [SY922: $i,SY923: $i,SY924: $i,SY925: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY925 ) @ SY924 ) @ SY923 )
!= SY922 )
| ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY925 ) @ SY923 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY925 ) @ SY924 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY925 ) @ SY922 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5645,plain,
! [SV43: $i,SV146: $i] :
( ( ! [SY926: $i,SY927: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY927 ) @ SY926 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY927 ) @ SY926 ) @ SV43 ) )
| ( SV146 = SV43 ) )
| ~ ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY927 ) @ SY926 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY927 ) @ SY926 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(5646,plain,
! [SV44: $i,SV147: $i] :
( ( ! [SY928: $i,SY929: $i,SY930: $i,SY931: $i,SY932: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY932 @ SY931 @ SY930 @ SY929 @ SY928 @ SV147 )
| ( ( hAPP @ ( hAPP @ SY930 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5647,plain,
! [SV45: $i,SV148: $i] :
( ( ! [SY933: $i,SY934: $i,SY935: $i,SY936: $i,SY937: $i,SY938: $i,SY939: $i,SY940: $i,SY941: $i] :
( ( ( hAPP @ SY941 @ ( hAPP @ SY940 @ SY939 ) )
!= ( hAPP @ SY938 @ ( hAPP @ SY937 @ SY936 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY935 @ SY934 @ SY933 @ SY941 ) @ SY940 ) @ SY939 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SY934 @ SV45 @ SY938 ) @ SY937 ) @ SY936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5541]) ).
thf(5648,plain,
! [SV46: $i,SV149: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
| ( SV149 = SV46 ) )
| ~ ( ( SV149 != SV46 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5542]) ).
thf(5649,plain,
! [SV47: $i,SV150: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
| ( SV150 = SV47 ) )
| ~ ( ( SV150 != SV47 )
| ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(5650,plain,
! [SV48: $i,SV151: $i] :
( ( ! [SY942: $i,SY943: $i,SY944: $i,SY945: $i,SY946: $i] :
( ( SY946 != SY945 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY944 @ SY943 @ SY942 @ SV151 @ SV48 ) @ SY946 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY944 @ SY943 @ SY942 @ SV151 @ SV48 ) @ SY945 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(5651,plain,
! [SV49: $i,SV152: $i] :
( ( ! [SY947: $i,SY948: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY948 @ SY947 @ SV152 )
| ( ( hAPP @ ( hAPP @ SY947 @ SV49 ) @ SV49 )
= SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(5652,plain,
! [SV50: $i,SV153: $i] :
( ( ! [SY949: $i,SY950: $i,SY951: $i,SY952: $i] :
( ~ ( ( SY952 != SY951 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY950 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY950 @ SY949 ) @ SY952 ) @ SV153 ) ) @ SY951 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY950 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY950 @ SY949 ) @ SY951 ) @ SV50 ) ) @ SY952 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5653,plain,
! [SV51: $i,SV154: $i] :
( ( ! [SY953: $i,SY954: $i,SY955: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY955 @ SY954 ) @ SY953 ) @ SV154 ) @ SV51 )
!= SY953 )
| ( ( hAPP @ SY953 @ SV154 )
= SV51 ) )
| ~ ( ( ( hAPP @ SY953 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY955 @ SY954 ) @ SY953 ) @ SV154 ) @ SV51 )
= SY953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(5654,plain,
! [SV52: $i,SV155: $i] :
( ( ! [SY956: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY956 ) @ SV155 @ SV52 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY956 ) ) @ SV155 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(5655,plain,
! [SV53: $i,SV156: $i] :
( ( ! [SY957: $i,SY958: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY958 ) ) @ SY957 @ SV156 @ SV53 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY958 ) @ SY957 @ ( hAPP @ c_Nat_OSuc @ SV156 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(5656,plain,
! [SV54: $i,SV157: $i] :
( ( ! [SY959: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY959 @ SV157 @ SV54 )
| ( SV54 = SY959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(5657,plain,
! [SV55: $i,SV158: $i] :
( ( ! [SY960: $i,SY961: $i,SY962: $i,SY963: $i,SY964: $i,SY965: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY965 @ SY964 @ SY963 @ SY962 ) @ SY961 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY960 @ SY964 @ SY963 @ SV158 ) @ SV55 ) )
| ! [SY966: $i] :
( ( hAPP @ SY962 @ ( hAPP @ SY961 @ SY966 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY966 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5551]) ).
thf(5658,plain,
! [SV56: $i,SV159: $i] :
( ( ~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SV159 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
| ( SV159 = SV56 ) )
| ~ ( ( SV159 != SV56 )
| ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5552]) ).
thf(5659,plain,
! [SV57: $i,SV160: $i] :
( ( ! [SY967: $i,SY968: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY968 @ SY967 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY968 @ SY967 ) @ SV57 ) )
| ( SV160 = SV57 ) )
| ~ ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY968 @ SY967 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY968 @ SY967 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5553]) ).
thf(5660,plain,
! [SV58: $i,SV161: $i] :
( ( ! [SY969: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY969 ) @ SV161 ) @ SV58 )
!= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5661,plain,
! [SV59: $i,SV162: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV162 )
!= ( hAPP @ c_Nat_OSuc @ SV59 ) )
| ( SV162 = SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(5662,plain,
! [SV60: $i,SV163: $i] :
( ( ! [SY970: $i,SY971: $i,SY972: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY972 ) @ SY971 ) @ SY970 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY972 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SY971 != SV163 )
| ( SY970 != SV60 ) ) )
| ~ ( ~ ~ ( ( SY971 != SV163 )
| ( SY970 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY972 ) @ SY971 ) @ SY970 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY972 ) @ SV163 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(5663,plain,
! [SV61: $i,SV164: $i] :
( ( ! [SY973: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY973 ) @ SV164 )
!= SV61 )
| ( SV164
= ( hAPP @ ( c_List_Orev @ SY973 ) @ SV61 ) ) )
| ~ ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SY973 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SY973 ) @ SV164 )
= SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(5664,plain,
! [SV62: $i,SV165: $i] :
( ( ! [SY974: $i,SY975: $i] :
( ( c_Com_Ocom_OBODY @ SY975 )
!= ( c_Com_Ocom_OCond @ SY974 @ SV165 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5558]) ).
thf(5665,plain,
! [SV63: $i,SV166: $i] :
( ( ! [SY976: $i] :
( ( c_Com_Ocom_OAss @ SY976 @ SV166 )
!= ( c_Com_Ocom_OBODY @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5559]) ).
thf(5666,plain,
! [SV64: $i,SV167: $i] :
( ( ~ ! [SY977: $i] :
( ( hAPP @ SV167 @ SY977 )
= ( hAPP @ SV64 @ SY977 ) )
| ( SV167 = SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5667,plain,
! [SV65: $i,SV168: $i] :
( ( ! [SY978: $i,SY979: $i,SY980: $i] :
( ( ( hAPP @ SY980 @ SY979 )
!= SY978 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SY980 ) @ SY979 ) @ SY978 )
= SY980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5668,plain,
! [SV66: $i,SV169: $i] :
( ( ! [SY981: $i,SY982: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY982 ) @ SY981 @ SV169 @ SV66 )
| ~ ! [SY983: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY983 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY982 ) ) @ SY981 @ SY983 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5562]) ).
thf(5669,plain,
! [SV67: $i,SV170: $i] :
( ( ! [SY984: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY984 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY984 ) @ SV67 ) )
| ( SV170 = SV67 ) )
| ~ ( ( SV170 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY984 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY984 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5563]) ).
thf(5670,plain,
! [SV68: $i,SV171: $i] :
( ( ! [SY985: $i,SY986: $i] :
( ~ ( c_Natural_Oevaln @ SY986 @ SY985 @ SV171 @ SV68 )
| ( c_Natural_Oevalc @ SY986 @ SY985 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5564]) ).
thf(5671,plain,
! [SV69: $i,SV172: $i] :
( ( ! [SY987: $i,SY988: $i,SY989: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY988 ) @ SY987 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY990: $i] :
~ ( ~ ( ( SY988
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SV172 ) @ SY990 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY990 ) @ SY987 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY988 ) @ SY990 )
!= SV172 )
| ( SY987
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY990 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY991: $i] :
~ ( ~ ( ( SY988
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SV172 ) @ SY991 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY991 ) @ SY987 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY988 ) @ SY991 )
!= SV172 )
| ( SY987
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY991 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SY988 ) @ SY987 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY989 ) @ SV172 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5672,plain,
! [SV70: $i,SV173: $i] :
( ( ! [SY992: $i,SY993: $i,SY994: $i,SY995: $i] :
( ~ ( c_Typedef_Otype__definition @ SY995 @ SY994 @ SY993 @ SY992 @ SV173 )
| ( ( hAPP @ SY992 @ ( hAPP @ SY993 @ SV70 ) )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(5673,plain,
! [SV71: $i,SV174: $i] :
( ( ! [SY996: $i] :
( ( c_Com_Ocom_OSemi @ SY996 @ SV174 )
!= ( c_Com_Ocom_OBODY @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5674,plain,
! [SV72: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OBODY @ SV72 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(5675,plain,
! [SV73: $i,SV175: $i] :
( ( ! [SY997: $i,SY998: $i,SY999: $i,SY1000: $i,SY1001: $i] :
( ~ ( ( SY1001 != SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY999 @ SY998 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY999 @ SY998 ) @ SY997 ) @ SY1001 ) @ SV175 ) ) @ SY1000 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY999 @ SY998 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY999 @ SY998 ) @ SY997 ) @ SY1000 ) @ SV73 ) ) @ SY1001 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5569]) ).
thf(5676,plain,
! [SV74: $i,SV176: $i] :
( ( ! [SY1002: $i,SY1003: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1003 ) @ SY1002 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1003 ) ) @ SY1002 @ SV176 @ SV74 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1003 ) ) @ SY1002 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1003 ) @ SY1002 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(5677,plain,
! [SV75: $i,SV177: $i] :
( ( ! [SY1004: $i,SY1005: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1005 @ SY1004 ) @ SV177 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1005 @ SY1004 ) @ SV75 ) )
| ( SV177 = SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5678,plain,
! [SV76: $i,SV178: $i] :
( ( ! [SY1006: $i,SY1007: $i,SY1008: $i,SY1009: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1009 @ SY1008 ) @ SY1007 ) @ SY1006 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1009 @ SY1008 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SY1007 != SV178 )
| ( SY1006 != SV76 ) ) )
| ~ ( ~ ~ ( ( SY1007 != SV178 )
| ( SY1006 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1009 @ SY1008 ) @ SY1007 ) @ SY1006 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1009 @ SY1008 ) @ SV178 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5679,plain,
! [SV77: $i,SV179: $i] :
( ( ! [SY1010: $i,SY1011: $i,SY1012: $i] :
( ~ ! [SY1013: $i] :
( ( hAPP @ SY1012 @ SY1013 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1011 @ SY1010 @ SV179 ) @ SY1013 ) )
| ( ( hAPP @ SY1012 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SY1012 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5573]) ).
thf(5680,plain,
! [SV78: $i,SV180: $i] :
( ( ! [SY1014: $i] :
( ( c_Com_Ocom_OWhile @ SY1014 @ SV180 )
!= ( c_Com_Ocom_OBODY @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5681,plain,
! [SV79: $i,SV181: $i] :
( ( ! [SY1015: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1015 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SY1015 ) @ SV79 ) )
| ( SV181 = SV79 ) )
| ~ ( ( SV181 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SY1015 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SY1015 ) @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5682,plain,
! [SV80: $i,SV182: $i] :
( ( ! [SY1016: $i] :
( ( c_Com_Ocom_OBODY @ SY1016 )
!= ( c_Com_Ocom_OAss @ SV182 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(5683,plain,
! [SV81: $i,SV183: $i] :
( ( ! [SY1017: $i] :
( ~ ( c_Natural_Oevalc @ SY1017 @ SV183 @ SV81 )
| ~ ! [SY1018: $i] :
~ ( c_Natural_Oevaln @ SY1017 @ SV183 @ SY1018 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(5684,plain,
! [SV82: $i,SV184: $i] :
( ( ! [SY1019: $i,SY1020: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1020 @ SY1019 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1020 @ SY1019 ) @ SV82 ) )
| ( SV184 = SV82 ) )
| ~ ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY1020 @ SY1019 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY1020 @ SY1019 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(5685,plain,
! [SV83: $i,SV185: $i] :
( ( ! [SY1021: $i,SY1022: $i,SY1023: $i,SY1024: $i] :
~ ( ~ ( ( SY1024 != SY1023 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1022 @ SY1021 ) @ SV185 ) @ SY1023 ) @ SV83 ) @ SY1024 )
= SV83 ) )
| ~ ( ~ ( ( SY1024 != SY1023 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1022 @ SY1021 ) @ SV185 ) @ SY1023 ) @ SV83 ) @ SY1024 )
= ( hAPP @ SV185 @ SY1024 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5579]) ).
thf(5686,plain,
! [SV84: $i,SV186: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
| ( SV186 = SV84 ) )
| ~ ( ( SV186 != SV84 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5580]) ).
thf(5687,plain,
! [SV85: $i,SV187: $i] :
( ( ! [SY1025: $i,SY1026: $i,SY1027: $i,SY1028: $i] :
( ( SY1028 != SY1027 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1026 @ SY1025 @ SV187 ) @ SV85 ) @ SY1028 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1026 @ SY1025 @ SV187 ) @ SV85 ) @ SY1027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5581]) ).
thf(5688,plain,
! [SV86: $i] :
( ( ( c_Com_Ocom_OBODY @ SV86 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(5689,plain,
! [SV87: $i,SV188: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i,SY1032: $i] :
( ~ ( c_Natural_Oevaln @ SY1032 @ SY1031 @ SY1030 @ SY1029 )
| ~ ( c_Natural_Oevaln @ SV188 @ SY1029 @ SY1030 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1032 @ SV188 ) @ SY1031 @ SY1030 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5583]) ).
thf(5690,plain,
! [SV88: $i,SV189: $i] :
( ( ! [SY1033: $i] :
( ( c_Com_Ocom_OBODY @ SY1033 )
!= ( c_Com_Ocom_OSemi @ SV189 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(5691,plain,
! [SV89: $i,SV190: $i] :
( ( ! [SY1034: $i,SY1035: $i,SY1036: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1036 @ SY1035 ) @ SY1034 @ SV190 @ SV89 )
| ~ ! [SY1037: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1036 @ SY1034 @ SV190 @ SY1037 )
| ~ ( c_Natural_Oevaln @ SY1035 @ SY1037 @ SV190 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY1038: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1036 @ SY1034 @ SV190 @ SY1038 )
| ~ ( c_Natural_Oevaln @ SY1035 @ SY1038 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1036 @ SY1035 ) @ SY1034 @ SV190 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(5692,plain,
! [SV90: $i,SV191: $i] :
( ( ! [SY1039: $i,SY1040: $i,SY1041: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1041 @ SY1040 @ SY1039 )
| ( ( hAPP @ ( hAPP @ SY1039 @ SV191 ) @ ( hAPP @ ( hAPP @ SY1039 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SY1039 @ SV191 ) @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(5693,plain,
! [SV91: $i,SV192: $i] :
( ( ! [SY1042: $i] :
( ( c_Com_Ocom_OBODY @ SY1042 )
!= ( c_Com_Ocom_OWhile @ SV192 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(5694,plain,
! [SV92: $i,SV193: $i] :
( ( ! [SY1043: $i,SY1044: $i] :
( ( c_Com_Ocom_OBODY @ SY1044 )
!= ( c_Com_Ocom_OCall @ SY1043 @ SV193 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(5695,plain,
! [SV93: $i,SV194: $i] :
( ( ! [SY1045: $i,SY1046: $i] :
( ~ ( c_Natural_Oevaln @ SY1046 @ SY1045 @ SV194 @ SV93 )
| ( c_Natural_Oevaln @ SY1046 @ SY1045 @ ( hAPP @ c_Nat_OSuc @ SV194 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(5696,plain,
! [SV94: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV94 )
= SV94 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(5697,plain,
! [SV95: $i,SV195: $i] :
( ( ! [SY1047: $i,SY1048: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1048 @ SY1047 ) @ SV195 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1048 @ SY1047 ) @ SV95 ) )
| ( SV195 = SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(5698,plain,
! [SV96: $i,SV196: $i] :
( ( ! [SY1049: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SY1049 @ SV196 @ SV96 )
| ~ ! [SY1050: $i] :
~ ( c_Natural_Oevaln @ SY1049 @ SV196 @ SY1050 @ SV96 ) )
| ~ ( ~ ~ ! [SY1051: $i] :
~ ( c_Natural_Oevaln @ SY1049 @ SV196 @ SY1051 @ SV96 )
| ( c_Natural_Oevalc @ SY1049 @ SV196 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(5699,plain,
! [SV97: $i,SV197: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
( ( c_Com_Ocom_OLocal @ SY1053 @ SY1052 @ SV197 )
!= ( c_Com_Ocom_OBODY @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(5700,plain,
! [SV98: $i,SV198: $i] :
( ( ! [SY1054: $i,SY1055: $i,SY1056: $i,SY1057: $i,SY1058: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1058 @ SY1057 @ SY1056 @ SY1055 @ SY1054 )
| ~ ( ~ ( ( ( hAPP @ SY1056 @ SV198 )
!= ( hAPP @ SY1056 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SY1056 @ SV198 )
= ( hAPP @ SY1056 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5594]) ).
thf(5701,plain,
! [SV99: $i,SV199: $i] :
( ( ! [SY1059: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1059 ) ) @ SV199 @ SV99 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1059 ) @ SV199 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5595]) ).
thf(5702,plain,
! [SV100: $i,SV200: $i] :
( ( ! [SY1060: $i,SY1061: $i] :
( ( c_Com_Ocom_OBODY @ SY1061 )
!= ( c_Com_Ocom_OLocal @ SY1060 @ SV200 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(5703,plain,
! [SV101: $i,SV201: $i] :
( ( ! [SY1062: $i,SY1063: $i] :
( ( c_Com_Ocom_OCall @ SY1063 @ SY1062 @ SV201 )
!= ( c_Com_Ocom_OBODY @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(5704,plain,
! [SV102: $i,SV202: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
| ( SV202 = SV102 ) )
| ~ ( ( SV202 != SV102 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5598]) ).
thf(5705,plain,
! [SV103: $i,SV203: $i] :
( ( ! [SY1064: $i,SY1065: $i,SY1066: $i,SY1067: $i] :
( ~ ( ( SY1067 != SY1066 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1065 @ SY1064 ) @ SV203 ) @ SY1066 ) @ SV103 ) @ SY1067 )
= ( hAPP @ SV203 @ SY1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5599]) ).
thf(5706,plain,
! [SV104: $i,SV204: $i] :
( ( ! [SY1068: $i,SY1069: $i,SY1070: $i,SY1071: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1071 @ SY1070 @ SY1069 )
| ( ( hAPP @ ( hAPP @ SY1069 @ SY1068 ) @ ( hAPP @ ( hAPP @ SY1069 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SY1069 @ SV204 ) @ ( hAPP @ ( hAPP @ SY1069 @ SY1068 ) @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5600]) ).
thf(5707,plain,
! [SV1: $i,SV105: $i,SV205: $i] :
( ( ! [SY1072: $i] :
( ( c_Nat_Onat_Onat__case @ SY1072 @ SV205 @ SV105 @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ SV105 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5708,plain,
! [SV2: $i,SV106: $i,SV206: $i] :
( ( ! [SY1073: $i,SY1074: $i,SY1075: $i,SY1076: $i,SY1077: $i,SY1078: $i,SY1079: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1079 @ SY1078 @ SY1077 @ SY1076 @ SY1075 @ SY1074 @ SY1073 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(5709,plain,
! [SV4: $i,SV108: $i,SV207: $i] :
( ( ! [SY1080: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1080 @ SV207 @ SV108 ) @ ( hAPP @ c_Nat_OSuc @ SV4 ) )
= ( hAPP @ ( hAPP @ SV108 @ SV4 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1080 @ SV207 @ SV108 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5604]) ).
thf(5710,plain,
! [SV5: $i,SV109: $i,SV208: $i] :
( ( ! [SY1081: $i,SY1082: $i,SY1083: $i,SY1084: $i,SY1085: $i,SY1086: $i,SY1087: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1087 @ SY1086 @ SY1085 @ SY1084 @ SY1083 @ SY1082 @ SY1081 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(5711,plain,
! [SV8: $i,SV112: $i,SV209: $i] :
( ( ! [SY1088: $i,SY1089: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1089 @ SY1088 @ SV209 ) @ SV112 ) @ ( hAPP @ c_Nat_OSuc @ SV8 ) )
= ( hAPP @ ( hAPP @ SV209 @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1089 @ SY1088 @ SV209 ) @ SV112 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5608]) ).
thf(5712,plain,
! [SV9: $i,SV113: $i,SV210: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV210 ) @ SV113 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV210 ) @ SV113 ) @ SV9 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV210 ) @ SV113 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5609]) ).
thf(5713,plain,
! [SV10: $i,SV114: $i,SV211: $i] :
( ( ! [SY1090: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1090 ) @ SV211 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1090 ) @ SV114 ) @ SV10 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1090 ) @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1090 ) @ SV211 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(5714,plain,
! [SV11: $i,SV115: $i,SV212: $i] :
( ( ! [SY1091: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1091 @ SV212 ) @ SV115 ) @ SV11 ) @ ( hAPP @ SV115 @ SV11 ) )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5715,plain,
! [SV12: $i,SV116: $i,SV213: $i] :
( ( ! [SY1092: $i,SY1093: $i,SY1094: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1094 @ SY1093 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1094 @ SY1093 ) @ SY1092 ) @ SV213 ) @ SV116 ) ) @ SV213 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1094 @ SY1093 ) @ SY1092 ) @ SV213 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(5716,plain,
! [SV13: $i,SV117: $i,SV214: $i] :
( ( ! [SY1095: $i,SY1096: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1096 @ SY1095 ) @ SV214 ) @ SV117 ) @ SV13 ) @ SV117 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5613]) ).
thf(5717,plain,
! [SV14: $i,SV118: $i,SV215: $i] :
( ( ! [SY1097: $i,SY1098: $i,SY1099: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1099 @ SY1098 @ SY1097 @ SV215 ) @ SV118 ) @ SV14 )
= ( hAPP @ SV215 @ ( hAPP @ SV118 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5614]) ).
thf(5718,plain,
! [SV15: $i,SV119: $i,SV216: $i] :
( ( ! [SY1100: $i,SY1101: $i,SY1102: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1102 @ SY1101 @ SY1100 @ SV216 ) @ SV119 ) @ SV15 )
= ( hAPP @ SV216 @ ( hAPP @ SV119 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5615]) ).
thf(5719,plain,
! [SV16: $i,SV120: $i,SV217: $i] :
( ( ! [SY1103: $i,SY1104: $i,SY1105: $i,SY1106: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1106 @ SY1105 @ SY1104 @ SY1103 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1106 @ SY1104 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1105 @ SY1104 @ ( hAPP @ ( c_Fun_Ocomp @ SY1106 @ SY1105 @ SV217 @ SY1103 ) @ SV120 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5616]) ).
thf(5720,plain,
! [SV20: $i,SV124: $i,SV218: $i] :
( ( ! [SY1107: $i,SY1108: $i,SY1109: $i,SY1110: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1110 @ SY1109 @ SY1108 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1110 @ SY1107 @ SY1109 ) @ SV218 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1110 @ SY1107 @ SY1108 ) @ SV218 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1107 @ SY1109 @ SY1108 ) @ SV124 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5620]) ).
thf(5721,plain,
! [SV21: $i,SV125: $i,SV219: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV219 @ SV125 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV125 @ SV219 ) @ SV21 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5621]) ).
thf(5722,plain,
! [SV22: $i,SV126: $i,SV220: $i] :
( ( ! [SY1111: $i] :
( ( hAPP @ SY1111 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV220 @ SV220 ) @ SV126 ) @ SY1111 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV220 @ SV220 ) @ SV126 ) @ SY1111 ) @ ( hAPP @ SY1111 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5622]) ).
thf(5723,plain,
! [SV23: $i,SV127: $i,SV221: $i] :
( ( ! [SY1112: $i,SY1113: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1113 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1113 @ SY1112 ) @ SV221 ) @ SV127 ) ) @ SV221 ) @ SV23 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1113 @ SY1112 ) @ SV221 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(5724,plain,
! [SV24: $i,SV128: $i,SV222: $i] :
( ( ! [SY1114: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1114 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1114 ) @ SV222 ) @ SV128 ) ) @ SV24 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1114 ) @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1114 ) @ SV128 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5624]) ).
thf(5725,plain,
! [SV27: $i,SV131: $i,SV223: $i] :
( ( ! [SY1115: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1115 @ SV223 ) @ SV131 ) @ SV27 )
= SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5627]) ).
thf(5726,plain,
! [SV28: $i,SV132: $i,SV224: $i] :
( ( ! [SY1116: $i,SY1117: $i,SY1118: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1118 @ SY1117 @ SY1116 ) @ SV224 ) @ SV132 ) @ SV28 )
= ( hAPP @ SV224 @ ( hAPP @ SV132 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5628]) ).
thf(5727,plain,
! [SV29: $i,SV133: $i,SV225: $i] :
( ( ! [SY1119: $i,SY1120: $i,SY1121: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1121 @ SY1120 @ SY1119 ) @ SV225 ) @ SV133 ) @ SV29 )
= ( hAPP @ ( hAPP @ SV225 @ SV29 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(5728,plain,
! [SV30: $i,SV134: $i,SV226: $i] :
( ( ! [SY1122: $i,SY1123: $i,SY1124: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1124 @ SY1123 @ SY1122 ) @ SV226 ) @ SV134 ) @ SV30 )
= ( hAPP @ ( hAPP @ SV226 @ SV30 ) @ ( hAPP @ SV134 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(5729,plain,
! [SV31: $i,SV135: $i,SV227: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1126 @ SY1125 ) @ SV227 @ SV135 @ SV31 )
| ~ ! [SY1127: $i] :
( ~ ( c_Natural_Oevaln @ SY1126 @ SV227 @ SV135 @ SY1127 )
| ~ ( c_Natural_Oevaln @ SY1125 @ SY1127 @ SV135 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(5730,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(5731,plain,
! [SV33: $i,SV137: $i,SV229: $i] :
( ( ! [SY1128: $i,SY1129: $i,SY1130: $i] :
~ ( ~ ( ( SY1130 != SY1129 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1128 @ SV229 ) @ SV137 ) @ SY1129 ) @ SV33 ) @ SY1130 )
= SV33 ) )
| ~ ( ~ ( ( SY1130 != SY1129 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1128 @ SV229 ) @ SV137 ) @ SY1129 ) @ SV33 ) @ SY1130 )
= ( hAPP @ SV137 @ SY1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5633]) ).
thf(5732,plain,
! [SV34: $i,SV138: $i,SV230: $i] :
( ( ! [SY1131: $i,SY1132: $i,SY1133: $i,SY1134: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1134 @ SY1133 @ SY1132 @ SY1131 ) @ SV230 )
!= SV138 )
| ( ( hAPP @ SY1131 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(5733,plain,
! [SV35: $i,SV139: $i,SV231: $i] :
( ( ! [SY1135: $i,SY1136: $i,SY1137: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1137 @ SY1136 ) @ SY1135 ) @ SV231 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1137 @ SY1136 ) @ SV139 ) @ SV35 ) )
| ~ ( ( SY1135 != SV139 )
| ( SV231 != SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5635]) ).
thf(5734,plain,
! [SV36: $i,SV140: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
| ( SV140 = SV36 ) )
| ~ ( ( SV140 != SV36 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5735,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5637]) ).
thf(5736,plain,
( ( ! [SY1138: $i] :
( ~ ( v_P @ sK1_SX0 @ SY1138 )
| ! [SY1139: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY1139 )
| ( v_Q @ sK1_SX0 @ SY1139 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5638]) ).
thf(5737,plain,
! [SV37: $i,SV141: $i,SV232: $i] :
( ( ! [SY1140: $i,SY1141: $i,SY1142: $i,SY1143: $i,SY1144: $i,SY1145: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1145 @ SY1144 @ SY1143 @ SY1142 ) @ SY1141 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1140 @ SY1144 @ SY1143 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SY1142 @ ( hAPP @ SY1141 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(5738,plain,
! [SV38: $i,SV142: $i,SV233: $i] :
( ( ! [SY1146: $i] :
( ( c_Com_Ocom_OCond @ SY1146 @ SV233 @ SV142 )
!= ( c_Com_Ocom_OBODY @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(5739,plain,
! [SV39: $i,SV143: $i,SV234: $i] :
( ( ! [SY1147: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1147 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1147 ) @ SV39 ) @ SV143 ) )
| ( SV234 = SV39 ) )
| ~ ( ( SV234 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1147 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1147 ) @ SV39 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5641]) ).
thf(5740,plain,
! [SV41: $i,SV144: $i,SV235: $i] :
( ( SV235
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV144 ) @ SV41 ) @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5643]) ).
thf(5741,plain,
! [SV42: $i,SV145: $i,SV236: $i] :
( ( ! [SY1148: $i,SY1149: $i,SY1150: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1150 ) @ SY1149 ) @ SY1148 )
!= SV236 )
| ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1150 ) @ SY1148 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1150 ) @ SY1149 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1150 ) @ SV236 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(5742,plain,
! [SV43: $i,SV146: $i,SV237: $i] :
( ( ! [SY1151: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1151 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1151 ) @ SV237 ) @ SV43 ) )
| ( SV146 = SV43 ) )
| ~ ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1151 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1151 ) @ SV237 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5645]) ).
thf(5743,plain,
! [SV44: $i,SV147: $i,SV238: $i] :
( ( ! [SY1152: $i,SY1153: $i,SY1154: $i,SY1155: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1155 @ SY1154 @ SY1153 @ SY1152 @ SV238 @ SV147 )
| ( ( hAPP @ ( hAPP @ SY1153 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(5744,plain,
! [SV45: $i,SV148: $i,SV239: $i] :
( ( ! [SY1156: $i,SY1157: $i,SY1158: $i,SY1159: $i,SY1160: $i,SY1161: $i,SY1162: $i,SY1163: $i] :
( ( ( hAPP @ SY1163 @ ( hAPP @ SY1162 @ SY1161 ) )
!= ( hAPP @ SY1160 @ ( hAPP @ SY1159 @ SY1158 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1157 @ SY1156 @ SV239 @ SY1163 ) @ SY1162 ) @ SY1161 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SY1156 @ SV45 @ SY1160 ) @ SY1159 ) @ SY1158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5647]) ).
thf(5745,plain,
! [SV46: $i,SV149: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
| ( SV149 = SV46 ) )
| ~ ( ( SV149 != SV46 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5648]) ).
thf(5746,plain,
! [SV47: $i,SV150: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
| ( SV150 = SV47 ) )
| ~ ( ( SV150 != SV47 )
| ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5649]) ).
thf(5747,plain,
! [SV48: $i,SV151: $i,SV240: $i] :
( ( ! [SY1164: $i,SY1165: $i,SY1166: $i,SY1167: $i] :
( ( SY1167 != SY1166 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1165 @ SY1164 @ SV240 @ SV151 @ SV48 ) @ SY1167 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1165 @ SY1164 @ SV240 @ SV151 @ SV48 ) @ SY1166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(5748,plain,
! [SV49: $i,SV152: $i,SV241: $i] :
( ( ! [SY1168: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1168 @ SV241 @ SV152 )
| ( ( hAPP @ ( hAPP @ SV241 @ SV49 ) @ SV49 )
= SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(5749,plain,
! [SV50: $i,SV153: $i,SV242: $i] :
( ( ! [SY1169: $i,SY1170: $i,SY1171: $i] :
( ~ ( ( SY1171 != SY1170 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1169 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1169 @ SV242 ) @ SY1171 ) @ SV153 ) ) @ SY1170 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1169 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1169 @ SV242 ) @ SY1170 ) @ SV50 ) ) @ SY1171 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(5750,plain,
! [SV51: $i,SV154: $i,SV243: $i] :
( ( ! [SY1172: $i,SY1173: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1173 @ SY1172 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) )
| ~ ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1173 @ SY1172 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5653]) ).
thf(5751,plain,
! [SV52: $i,SV155: $i,SV244: $i] :
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV244 ) @ SV155 @ SV52 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV244 ) ) @ SV155 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(5752,plain,
! [SV53: $i,SV156: $i,SV245: $i] :
( ( ! [SY1174: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1174 ) ) @ SV245 @ SV156 @ SV53 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1174 ) @ SV245 @ ( hAPP @ c_Nat_OSuc @ SV156 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5655]) ).
thf(5753,plain,
! [SV54: $i,SV157: $i,SV246: $i] :
( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV246 @ SV157 @ SV54 )
| ( SV54 = SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5656]) ).
thf(5754,plain,
! [SV55: $i,SV158: $i,SV247: $i] :
( ( ! [SY1175: $i,SY1176: $i,SY1177: $i,SY1178: $i,SY1179: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1179 @ SY1178 @ SY1177 @ SY1176 ) @ SY1175 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SY1178 @ SY1177 @ SV158 ) @ SV55 ) )
| ! [SY966: $i] :
( ( hAPP @ SY1176 @ ( hAPP @ SY1175 @ SY966 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY966 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(5755,plain,
! [SV56: $i,SV159: $i] :
( ( ~ ( ( ( c_Com_Ocom_OBODY @ SV159 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
| ( SV159 = SV56 ) )
| ~ ( ( SV159 != SV56 )
| ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(5756,plain,
! [SV57: $i,SV160: $i,SV248: $i] :
( ( ! [SY1181: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1181 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1181 @ SV248 ) @ SV57 ) )
| ( SV160 = SV57 ) )
| ~ ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY1181 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY1181 @ SV248 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5757,plain,
! [SV58: $i,SV161: $i,SV249: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV249 ) @ SV161 ) @ SV58 )
!= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5660]) ).
thf(5758,plain,
! [SV59: $i,SV162: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV162 )
!= ( hAPP @ c_Nat_OSuc @ SV59 ) )
= $true )
| ( ( SV162 = SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5661]) ).
thf(5759,plain,
! [SV60: $i,SV163: $i,SV250: $i] :
( ( ! [SY1182: $i,SY1183: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1183 ) @ SY1182 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1183 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SY1182 != SV163 )
| ( SV250 != SV60 ) ) )
| ~ ( ~ ~ ( ( SY1182 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1183 ) @ SY1182 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1183 ) @ SV163 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5662]) ).
thf(5760,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
!= SV61 )
| ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) ) )
| ~ ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(5761,plain,
! [SV62: $i,SV165: $i,SV252: $i] :
( ( ! [SY1184: $i] :
( ( c_Com_Ocom_OBODY @ SY1184 )
!= ( c_Com_Ocom_OCond @ SV252 @ SV165 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5664]) ).
thf(5762,plain,
! [SV63: $i,SV166: $i,SV253: $i] :
( ( ( c_Com_Ocom_OAss @ SV253 @ SV166 )
!= ( c_Com_Ocom_OBODY @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5665]) ).
thf(5763,plain,
! [SV64: $i,SV167: $i] :
( ( ( ~ ! [SY977: $i] :
( ( hAPP @ SV167 @ SY977 )
= ( hAPP @ SV64 @ SY977 ) ) )
= $true )
| ( ( SV167 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5666]) ).
thf(5764,plain,
! [SV65: $i,SV168: $i,SV254: $i] :
( ( ! [SY1185: $i,SY1186: $i] :
( ( ( hAPP @ SY1186 @ SY1185 )
!= SV254 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SY1186 ) @ SY1185 ) @ SV254 )
= SY1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5765,plain,
! [SV66: $i,SV169: $i,SV255: $i] :
( ( ! [SY1187: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1187 ) @ SV255 @ SV169 @ SV66 )
| ~ ! [SY1188: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY1188 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1187 ) ) @ SV255 @ SY1188 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(5766,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
| ( SV170 = SV67 ) )
| ~ ( ( SV170 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5669]) ).
thf(5767,plain,
! [SV68: $i,SV171: $i,SV257: $i] :
( ( ! [SY1189: $i] :
( ~ ( c_Natural_Oevaln @ SY1189 @ SV257 @ SV171 @ SV68 )
| ( c_Natural_Oevalc @ SY1189 @ SV257 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5768,plain,
! [SV69: $i,SV172: $i,SV258: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1190 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1192: $i] :
~ ( ~ ( ( SY1190
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SV172 ) @ SY1192 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1192 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1190 ) @ SY1192 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1192 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ( ~ ( ( SY1190
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SV172 ) @ SY1193 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1193 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1190 ) @ SY1193 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1193 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SY1190 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1191 ) @ SV172 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5671]) ).
thf(5769,plain,
! [SV70: $i,SV173: $i,SV259: $i] :
( ( ! [SY1194: $i,SY1195: $i,SY1196: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1196 @ SY1195 @ SY1194 @ SV259 @ SV173 )
| ( ( hAPP @ SV259 @ ( hAPP @ SY1194 @ SV70 ) )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5672]) ).
thf(5770,plain,
! [SV71: $i,SV174: $i,SV260: $i] :
( ( ( c_Com_Ocom_OSemi @ SV260 @ SV174 )
!= ( c_Com_Ocom_OBODY @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5673]) ).
thf(5771,plain,
! [SV73: $i,SV175: $i,SV261: $i] :
( ( ! [SY1197: $i,SY1198: $i,SY1199: $i,SY1200: $i] :
( ~ ( ( SY1200 != SY1199 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1198 @ SY1197 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1198 @ SY1197 ) @ SV261 ) @ SY1200 ) @ SV175 ) ) @ SY1199 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1198 @ SY1197 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1198 @ SY1197 ) @ SV261 ) @ SY1199 ) @ SV73 ) ) @ SY1200 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5675]) ).
thf(5772,plain,
! [SV74: $i,SV176: $i,SV262: $i] :
( ( ! [SY1201: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1201 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1201 ) ) @ SV262 @ SV176 @ SV74 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1201 ) ) @ SV262 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1201 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(5773,plain,
! [SV75: $i,SV177: $i,SV263: $i] :
( ( ! [SY1202: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1202 @ SV263 ) @ SV177 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1202 @ SV263 ) @ SV75 ) )
| ( SV177 = SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5677]) ).
thf(5774,plain,
! [SV76: $i,SV178: $i,SV264: $i] :
( ( ! [SY1203: $i,SY1204: $i,SY1205: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1205 @ SY1204 ) @ SY1203 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1205 @ SY1204 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SY1203 != SV178 )
| ( SV264 != SV76 ) ) )
| ~ ( ~ ~ ( ( SY1203 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1205 @ SY1204 ) @ SY1203 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1205 @ SY1204 ) @ SV178 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5678]) ).
thf(5775,plain,
! [SV77: $i,SV179: $i,SV265: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
( ~ ! [SY1208: $i] :
( ( hAPP @ SY1207 @ SY1208 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1206 @ SV265 @ SV179 ) @ SY1208 ) )
| ( ( hAPP @ SY1207 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SY1207 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5679]) ).
thf(5776,plain,
! [SV78: $i,SV180: $i,SV266: $i] :
( ( ( c_Com_Ocom_OWhile @ SV266 @ SV180 )
!= ( c_Com_Ocom_OBODY @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(5777,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
| ( SV181 = SV79 ) )
| ~ ( ( SV181 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5778,plain,
! [SV80: $i,SV182: $i,SV268: $i] :
( ( ( c_Com_Ocom_OBODY @ SV268 )
!= ( c_Com_Ocom_OAss @ SV182 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(5779,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ~ ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 )
| ~ ! [SY1209: $i] :
~ ( c_Natural_Oevaln @ SV269 @ SV183 @ SY1209 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(5780,plain,
! [SV82: $i,SV184: $i,SV270: $i] :
( ( ! [SY1210: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1210 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1210 @ SV270 ) @ SV82 ) )
| ( SV184 = SV82 ) )
| ~ ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY1210 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY1210 @ SV270 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(5781,plain,
! [SV83: $i,SV185: $i,SV271: $i] :
( ( ! [SY1211: $i,SY1212: $i,SY1213: $i] :
~ ( ~ ( ( SY1213 != SY1212 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1211 @ SV271 ) @ SV185 ) @ SY1212 ) @ SV83 ) @ SY1213 )
= SV83 ) )
| ~ ( ~ ( ( SY1213 != SY1212 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1211 @ SV271 ) @ SV185 ) @ SY1212 ) @ SV83 ) @ SY1213 )
= ( hAPP @ SV185 @ SY1213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(5782,plain,
! [SV84: $i,SV186: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
| ( SV186 = SV84 ) )
| ~ ( ( SV186 != SV84 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5686]) ).
thf(5783,plain,
! [SV85: $i,SV187: $i,SV272: $i] :
( ( ! [SY1214: $i,SY1215: $i,SY1216: $i] :
( ( SY1216 != SY1215 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1214 @ SV272 @ SV187 ) @ SV85 ) @ SY1216 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1214 @ SV272 @ SV187 ) @ SV85 ) @ SY1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(5784,plain,
! [SV87: $i,SV188: $i,SV273: $i] :
( ( ! [SY1217: $i,SY1218: $i,SY1219: $i] :
( ~ ( c_Natural_Oevaln @ SY1219 @ SY1218 @ SY1217 @ SV273 )
| ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SY1217 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1219 @ SV188 ) @ SY1218 @ SY1217 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(5785,plain,
! [SV88: $i,SV189: $i,SV274: $i] :
( ( ( c_Com_Ocom_OBODY @ SV274 )
!= ( c_Com_Ocom_OSemi @ SV189 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(5786,plain,
! [SV89: $i,SV190: $i,SV275: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1221 @ SY1220 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1222: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1221 @ SV275 @ SV190 @ SY1222 )
| ~ ( c_Natural_Oevaln @ SY1220 @ SY1222 @ SV190 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY1223: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1221 @ SV275 @ SV190 @ SY1223 )
| ~ ( c_Natural_Oevaln @ SY1220 @ SY1223 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1221 @ SY1220 ) @ SV275 @ SV190 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5691]) ).
thf(5787,plain,
! [SV90: $i,SV191: $i,SV276: $i] :
( ( ! [SY1224: $i,SY1225: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1225 @ SY1224 @ SV276 )
| ( ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5692]) ).
thf(5788,plain,
! [SV91: $i,SV192: $i,SV277: $i] :
( ( ( c_Com_Ocom_OBODY @ SV277 )
!= ( c_Com_Ocom_OWhile @ SV192 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(5789,plain,
! [SV92: $i,SV193: $i,SV278: $i] :
( ( ! [SY1226: $i] :
( ( c_Com_Ocom_OBODY @ SY1226 )
!= ( c_Com_Ocom_OCall @ SV278 @ SV193 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5694]) ).
thf(5790,plain,
! [SV93: $i,SV194: $i,SV279: $i] :
( ( ! [SY1227: $i] :
( ~ ( c_Natural_Oevaln @ SY1227 @ SV279 @ SV194 @ SV93 )
| ( c_Natural_Oevaln @ SY1227 @ SV279 @ ( hAPP @ c_Nat_OSuc @ SV194 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5695]) ).
thf(5791,plain,
! [SV95: $i,SV195: $i,SV280: $i] :
( ( ! [SY1228: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1228 @ SV280 ) @ SV195 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1228 @ SV280 ) @ SV95 ) )
| ( SV195 = SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(5792,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
| ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
| ~ ( ~ ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 )
| ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(5793,plain,
! [SV97: $i,SV197: $i,SV282: $i] :
( ( ! [SY1231: $i] :
( ( c_Com_Ocom_OLocal @ SY1231 @ SV282 @ SV197 )
!= ( c_Com_Ocom_OBODY @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(5794,plain,
! [SV98: $i,SV198: $i,SV283: $i] :
( ( ! [SY1232: $i,SY1233: $i,SY1234: $i,SY1235: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1235 @ SY1234 @ SY1233 @ SY1232 @ SV283 )
| ~ ( ~ ( ( ( hAPP @ SY1233 @ SV198 )
!= ( hAPP @ SY1233 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SY1233 @ SV198 )
= ( hAPP @ SY1233 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(5795,plain,
! [SV99: $i,SV199: $i,SV284: $i] :
( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV284 ) ) @ SV199 @ SV99 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV284 ) @ SV199 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5701]) ).
thf(5796,plain,
! [SV100: $i,SV200: $i,SV285: $i] :
( ( ! [SY1236: $i] :
( ( c_Com_Ocom_OBODY @ SY1236 )
!= ( c_Com_Ocom_OLocal @ SV285 @ SV200 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(5797,plain,
! [SV101: $i,SV201: $i,SV286: $i] :
( ( ! [SY1237: $i] :
( ( c_Com_Ocom_OCall @ SY1237 @ SV286 @ SV201 )
!= ( c_Com_Ocom_OBODY @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(5798,plain,
! [SV102: $i,SV202: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
| ( SV202 = SV102 ) )
| ~ ( ( SV202 != SV102 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(5799,plain,
! [SV103: $i,SV203: $i,SV287: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ~ ( ( SY1240 != SY1239 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1238 @ SV287 ) @ SV203 ) @ SY1239 ) @ SV103 ) @ SY1240 )
= ( hAPP @ SV203 @ SY1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(5800,plain,
! [SV104: $i,SV204: $i,SV288: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1243 @ SY1242 @ SY1241 )
| ( ( hAPP @ ( hAPP @ SY1241 @ SV288 ) @ ( hAPP @ ( hAPP @ SY1241 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SY1241 @ SV204 ) @ ( hAPP @ ( hAPP @ SY1241 @ SV288 ) @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(5801,plain,
! [SV1: $i,SV105: $i,SV205: $i,SV289: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV289 @ SV205 @ SV105 @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ SV105 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5707]) ).
thf(5802,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i] :
( ( ! [SY1244: $i,SY1245: $i,SY1246: $i,SY1247: $i,SY1248: $i,SY1249: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1249 @ SY1248 @ SY1247 @ SY1246 @ SY1245 @ SY1244 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(5803,plain,
! [SV4: $i,SV108: $i,SV207: $i,SV291: $i] :
( ( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV291 @ SV207 @ SV108 ) @ ( hAPP @ c_Nat_OSuc @ SV4 ) )
= ( hAPP @ ( hAPP @ SV108 @ SV4 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV291 @ SV207 @ SV108 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5804,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i] :
( ( ! [SY1250: $i,SY1251: $i,SY1252: $i,SY1253: $i,SY1254: $i,SY1255: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1255 @ SY1254 @ SY1253 @ SY1252 @ SY1251 @ SY1250 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5710]) ).
thf(5805,plain,
! [SV8: $i,SV112: $i,SV209: $i,SV293: $i] :
( ( ! [SY1256: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1256 @ SV293 @ SV209 ) @ SV112 ) @ ( hAPP @ c_Nat_OSuc @ SV8 ) )
= ( hAPP @ ( hAPP @ SV209 @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1256 @ SV293 @ SV209 ) @ SV112 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5711]) ).
thf(5806,plain,
! [SV10: $i,SV114: $i,SV211: $i,SV294: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV294 ) @ SV211 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV294 ) @ SV114 ) @ SV10 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV294 ) @ SV114 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV294 ) @ SV211 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(5807,plain,
! [SV11: $i,SV115: $i,SV212: $i,SV295: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV295 @ SV212 ) @ SV115 ) @ SV11 ) @ ( hAPP @ SV115 @ SV11 ) )
= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5714]) ).
thf(5808,plain,
! [SV12: $i,SV116: $i,SV213: $i,SV296: $i] :
( ( ! [SY1257: $i,SY1258: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1258 @ SY1257 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1258 @ SY1257 ) @ SV296 ) @ SV213 ) @ SV116 ) ) @ SV213 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1258 @ SY1257 ) @ SV296 ) @ SV213 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5715]) ).
thf(5809,plain,
! [SV13: $i,SV117: $i,SV214: $i,SV297: $i] :
( ( ! [SY1259: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1259 @ SV297 ) @ SV214 ) @ SV117 ) @ SV13 ) @ SV117 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(5810,plain,
! [SV14: $i,SV118: $i,SV215: $i,SV298: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1261 @ SY1260 @ SV298 @ SV215 ) @ SV118 ) @ SV14 )
= ( hAPP @ SV215 @ ( hAPP @ SV118 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5717]) ).
thf(5811,plain,
! [SV15: $i,SV119: $i,SV216: $i,SV299: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1263 @ SY1262 @ SV299 @ SV216 ) @ SV119 ) @ SV15 )
= ( hAPP @ SV216 @ ( hAPP @ SV119 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5718]) ).
thf(5812,plain,
! [SV16: $i,SV120: $i,SV217: $i,SV300: $i] :
( ( ! [SY1264: $i,SY1265: $i,SY1266: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1266 @ SY1265 @ SY1264 @ SV300 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1266 @ SY1264 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1265 @ SY1264 @ ( hAPP @ ( c_Fun_Ocomp @ SY1266 @ SY1265 @ SV217 @ SV300 ) @ SV120 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5719]) ).
thf(5813,plain,
! [SV20: $i,SV124: $i,SV218: $i,SV301: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1269 @ SY1268 @ SY1267 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1269 @ SV301 @ SY1268 ) @ SV218 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1269 @ SV301 @ SY1267 ) @ SV218 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV301 @ SY1268 @ SY1267 ) @ SV124 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5720]) ).
thf(5814,plain,
! [SV22: $i,SV126: $i,SV220: $i,SV302: $i] :
( ( ( hAPP @ SV302 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV220 @ SV220 ) @ SV126 ) @ SV302 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV220 @ SV220 ) @ SV126 ) @ SV302 ) @ ( hAPP @ SV302 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5722]) ).
thf(5815,plain,
! [SV23: $i,SV127: $i,SV221: $i,SV303: $i] :
( ( ! [SY1270: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ SV303 ) @ SV221 ) @ SV127 ) ) @ SV221 ) @ SV23 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1270 @ SV303 ) @ SV221 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5723]) ).
thf(5816,plain,
! [SV24: $i,SV128: $i,SV222: $i,SV304: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV304 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV304 ) @ SV222 ) @ SV128 ) ) @ SV24 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV304 ) @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV304 ) @ SV128 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5724]) ).
thf(5817,plain,
! [SV27: $i,SV131: $i,SV223: $i,SV305: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV305 @ SV223 ) @ SV131 ) @ SV27 )
= SV131 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(5818,plain,
! [SV28: $i,SV132: $i,SV224: $i,SV306: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1272 @ SY1271 @ SV306 ) @ SV224 ) @ SV132 ) @ SV28 )
= ( hAPP @ SV224 @ ( hAPP @ SV132 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5726]) ).
thf(5819,plain,
! [SV29: $i,SV133: $i,SV225: $i,SV307: $i] :
( ( ! [SY1273: $i,SY1274: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1274 @ SY1273 @ SV307 ) @ SV225 ) @ SV133 ) @ SV29 )
= ( hAPP @ ( hAPP @ SV225 @ SV29 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5727]) ).
thf(5820,plain,
! [SV30: $i,SV134: $i,SV226: $i,SV308: $i] :
( ( ! [SY1275: $i,SY1276: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1276 @ SY1275 @ SV308 ) @ SV226 ) @ SV134 ) @ SV30 )
= ( hAPP @ ( hAPP @ SV226 @ SV30 ) @ ( hAPP @ SV134 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5728]) ).
thf(5821,plain,
! [SV31: $i,SV135: $i,SV227: $i,SV309: $i] :
( ( ! [SY1277: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1277 @ SV309 ) @ SV227 @ SV135 @ SV31 )
| ~ ! [SY1278: $i] :
( ~ ( c_Natural_Oevaln @ SY1277 @ SV227 @ SV135 @ SY1278 )
| ~ ( c_Natural_Oevaln @ SV309 @ SY1278 @ SV135 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5729]) ).
thf(5822,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5730]) ).
thf(5823,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i] :
( ( ! [SY1279: $i,SY1280: $i] :
~ ( ~ ( ( SY1280 != SY1279 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SY1279 ) @ SV33 ) @ SY1280 )
= SV33 ) )
| ~ ( ~ ( ( SY1280 != SY1279 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SY1279 ) @ SV33 ) @ SY1280 )
= ( hAPP @ SV137 @ SY1280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5731]) ).
thf(5824,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i] :
( ( ! [SY1281: $i,SY1282: $i,SY1283: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1283 @ SY1282 @ SY1281 @ SV311 ) @ SV230 )
!= SV138 )
| ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5732]) ).
thf(5825,plain,
! [SV35: $i,SV139: $i,SV231: $i,SV312: $i] :
( ( ! [SY1284: $i,SY1285: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1285 @ SY1284 ) @ SV312 ) @ SV231 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1285 @ SY1284 ) @ SV139 ) @ SV35 ) )
| ~ ( ( SV312 != SV139 )
| ( SV231 != SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5733]) ).
thf(5826,plain,
! [SV36: $i,SV140: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
| ( SV140 = SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5734]) ).
thf(5827,plain,
! [SV36: $i,SV140: $i] :
( ( ~ ( ( SV140 != SV36 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5734]) ).
thf(5828,plain,
! [SV313: $i] :
( ( ! [SY1286: $i] :
( ~ ( v_P @ SV313 @ SY1286 )
| ! [SY1287: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SY1286 @ v_n @ SY1287 )
| ( v_Q @ SV313 @ SY1287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5735]) ).
thf(5829,plain,
( ( ~ ( v_P @ sK1_SX0 @ sK2_SY1138 )
| ! [SY1288: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ sK2_SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY1288 )
| ( v_Q @ sK1_SX0 @ SY1288 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5736]) ).
thf(5830,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i] :
( ( ! [SY1289: $i,SY1290: $i,SY1291: $i,SY1292: $i,SY1293: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1293 @ SY1292 @ SY1291 @ SY1290 ) @ SY1289 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SY1292 @ SY1291 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SY1290 @ ( hAPP @ SY1289 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5737]) ).
thf(5831,plain,
! [SV38: $i,SV142: $i,SV233: $i,SV315: $i] :
( ( ( c_Com_Ocom_OCond @ SV315 @ SV233 @ SV142 )
!= ( c_Com_Ocom_OBODY @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5738]) ).
thf(5832,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
| ( SV234 = SV39 ) )
| ~ ( ( SV234 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5739]) ).
thf(5833,plain,
! [SV41: $i,SV144: $i,SV235: $i] :
( ( SV235
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV144 ) @ SV41 ) @ SV235 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(5834,plain,
! [SV42: $i,SV145: $i,SV236: $i,SV317: $i] :
( ( ! [SY1294: $i,SY1295: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1295 ) @ SY1294 ) @ SV317 )
!= SV236 )
| ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1295 ) @ SV317 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1295 ) @ SY1294 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1295 ) @ SV236 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5741]) ).
thf(5835,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
| ( SV146 = SV43 ) )
| ~ ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(5836,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i] :
( ( ! [SY1296: $i,SY1297: $i,SY1298: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1298 @ SY1297 @ SY1296 @ SV319 @ SV238 @ SV147 )
| ( ( hAPP @ ( hAPP @ SY1296 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(5837,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i] :
( ( ! [SY1299: $i,SY1300: $i,SY1301: $i,SY1302: $i,SY1303: $i,SY1304: $i,SY1305: $i] :
( ( ( hAPP @ SY1305 @ ( hAPP @ SY1304 @ SY1303 ) )
!= ( hAPP @ SY1302 @ ( hAPP @ SY1301 @ SY1300 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1299 @ SV320 @ SV239 @ SY1305 ) @ SY1304 ) @ SY1303 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SY1302 ) @ SY1301 ) @ SY1300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5744]) ).
thf(5838,plain,
! [SV46: $i,SV149: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
| ( SV149 = SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5745]) ).
thf(5839,plain,
! [SV46: $i,SV149: $i] :
( ( ~ ( ( SV149 != SV46 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5745]) ).
thf(5840,plain,
! [SV47: $i,SV150: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
| ( SV150 = SV47 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5746]) ).
thf(5841,plain,
! [SV47: $i,SV150: $i] :
( ( ~ ( ( SV150 != SV47 )
| ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5746]) ).
thf(5842,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i] :
( ( ! [SY1306: $i,SY1307: $i,SY1308: $i] :
( ( SY1308 != SY1307 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1306 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SY1308 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1306 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SY1307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(5843,plain,
! [SV49: $i,SV152: $i,SV241: $i,SV322: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV322 @ SV241 @ SV152 )
| ( ( hAPP @ ( hAPP @ SV241 @ SV49 ) @ SV49 )
= SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(5844,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i] :
( ( ! [SY1309: $i,SY1310: $i] :
( ~ ( ( SY1310 != SY1309 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SY1310 ) @ SV153 ) ) @ SY1309 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SY1309 ) @ SV50 ) ) @ SY1310 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5749]) ).
thf(5845,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i] :
( ( ! [SY1311: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1311 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) )
| ~ ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1311 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5750]) ).
thf(5846,plain,
! [SV52: $i,SV155: $i,SV244: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV244 ) @ SV155 @ SV52 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV244 ) ) @ SV155 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5751]) ).
thf(5847,plain,
! [SV53: $i,SV156: $i,SV245: $i,SV325: $i] :
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV325 ) ) @ SV245 @ SV156 @ SV53 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV325 ) @ SV245 @ ( hAPP @ c_Nat_OSuc @ SV156 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5752]) ).
thf(5848,plain,
! [SV54: $i,SV157: $i,SV246: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV246 @ SV157 @ SV54 ) )
= $true )
| ( ( SV54 = SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5753]) ).
thf(5849,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i] :
( ( ! [SY1312: $i,SY1313: $i,SY1314: $i,SY1315: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1315 @ SY1314 @ SY1313 @ SY1312 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SY1314 @ SY1313 @ SV158 ) @ SV55 ) )
| ! [SY1316: $i] :
( ( hAPP @ SY1312 @ ( hAPP @ SV326 @ SY1316 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(5850,plain,
! [SV56: $i,SV159: $i] :
( ( ~ ( ( ( c_Com_Ocom_OBODY @ SV159 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
| ( SV159 = SV56 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5755]) ).
thf(5851,plain,
! [SV56: $i,SV159: $i] :
( ( ~ ( ( SV159 != SV56 )
| ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5755]) ).
thf(5852,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
| ( SV160 = SV57 ) )
| ~ ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(5853,plain,
! [SV58: $i,SV161: $i,SV249: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV249 ) @ SV161 ) @ SV58 )
= SV58 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5854,plain,
! [SV59: $i,SV162: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV162 )
= ( hAPP @ c_Nat_OSuc @ SV59 ) )
= $false )
| ( ( SV162 = SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5758]) ).
thf(5855,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i] :
( ( ! [SY1317: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1317 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1317 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
| ~ ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1317 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1317 ) @ SV163 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5759]) ).
thf(5856,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
!= SV61 )
| ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) ) )
| ~ ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(5857,plain,
! [SV62: $i,SV165: $i,SV252: $i,SV329: $i] :
( ( ( c_Com_Ocom_OBODY @ SV329 )
!= ( c_Com_Ocom_OCond @ SV252 @ SV165 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(5858,plain,
! [SV63: $i,SV166: $i,SV253: $i] :
( ( ( c_Com_Ocom_OAss @ SV253 @ SV166 )
= ( c_Com_Ocom_OBODY @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(5859,plain,
! [SV64: $i,SV167: $i] :
( ( ( ! [SY977: $i] :
( ( hAPP @ SV167 @ SY977 )
= ( hAPP @ SV64 @ SY977 ) ) )
= $false )
| ( ( SV167 = SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(5860,plain,
! [SV65: $i,SV168: $i,SV254: $i,SV330: $i] :
( ( ! [SY1318: $i] :
( ( ( hAPP @ SY1318 @ SV330 )
!= SV254 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SY1318 ) @ SV330 ) @ SV254 )
= SY1318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(5861,plain,
! [SV66: $i,SV169: $i,SV255: $i,SV331: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
| ~ ! [SY1319: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY1319 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ SY1319 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5765]) ).
thf(5862,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
| ( SV170 = SV67 ) )
| ~ ( ( SV170 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5863,plain,
! [SV68: $i,SV171: $i,SV257: $i,SV332: $i] :
( ( ~ ( c_Natural_Oevaln @ SV332 @ SV257 @ SV171 @ SV68 )
| ( c_Natural_Oevalc @ SV332 @ SV257 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5767]) ).
thf(5864,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i] :
( ( ! [SY1320: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1321: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV172 ) @ SY1321 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SY1321 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV333 ) @ SY1321 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SY1321 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY1322: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV172 ) @ SY1322 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SY1322 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV333 ) @ SY1322 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SY1322 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1320 ) @ SV172 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5768]) ).
thf(5865,plain,
! [SV70: $i,SV173: $i,SV259: $i,SV334: $i] :
( ( ! [SY1323: $i,SY1324: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1324 @ SY1323 @ SV334 @ SV259 @ SV173 )
| ( ( hAPP @ SV259 @ ( hAPP @ SV334 @ SV70 ) )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(5866,plain,
! [SV71: $i,SV174: $i,SV260: $i] :
( ( ( c_Com_Ocom_OSemi @ SV260 @ SV174 )
= ( c_Com_Ocom_OBODY @ SV71 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(5867,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i] :
( ( ! [SY1325: $i,SY1326: $i,SY1327: $i] :
( ~ ( ( SY1327 != SY1326 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1325 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1325 @ SV335 ) @ SV261 ) @ SY1327 ) @ SV175 ) ) @ SY1326 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1325 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1325 @ SV335 ) @ SV261 ) @ SY1326 ) @ SV73 ) ) @ SY1327 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(5868,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5772]) ).
thf(5869,plain,
! [SV75: $i,SV177: $i,SV263: $i,SV337: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV177 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV75 ) )
| ( SV177 = SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(5870,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1329 @ SY1328 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1329 @ SY1328 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
| ~ ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1329 @ SY1328 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1329 @ SY1328 ) @ SV178 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5774]) ).
thf(5871,plain,
! [SV77: $i,SV179: $i,SV265: $i,SV339: $i] :
( ( ! [SY1330: $i] :
( ~ ! [SY1331: $i] :
( ( hAPP @ SY1330 @ SY1331 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV339 @ SV265 @ SV179 ) @ SY1331 ) )
| ( ( hAPP @ SY1330 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SY1330 @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(5872,plain,
! [SV78: $i,SV180: $i,SV266: $i] :
( ( ( c_Com_Ocom_OWhile @ SV266 @ SV180 )
= ( c_Com_Ocom_OBODY @ SV78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(5873,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
| ( SV181 = SV79 ) )
| ~ ( ( SV181 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(5874,plain,
! [SV80: $i,SV182: $i,SV268: $i] :
( ( ( c_Com_Ocom_OBODY @ SV268 )
= ( c_Com_Ocom_OAss @ SV182 @ SV80 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(5875,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 ) )
= $true )
| ( ( ~ ! [SY1209: $i] :
~ ( c_Natural_Oevaln @ SV269 @ SV183 @ SY1209 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5779]) ).
thf(5876,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
| ( SV184 = SV82 ) )
| ~ ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(5877,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i] :
( ( ! [SY1332: $i,SY1333: $i] :
~ ( ~ ( ( SY1333 != SY1332 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SY1332 ) @ SV83 ) @ SY1333 )
= SV83 ) )
| ~ ( ~ ( ( SY1333 != SY1332 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SY1332 ) @ SV83 ) @ SY1333 )
= ( hAPP @ SV185 @ SY1333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5781]) ).
thf(5878,plain,
! [SV84: $i,SV186: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
| ( SV186 = SV84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5782]) ).
thf(5879,plain,
! [SV84: $i,SV186: $i] :
( ( ~ ( ( SV186 != SV84 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5782]) ).
thf(5880,plain,
! [SV85: $i,SV187: $i,SV272: $i,SV342: $i] :
( ( ! [SY1334: $i,SY1335: $i] :
( ( SY1335 != SY1334 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SY1335 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SY1334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5783]) ).
thf(5881,plain,
! [SV87: $i,SV188: $i,SV273: $i,SV343: $i] :
( ( ! [SY1336: $i,SY1337: $i] :
( ~ ( c_Natural_Oevaln @ SY1337 @ SY1336 @ SV343 @ SV273 )
| ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1337 @ SV188 ) @ SY1336 @ SV343 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5784]) ).
thf(5882,plain,
! [SV88: $i,SV189: $i,SV274: $i] :
( ( ( c_Com_Ocom_OBODY @ SV274 )
= ( c_Com_Ocom_OSemi @ SV189 @ SV88 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(5883,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i] :
( ( ! [SY1338: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1338 @ SV344 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1339: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1338 @ SV275 @ SV190 @ SY1339 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1339 @ SV190 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY1340: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1338 @ SV275 @ SV190 @ SY1340 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1340 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1338 @ SV344 ) @ SV275 @ SV190 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5786]) ).
thf(5884,plain,
! [SV90: $i,SV191: $i,SV276: $i,SV345: $i] :
( ( ! [SY1341: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1341 @ SV345 @ SV276 )
| ( ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5787]) ).
thf(5885,plain,
! [SV91: $i,SV192: $i,SV277: $i] :
( ( ( c_Com_Ocom_OBODY @ SV277 )
= ( c_Com_Ocom_OWhile @ SV192 @ SV91 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5886,plain,
! [SV92: $i,SV193: $i,SV278: $i,SV346: $i] :
( ( ( c_Com_Ocom_OBODY @ SV346 )
!= ( c_Com_Ocom_OCall @ SV278 @ SV193 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5789]) ).
thf(5887,plain,
! [SV93: $i,SV194: $i,SV279: $i,SV347: $i] :
( ( ~ ( c_Natural_Oevaln @ SV347 @ SV279 @ SV194 @ SV93 )
| ( c_Natural_Oevaln @ SV347 @ SV279 @ ( hAPP @ c_Nat_OSuc @ SV194 ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5790]) ).
thf(5888,plain,
! [SV95: $i,SV195: $i,SV280: $i,SV348: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV195 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV95 ) )
| ( SV195 = SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5791]) ).
thf(5889,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
| ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
| ~ ( ~ ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 )
| ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(5890,plain,
! [SV97: $i,SV197: $i,SV282: $i,SV349: $i] :
( ( ( c_Com_Ocom_OLocal @ SV349 @ SV282 @ SV197 )
!= ( c_Com_Ocom_OBODY @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(5891,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i] :
( ( ! [SY1342: $i,SY1343: $i,SY1344: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1344 @ SY1343 @ SY1342 @ SV350 @ SV283 )
| ~ ( ~ ( ( ( hAPP @ SY1342 @ SV198 )
!= ( hAPP @ SY1342 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SY1342 @ SV198 )
= ( hAPP @ SY1342 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5794]) ).
thf(5892,plain,
! [SV99: $i,SV199: $i,SV284: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV284 ) ) @ SV199 @ SV99 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV284 ) @ SV199 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(5893,plain,
! [SV100: $i,SV200: $i,SV285: $i,SV351: $i] :
( ( ( c_Com_Ocom_OBODY @ SV351 )
!= ( c_Com_Ocom_OLocal @ SV285 @ SV200 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5796]) ).
thf(5894,plain,
! [SV101: $i,SV201: $i,SV286: $i,SV352: $i] :
( ( ( c_Com_Ocom_OCall @ SV352 @ SV286 @ SV201 )
!= ( c_Com_Ocom_OBODY @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(5895,plain,
! [SV102: $i,SV202: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
| ( SV202 = SV102 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5798]) ).
thf(5896,plain,
! [SV102: $i,SV202: $i] :
( ( ~ ( ( SV202 != SV102 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5798]) ).
thf(5897,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i] :
( ( ! [SY1345: $i,SY1346: $i] :
( ~ ( ( SY1346 != SY1345 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SY1345 ) @ SV103 ) @ SY1346 )
= ( hAPP @ SV203 @ SY1346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(5898,plain,
! [SV104: $i,SV204: $i,SV288: $i,SV354: $i] :
( ( ! [SY1347: $i,SY1348: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1348 @ SY1347 @ SV354 )
| ( ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(5899,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i,SY1352: $i,SY1353: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1353 @ SY1352 @ SY1351 @ SY1350 @ SY1349 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5802]) ).
thf(5900,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i] :
( ( ! [SY1354: $i,SY1355: $i,SY1356: $i,SY1357: $i,SY1358: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1358 @ SY1357 @ SY1356 @ SY1355 @ SY1354 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(5901,plain,
! [SV8: $i,SV112: $i,SV209: $i,SV293: $i,SV357: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV357 @ SV293 @ SV209 ) @ SV112 ) @ ( hAPP @ c_Nat_OSuc @ SV8 ) )
= ( hAPP @ ( hAPP @ SV209 @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV357 @ SV293 @ SV209 ) @ SV112 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5805]) ).
thf(5902,plain,
! [SV12: $i,SV116: $i,SV213: $i,SV296: $i,SV358: $i] :
( ( ! [SY1359: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1359 @ SV358 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1359 @ SV358 ) @ SV296 ) @ SV213 ) @ SV116 ) ) @ SV213 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1359 @ SV358 ) @ SV296 ) @ SV213 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(5903,plain,
! [SV13: $i,SV117: $i,SV214: $i,SV297: $i,SV359: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV359 @ SV297 ) @ SV214 ) @ SV117 ) @ SV13 ) @ SV117 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(5904,plain,
! [SV14: $i,SV118: $i,SV215: $i,SV298: $i,SV360: $i] :
( ( ! [SY1360: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1360 @ SV360 @ SV298 @ SV215 ) @ SV118 ) @ SV14 )
= ( hAPP @ SV215 @ ( hAPP @ SV118 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(5905,plain,
! [SV15: $i,SV119: $i,SV216: $i,SV299: $i,SV361: $i] :
( ( ! [SY1361: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1361 @ SV361 @ SV299 @ SV216 ) @ SV119 ) @ SV15 )
= ( hAPP @ SV216 @ ( hAPP @ SV119 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5811]) ).
thf(5906,plain,
! [SV16: $i,SV120: $i,SV217: $i,SV300: $i,SV362: $i] :
( ( ! [SY1362: $i,SY1363: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1363 @ SY1362 @ SV362 @ SV300 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1363 @ SV362 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1362 @ SV362 @ ( hAPP @ ( c_Fun_Ocomp @ SY1363 @ SY1362 @ SV217 @ SV300 ) @ SV120 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(5907,plain,
! [SV20: $i,SV124: $i,SV218: $i,SV301: $i,SV363: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1365 @ SY1364 @ SV363 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1365 @ SV301 @ SY1364 ) @ SV218 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1365 @ SV301 @ SV363 ) @ SV218 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV301 @ SY1364 @ SV363 ) @ SV124 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5813]) ).
thf(5908,plain,
! [SV23: $i,SV127: $i,SV221: $i,SV303: $i,SV364: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV364 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV364 @ SV303 ) @ SV221 ) @ SV127 ) ) @ SV221 ) @ SV23 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV364 @ SV303 ) @ SV221 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(5909,plain,
! [SV28: $i,SV132: $i,SV224: $i,SV306: $i,SV365: $i] :
( ( ! [SY1366: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1366 @ SV365 @ SV306 ) @ SV224 ) @ SV132 ) @ SV28 )
= ( hAPP @ SV224 @ ( hAPP @ SV132 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(5910,plain,
! [SV29: $i,SV133: $i,SV225: $i,SV307: $i,SV366: $i] :
( ( ! [SY1367: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1367 @ SV366 @ SV307 ) @ SV225 ) @ SV133 ) @ SV29 )
= ( hAPP @ ( hAPP @ SV225 @ SV29 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5819]) ).
thf(5911,plain,
! [SV30: $i,SV134: $i,SV226: $i,SV308: $i,SV367: $i] :
( ( ! [SY1368: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1368 @ SV367 @ SV308 ) @ SV226 ) @ SV134 ) @ SV30 )
= ( hAPP @ ( hAPP @ SV226 @ SV30 ) @ ( hAPP @ SV134 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5820]) ).
thf(5912,plain,
! [SV31: $i,SV135: $i,SV227: $i,SV309: $i,SV368: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
| ~ ! [SY1369: $i] :
( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ SY1369 )
| ~ ( c_Natural_Oevaln @ SV309 @ SY1369 @ SV135 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5821]) ).
thf(5913,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5822]) ).
thf(5914,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5822]) ).
thf(5915,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i] :
( ( ! [SY1370: $i] :
~ ( ~ ( ( SY1370 != SV369 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SY1370 )
= SV33 ) )
| ~ ( ~ ( ( SY1370 != SV369 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SY1370 )
= ( hAPP @ SV137 @ SY1370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5823]) ).
thf(5916,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i,SV370: $i] :
( ( ! [SY1371: $i,SY1372: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1372 @ SY1371 @ SV370 @ SV311 ) @ SV230 )
!= SV138 )
| ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(5917,plain,
! [SV35: $i,SV139: $i,SV231: $i,SV312: $i,SV371: $i] :
( ( ! [SY1373: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1373 @ SV371 ) @ SV312 ) @ SV231 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1373 @ SV371 ) @ SV139 ) @ SV35 ) )
| ~ ( ( SV312 != SV139 )
| ( SV231 != SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5825]) ).
thf(5918,plain,
! [SV36: $i,SV140: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
| ( SV140 = SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5826]) ).
thf(5919,plain,
! [SV36: $i,SV140: $i] :
( ( ( SV140 != SV36 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5827]) ).
thf(5920,plain,
! [SV372: $i,SV313: $i] :
( ( ~ ( v_P @ SV313 @ SV372 )
| ! [SY1374: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SY1374 )
| ( v_Q @ SV313 @ SY1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5828]) ).
thf(5921,plain,
( ( ~ ( v_P @ sK1_SX0 @ sK2_SY1138 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5829]) ).
thf(5922,plain,
( ( ! [SY1288: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ sK2_SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY1288 )
| ( v_Q @ sK1_SX0 @ SY1288 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5829]) ).
thf(5923,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i] :
( ( ! [SY1375: $i,SY1376: $i,SY1377: $i,SY1378: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1378 @ SY1377 @ SY1376 @ SY1375 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SY1377 @ SY1376 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SY1375 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5830]) ).
thf(5924,plain,
! [SV38: $i,SV142: $i,SV233: $i,SV315: $i] :
( ( ( c_Com_Ocom_OCond @ SV315 @ SV233 @ SV142 )
= ( c_Com_Ocom_OBODY @ SV38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(5925,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
| ( SV234 = SV39 ) )
| ~ ( ( SV234 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(5926,plain,
! [SV42: $i,SV145: $i,SV236: $i,SV317: $i,SV374: $i] :
( ( ! [SY1379: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1379 ) @ SV374 ) @ SV317 )
!= SV236 )
| ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1379 ) @ SV317 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1379 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1379 ) @ SV236 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(5927,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
| ( SV146 = SV43 ) )
| ~ ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(5928,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i,SV375: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1381 @ SY1380 @ SV375 @ SV319 @ SV238 @ SV147 )
| ( ( hAPP @ ( hAPP @ SV375 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5836]) ).
thf(5929,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i] :
( ( ! [SY1382: $i,SY1383: $i,SY1384: $i,SY1385: $i,SY1386: $i,SY1387: $i] :
( ( ( hAPP @ SY1387 @ ( hAPP @ SY1386 @ SY1385 ) )
!= ( hAPP @ SY1384 @ ( hAPP @ SY1383 @ SY1382 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1387 ) @ SY1386 ) @ SY1385 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SY1384 ) @ SY1383 ) @ SY1382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5837]) ).
thf(5930,plain,
! [SV46: $i,SV149: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
| ( SV149 = SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5838]) ).
thf(5931,plain,
! [SV46: $i,SV149: $i] :
( ( ( SV149 != SV46 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5839]) ).
thf(5932,plain,
! [SV47: $i,SV150: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
| ( SV150 = SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5840]) ).
thf(5933,plain,
! [SV47: $i,SV150: $i] :
( ( ( SV150 != SV47 )
| ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5841]) ).
thf(5934,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i,SV377: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ( SY1389 != SY1388 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SY1389 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5842]) ).
thf(5935,plain,
! [SV49: $i,SV152: $i,SV241: $i,SV322: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV322 @ SV241 @ SV152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV241 @ SV49 ) @ SV49 )
= SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5843]) ).
thf(5936,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i,SV378: $i] :
( ( ! [SY1390: $i] :
( ~ ( ( SY1390 != SV378 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SY1390 ) @ SV153 ) ) @ SV378 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV378 ) @ SV50 ) ) @ SY1390 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(5937,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) )
| ~ ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5845]) ).
thf(5938,plain,
! [SV52: $i,SV155: $i,SV244: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV244 ) @ SV155 @ SV52 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV244 ) ) @ SV155 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5939,plain,
! [SV53: $i,SV156: $i,SV245: $i,SV325: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV325 ) ) @ SV245 @ SV156 @ SV53 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV325 ) @ SV245 @ ( hAPP @ c_Nat_OSuc @ SV156 ) @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5847]) ).
thf(5940,plain,
! [SV54: $i,SV157: $i,SV246: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV246 @ SV157 @ SV54 )
= $false )
| ( ( SV54 = SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(5941,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i] :
( ( ! [SY1391: $i,SY1392: $i,SY1393: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1393 @ SY1392 @ SY1391 @ SV380 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SY1392 @ SY1391 @ SV158 ) @ SV55 ) )
| ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5849]) ).
thf(5942,plain,
! [SV56: $i,SV159: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV159 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
| ( SV159 = SV56 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5850]) ).
thf(5943,plain,
! [SV56: $i,SV159: $i] :
( ( ( SV159 != SV56 )
| ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5851]) ).
thf(5944,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
| ( SV160 = SV57 ) )
| ~ ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(5945,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
| ~ ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5855]) ).
thf(5946,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
!= SV61 )
| ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5856]) ).
thf(5947,plain,
! [SV61: $i,SV251: $i,SV164: $i] :
( ( ~ ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5856]) ).
thf(5948,plain,
! [SV62: $i,SV165: $i,SV252: $i,SV329: $i] :
( ( ( c_Com_Ocom_OBODY @ SV329 )
= ( c_Com_Ocom_OCond @ SV252 @ SV165 @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(5949,plain,
! [SV64: $i,SV167: $i] :
( ( ( ( hAPP @ SV167 @ ( sK3_SY977 @ SV64 @ SV167 ) )
= ( hAPP @ SV64 @ ( sK3_SY977 @ SV64 @ SV167 ) ) )
= $false )
| ( ( SV167 = SV64 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5859]) ).
thf(5950,plain,
! [SV65: $i,SV168: $i,SV254: $i,SV330: $i,SV382: $i] :
( ( ( ( hAPP @ SV382 @ SV330 )
!= SV254 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SV382 ) @ SV330 ) @ SV254 )
= SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5860]) ).
thf(5951,plain,
! [SV66: $i,SV169: $i,SV255: $i,SV331: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 ) )
= $true )
| ( ( ~ ! [SY1319: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY1319 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ SY1319 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5861]) ).
thf(5952,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
| ( SV170 = SV67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5862]) ).
thf(5953,plain,
! [SV256: $i,SV67: $i,SV170: $i] :
( ( ~ ( ( SV170 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5862]) ).
thf(5954,plain,
! [SV68: $i,SV171: $i,SV257: $i,SV332: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV332 @ SV257 @ SV171 @ SV68 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV332 @ SV257 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(5955,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5864]) ).
thf(5956,plain,
! [SV70: $i,SV173: $i,SV259: $i,SV334: $i,SV384: $i] :
( ( ! [SY1397: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1397 @ SV384 @ SV334 @ SV259 @ SV173 )
| ( ( hAPP @ SV259 @ ( hAPP @ SV334 @ SV70 ) )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5865]) ).
thf(5957,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i] :
( ( ! [SY1398: $i,SY1399: $i] :
( ~ ( ( SY1399 != SY1398 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SY1399 ) @ SV175 ) ) @ SY1398 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SY1398 ) @ SV73 ) ) @ SY1399 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5867]) ).
thf(5958,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(5959,plain,
! [SV75: $i,SV177: $i,SV263: $i,SV337: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV177 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV75 ) )
= $true )
| ( ( SV177 = SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5869]) ).
thf(5960,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i] :
( ( ! [SY1400: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1400 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1400 @ SV386 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
| ~ ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1400 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1400 @ SV386 ) @ SV178 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5870]) ).
thf(5961,plain,
! [SV77: $i,SV179: $i,SV265: $i,SV339: $i,SV387: $i] :
( ( ~ ! [SY1401: $i] :
( ( hAPP @ SV387 @ SY1401 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV339 @ SV265 @ SV179 ) @ SY1401 ) )
| ( ( hAPP @ SV387 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SV387 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5871]) ).
thf(5962,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
| ( SV181 = SV79 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5873]) ).
thf(5963,plain,
! [SV267: $i,SV79: $i,SV181: $i] :
( ( ~ ( ( SV181 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5873]) ).
thf(5964,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 )
= $false )
| ( ( ~ ! [SY1209: $i] :
~ ( c_Natural_Oevaln @ SV269 @ SV183 @ SY1209 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5875]) ).
thf(5965,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
| ( SV184 = SV82 ) )
| ~ ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5876]) ).
thf(5966,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i] :
( ( ! [SY1402: $i] :
~ ( ~ ( ( SY1402 != SV388 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SY1402 )
= SV83 ) )
| ~ ( ~ ( ( SY1402 != SV388 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SY1402 )
= ( hAPP @ SV185 @ SY1402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5877]) ).
thf(5967,plain,
! [SV84: $i,SV186: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
| ( SV186 = SV84 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5878]) ).
thf(5968,plain,
! [SV84: $i,SV186: $i] :
( ( ( SV186 != SV84 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5879]) ).
thf(5969,plain,
! [SV85: $i,SV187: $i,SV272: $i,SV342: $i,SV389: $i] :
( ( ! [SY1403: $i] :
( ( SY1403 != SV389 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SY1403 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5880]) ).
thf(5970,plain,
! [SV87: $i,SV188: $i,SV273: $i,SV343: $i,SV390: $i] :
( ( ! [SY1404: $i] :
( ~ ( c_Natural_Oevaln @ SY1404 @ SV390 @ SV343 @ SV273 )
| ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1404 @ SV188 ) @ SV390 @ SV343 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5881]) ).
thf(5971,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5883]) ).
thf(5972,plain,
! [SV90: $i,SV191: $i,SV276: $i,SV345: $i,SV392: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV392 @ SV345 @ SV276 )
| ( ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5884]) ).
thf(5973,plain,
! [SV92: $i,SV193: $i,SV278: $i,SV346: $i] :
( ( ( c_Com_Ocom_OBODY @ SV346 )
= ( c_Com_Ocom_OCall @ SV278 @ SV193 @ SV92 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(5974,plain,
! [SV93: $i,SV194: $i,SV279: $i,SV347: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV347 @ SV279 @ SV194 @ SV93 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV347 @ SV279 @ ( hAPP @ c_Nat_OSuc @ SV194 ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5887]) ).
thf(5975,plain,
! [SV95: $i,SV195: $i,SV280: $i,SV348: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV195 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV95 ) )
= $true )
| ( ( SV195 = SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5888]) ).
thf(5976,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
| ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5889]) ).
thf(5977,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ( ~ ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 )
| ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5889]) ).
thf(5978,plain,
! [SV97: $i,SV197: $i,SV282: $i,SV349: $i] :
( ( ( c_Com_Ocom_OLocal @ SV349 @ SV282 @ SV197 )
= ( c_Com_Ocom_OBODY @ SV97 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5890]) ).
thf(5979,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i,SV393: $i] :
( ( ! [SY1407: $i,SY1408: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1408 @ SY1407 @ SV393 @ SV350 @ SV283 )
| ~ ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5891]) ).
thf(5980,plain,
! [SV99: $i,SV199: $i,SV284: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV284 ) ) @ SV199 @ SV99 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV284 ) @ SV199 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(5981,plain,
! [SV100: $i,SV200: $i,SV285: $i,SV351: $i] :
( ( ( c_Com_Ocom_OBODY @ SV351 )
= ( c_Com_Ocom_OLocal @ SV285 @ SV200 @ SV100 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5893]) ).
thf(5982,plain,
! [SV101: $i,SV201: $i,SV286: $i,SV352: $i] :
( ( ( c_Com_Ocom_OCall @ SV352 @ SV286 @ SV201 )
= ( c_Com_Ocom_OBODY @ SV101 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5894]) ).
thf(5983,plain,
! [SV102: $i,SV202: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
| ( SV202 = SV102 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5895]) ).
thf(5984,plain,
! [SV102: $i,SV202: $i] :
( ( ( SV202 != SV102 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5896]) ).
thf(5985,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i,SV394: $i] :
( ( ! [SY1409: $i] :
( ~ ( ( SY1409 != SV394 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SV394 ) @ SV103 ) @ SY1409 )
= ( hAPP @ SV203 @ SY1409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5897]) ).
thf(5986,plain,
! [SV104: $i,SV204: $i,SV288: $i,SV354: $i,SV395: $i] :
( ( ! [SY1410: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1410 @ SV395 @ SV354 )
| ( ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ SV104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5898]) ).
thf(5987,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i,SV396: $i] :
( ( ! [SY1411: $i,SY1412: $i,SY1413: $i,SY1414: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1414 @ SY1413 @ SY1412 @ SY1411 @ SV396 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5899]) ).
thf(5988,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i,SV397: $i] :
( ( ! [SY1415: $i,SY1416: $i,SY1417: $i,SY1418: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1418 @ SY1417 @ SY1416 @ SY1415 @ SV397 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5900]) ).
thf(5989,plain,
! [SV12: $i,SV116: $i,SV213: $i,SV296: $i,SV358: $i,SV398: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV398 @ SV358 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV398 @ SV358 ) @ SV296 ) @ SV213 ) @ SV116 ) ) @ SV213 ) @ SV12 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV398 @ SV358 ) @ SV296 ) @ SV213 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5902]) ).
thf(5990,plain,
! [SV14: $i,SV118: $i,SV215: $i,SV298: $i,SV360: $i,SV399: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV399 @ SV360 @ SV298 @ SV215 ) @ SV118 ) @ SV14 )
= ( hAPP @ SV215 @ ( hAPP @ SV118 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(5991,plain,
! [SV15: $i,SV119: $i,SV216: $i,SV299: $i,SV361: $i,SV400: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV400 @ SV361 @ SV299 @ SV216 ) @ SV119 ) @ SV15 )
= ( hAPP @ SV216 @ ( hAPP @ SV119 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(5992,plain,
! [SV16: $i,SV120: $i,SV217: $i,SV300: $i,SV362: $i,SV401: $i] :
( ( ! [SY1419: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1419 @ SV401 @ SV362 @ SV300 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SY1419 @ SV362 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SV401 @ SV362 @ ( hAPP @ ( c_Fun_Ocomp @ SY1419 @ SV401 @ SV217 @ SV300 ) @ SV120 ) ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5906]) ).
thf(5993,plain,
! [SV20: $i,SV124: $i,SV218: $i,SV301: $i,SV363: $i,SV402: $i] :
( ( ! [SY1420: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1420 @ SV402 @ SV363 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1420 @ SV301 @ SV402 ) @ SV218 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1420 @ SV301 @ SV363 ) @ SV218 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV301 @ SV402 @ SV363 ) @ SV124 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5907]) ).
thf(5994,plain,
! [SV28: $i,SV132: $i,SV224: $i,SV306: $i,SV365: $i,SV403: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV403 @ SV365 @ SV306 ) @ SV224 ) @ SV132 ) @ SV28 )
= ( hAPP @ SV224 @ ( hAPP @ SV132 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5909]) ).
thf(5995,plain,
! [SV29: $i,SV133: $i,SV225: $i,SV307: $i,SV366: $i,SV404: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV404 @ SV366 @ SV307 ) @ SV225 ) @ SV133 ) @ SV29 )
= ( hAPP @ ( hAPP @ SV225 @ SV29 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5910]) ).
thf(5996,plain,
! [SV30: $i,SV134: $i,SV226: $i,SV308: $i,SV367: $i,SV405: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV405 @ SV367 @ SV308 ) @ SV226 ) @ SV134 ) @ SV30 )
= ( hAPP @ ( hAPP @ SV226 @ SV30 ) @ ( hAPP @ SV134 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5911]) ).
thf(5997,plain,
! [SV31: $i,SV135: $i,SV227: $i,SV309: $i,SV368: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 ) )
= $true )
| ( ( ~ ! [SY1369: $i] :
( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ SY1369 )
| ~ ( c_Natural_Oevaln @ SV309 @ SY1369 @ SV135 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5912]) ).
thf(5998,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5913]) ).
thf(5999,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5914]) ).
thf(6000,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ~ ( ~ ( ( SV406 != SV369 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 ) )
| ~ ( ~ ( ( SV406 != SV369 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5915]) ).
thf(6001,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i,SV370: $i,SV407: $i] :
( ( ! [SY1421: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1421 @ SV407 @ SV370 @ SV311 ) @ SV230 )
!= SV138 )
| ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5916]) ).
thf(6002,plain,
! [SV35: $i,SV139: $i,SV231: $i,SV312: $i,SV371: $i,SV408: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
| ~ ( ( SV312 != SV139 )
| ( SV231 != SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5917]) ).
thf(6003,plain,
! [SV36: $i,SV140: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
!= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
= $true )
| ( ( SV140 = SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5918]) ).
thf(6004,plain,
! [SV36: $i,SV140: $i] :
( ( ( SV140 != SV36 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5919]) ).
thf(6005,plain,
! [SV372: $i,SV313: $i] :
( ( ( ~ ( v_P @ SV313 @ SV372 ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SY1374 )
| ( v_Q @ SV313 @ SY1374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5920]) ).
thf(6006,plain,
( ( v_P @ sK1_SX0 @ sK2_SY1138 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5921]) ).
thf(6007,plain,
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ sK2_SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ sK4_SY1288 )
| ( v_Q @ sK1_SX0 @ sK4_SY1288 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5922]) ).
thf(6008,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i] :
( ( ! [SY1422: $i,SY1423: $i,SY1424: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1424 @ SY1423 @ SY1422 @ SV409 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SY1423 @ SY1422 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5923]) ).
thf(6009,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
| ( SV234 = SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5925]) ).
thf(6010,plain,
! [SV143: $i,SV316: $i,SV39: $i,SV234: $i] :
( ( ~ ( ( SV234 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5925]) ).
thf(6011,plain,
! [SV42: $i,SV145: $i,SV236: $i,SV317: $i,SV374: $i,SV410: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV317 )
!= SV236 )
| ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV317 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV236 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(6012,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
| ( SV146 = SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5927]) ).
thf(6013,plain,
! [SV237: $i,SV318: $i,SV43: $i,SV146: $i] :
( ( ~ ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5927]) ).
thf(6014,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i,SV375: $i,SV411: $i] :
( ( ! [SY1425: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1425 @ SV411 @ SV375 @ SV319 @ SV238 @ SV147 )
| ( ( hAPP @ ( hAPP @ SV375 @ SV44 ) @ SV44 )
= SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5928]) ).
thf(6015,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i] :
( ( ! [SY1426: $i,SY1427: $i,SY1428: $i,SY1429: $i,SY1430: $i] :
( ( ( hAPP @ SY1430 @ ( hAPP @ SY1429 @ SY1428 ) )
!= ( hAPP @ SY1427 @ ( hAPP @ SY1426 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1430 ) @ SY1429 ) @ SY1428 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SY1427 ) @ SY1426 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5929]) ).
thf(6016,plain,
! [SV46: $i,SV149: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
= $true )
| ( ( SV149 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5930]) ).
thf(6017,plain,
! [SV46: $i,SV149: $i] :
( ( ( SV149 != SV46 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5931]) ).
thf(6018,plain,
! [SV47: $i,SV150: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
!= ( hAPP @ c_Nat_OSuc @ SV47 ) )
= $true )
| ( ( SV150 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5932]) ).
thf(6019,plain,
! [SV47: $i,SV150: $i] :
( ( ( SV150 != SV47 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5933]) ).
thf(6020,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i,SV377: $i,SV413: $i] :
( ( ! [SY1431: $i] :
( ( SY1431 != SV413 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SY1431 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5934]) ).
thf(6021,plain,
! [SV49: $i,SV152: $i,SV241: $i,SV322: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV322 @ SV241 @ SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV241 @ SV49 ) @ SV49 )
= SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5935]) ).
thf(6022,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i,SV378: $i,SV414: $i] :
( ( ~ ( ( SV414 != SV378 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV414 ) @ SV153 ) ) @ SV378 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV378 ) @ SV50 ) ) @ SV414 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5936]) ).
thf(6023,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) )
| ~ ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(6024,plain,
! [SV53: $i,SV156: $i,SV245: $i,SV325: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV325 ) ) @ SV245 @ SV156 @ SV53 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV325 ) @ SV245 @ ( hAPP @ c_Nat_OSuc @ SV156 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5939]) ).
thf(6025,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i,SV415: $i] :
( ( ! [SY1432: $i,SY1433: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1433 @ SY1432 @ SV415 @ SV380 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SY1432 @ SV415 @ SV158 ) @ SV55 ) )
| ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5941]) ).
thf(6026,plain,
! [SV56: $i,SV159: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV159 )
!= ( c_Com_Ocom_OBODY @ SV56 ) )
= $true )
| ( ( SV159 = SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(6027,plain,
! [SV56: $i,SV159: $i] :
( ( ( SV159 != SV56 )
= $true )
| ( ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5943]) ).
thf(6028,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
| ( SV160 = SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5944]) ).
thf(6029,plain,
! [SV248: $i,SV327: $i,SV57: $i,SV160: $i] :
( ( ~ ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5944]) ).
thf(6030,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
| ~ ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5945]) ).
thf(6031,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
!= SV61 )
| ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5946]) ).
thf(6032,plain,
! [SV61: $i,SV251: $i,SV164: $i] :
( ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
| ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5947]) ).
thf(6033,plain,
! [SV65: $i,SV168: $i,SV254: $i,SV330: $i,SV382: $i] :
( ( ( ( hAPP @ SV382 @ SV330 )
!= SV254 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SV382 ) @ SV330 ) @ SV254 )
= SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5950]) ).
thf(6034,plain,
! [SV66: $i,SV169: $i,SV255: $i,SV331: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false )
| ( ( ~ ! [SY1319: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY1319 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ SY1319 @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5951]) ).
thf(6035,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
| ( SV170 = SV67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5952]) ).
thf(6036,plain,
! [SV256: $i,SV67: $i,SV170: $i] :
( ( ( SV170 != SV67 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5953]) ).
thf(6037,plain,
! [SV68: $i,SV171: $i,SV257: $i,SV332: $i] :
( ( ( c_Natural_Oevaln @ SV332 @ SV257 @ SV171 @ SV68 )
= $false )
| ( ( c_Natural_Oevalc @ SV332 @ SV257 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6038,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
| ~ ( ~ ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(6039,plain,
! [SV70: $i,SV173: $i,SV259: $i,SV334: $i,SV384: $i,SV416: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV416 @ SV384 @ SV334 @ SV259 @ SV173 )
| ( ( hAPP @ SV259 @ ( hAPP @ SV334 @ SV70 ) )
= SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(6040,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i,SV417: $i] :
( ( ! [SY1435: $i] :
( ~ ( ( SY1435 != SV417 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SY1435 ) @ SV175 ) ) @ SV417 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV417 ) @ SV73 ) ) @ SY1435 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5957]) ).
thf(6041,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5958]) ).
thf(6042,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5958]) ).
thf(6043,plain,
! [SV75: $i,SV177: $i,SV263: $i,SV337: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV177 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV337 @ SV263 ) @ SV75 ) )
= $false )
| ( ( SV177 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5959]) ).
thf(6044,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
| ~ ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(6045,plain,
! [SV77: $i,SV179: $i,SV265: $i,SV339: $i,SV387: $i] :
( ( ( ~ ! [SY1401: $i] :
( ( hAPP @ SV387 @ SY1401 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV339 @ SV265 @ SV179 ) @ SY1401 ) ) )
= $true )
| ( ( ( hAPP @ SV387 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SV387 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5961]) ).
thf(6046,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
| ( SV181 = SV79 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5962]) ).
thf(6047,plain,
! [SV267: $i,SV79: $i,SV181: $i] :
( ( ( SV181 != SV79 )
| ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5963]) ).
thf(6048,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ( ! [SY1209: $i] :
~ ( c_Natural_Oevaln @ SV269 @ SV183 @ SY1209 @ SV81 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(6049,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
| ( SV184 = SV82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5965]) ).
thf(6050,plain,
! [SV270: $i,SV340: $i,SV82: $i,SV184: $i] :
( ( ~ ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5965]) ).
thf(6051,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ~ ( ~ ( ( SV419 != SV388 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 ) )
| ~ ( ~ ( ( SV419 != SV388 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5966]) ).
thf(6052,plain,
! [SV84: $i,SV186: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
= $true )
| ( ( SV186 = SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5967]) ).
thf(6053,plain,
! [SV84: $i,SV186: $i] :
( ( ( SV186 != SV84 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5968]) ).
thf(6054,plain,
! [SV85: $i,SV187: $i,SV272: $i,SV342: $i,SV389: $i,SV420: $i] :
( ( ( SV420 != SV389 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV420 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5969]) ).
thf(6055,plain,
! [SV87: $i,SV188: $i,SV273: $i,SV343: $i,SV390: $i,SV421: $i] :
( ( ~ ( c_Natural_Oevaln @ SV421 @ SV390 @ SV343 @ SV273 )
| ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV421 @ SV188 ) @ SV390 @ SV343 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5970]) ).
thf(6056,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
| ~ ( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(6057,plain,
! [SV90: $i,SV191: $i,SV276: $i,SV345: $i,SV392: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV392 @ SV345 @ SV276 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5972]) ).
thf(6058,plain,
! [SV93: $i,SV194: $i,SV279: $i,SV347: $i] :
( ( ( c_Natural_Oevaln @ SV347 @ SV279 @ SV194 @ SV93 )
= $false )
| ( ( c_Natural_Oevaln @ SV347 @ SV279 @ ( hAPP @ c_Nat_OSuc @ SV194 ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5974]) ).
thf(6059,plain,
! [SV95: $i,SV195: $i,SV280: $i,SV348: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV195 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV348 @ SV280 ) @ SV95 ) )
= $false )
| ( ( SV195 = SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5975]) ).
thf(6060,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
| ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5976]) ).
thf(6061,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ~ ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 )
| ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5977]) ).
thf(6062,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i,SV393: $i,SV422: $i] :
( ( ! [SY1436: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1436 @ SV422 @ SV393 @ SV350 @ SV283 )
| ~ ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5979]) ).
thf(6063,plain,
! [SV102: $i,SV202: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
= $true )
| ( ( SV202 = SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5983]) ).
thf(6064,plain,
! [SV102: $i,SV202: $i] :
( ( ( SV202 != SV102 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5984]) ).
thf(6065,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i,SV394: $i,SV423: $i] :
( ( ~ ( ( SV423 != SV394 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SV394 ) @ SV103 ) @ SV423 )
= ( hAPP @ SV203 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5985]) ).
thf(6066,plain,
! [SV104: $i,SV204: $i,SV288: $i,SV354: $i,SV395: $i,SV424: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV424 @ SV395 @ SV354 )
| ( ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5986]) ).
thf(6067,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i,SV396: $i,SV425: $i] :
( ( ! [SY1437: $i,SY1438: $i,SY1439: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1439 @ SY1438 @ SY1437 @ SV425 @ SV396 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5987]) ).
thf(6068,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i,SV397: $i,SV426: $i] :
( ( ! [SY1440: $i,SY1441: $i,SY1442: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1442 @ SY1441 @ SY1440 @ SV426 @ SV397 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5988]) ).
thf(6069,plain,
! [SV16: $i,SV120: $i,SV217: $i,SV300: $i,SV362: $i,SV401: $i,SV427: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV427 @ SV401 @ SV362 @ SV300 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SV427 @ SV362 @ SV120 ) @ SV16 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV217 @ SV401 @ SV362 @ ( hAPP @ ( c_Fun_Ocomp @ SV427 @ SV401 @ SV217 @ SV300 ) @ SV120 ) ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6070,plain,
! [SV20: $i,SV124: $i,SV218: $i,SV301: $i,SV363: $i,SV402: $i,SV428: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV428 @ SV402 @ SV363 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV428 @ SV301 @ SV402 ) @ SV218 ) @ SV124 ) ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV428 @ SV301 @ SV363 ) @ SV218 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV301 @ SV402 @ SV363 ) @ SV124 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5993]) ).
thf(6071,plain,
! [SV31: $i,SV135: $i,SV227: $i,SV309: $i,SV368: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false )
| ( ( ~ ! [SY1369: $i] :
( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ SY1369 )
| ~ ( c_Natural_Oevaln @ SV309 @ SY1369 @ SV135 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5997]) ).
thf(6072,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5998]) ).
thf(6073,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5999]) ).
thf(6074,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ~ ( ( SV406 != SV369 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 ) )
| ~ ( ~ ( ( SV406 != SV369 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6000]) ).
thf(6075,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i,SV370: $i,SV407: $i,SV429: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV429 @ SV407 @ SV370 @ SV311 ) @ SV230 )
!= SV138 )
| ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6076,plain,
! [SV35: $i,SV139: $i,SV231: $i,SV312: $i,SV371: $i,SV408: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $true )
| ( ( ~ ( ( SV312 != SV139 )
| ( SV231 != SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6002]) ).
thf(6077,plain,
! [SV36: $i,SV140: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
= $false )
| ( ( SV140 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6003]) ).
thf(6078,plain,
! [SV36: $i,SV140: $i] :
( ( ( SV140 = SV36 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV140 )
= ( hAPP @ c_Int_ORep__Integ @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6004]) ).
thf(6079,plain,
! [SV372: $i,SV313: $i] :
( ( ( v_P @ SV313 @ SV372 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SY1374 )
| ( v_Q @ SV313 @ SY1374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6005]) ).
thf(6080,plain,
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ sK2_SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ sK4_SY1288 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6007]) ).
thf(6081,plain,
( ( v_Q @ sK1_SX0 @ sK4_SY1288 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6007]) ).
thf(6082,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i,SV430: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1444 @ SY1443 @ SV430 @ SV409 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SY1443 @ SV430 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6083,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
| ( SV234 = SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6009]) ).
thf(6084,plain,
! [SV143: $i,SV316: $i,SV39: $i,SV234: $i] :
( ( ( SV234 != SV39 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6010]) ).
thf(6085,plain,
! [SV42: $i,SV145: $i,SV236: $i,SV317: $i,SV374: $i,SV410: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV317 )
!= SV236 )
= $true )
| ( ( ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV317 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV236 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6011]) ).
thf(6086,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
| ( SV146 = SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6012]) ).
thf(6087,plain,
! [SV237: $i,SV318: $i,SV43: $i,SV146: $i] :
( ( ( SV146 != SV43 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6013]) ).
thf(6088,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i,SV375: $i,SV411: $i,SV431: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV431 @ SV411 @ SV375 @ SV319 @ SV238 @ SV147 )
| ( ( hAPP @ ( hAPP @ SV375 @ SV44 ) @ SV44 )
= SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6089,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i] :
( ( ! [SY1445: $i,SY1446: $i,SY1447: $i,SY1448: $i] :
( ( ( hAPP @ SY1448 @ ( hAPP @ SY1447 @ SY1446 ) )
!= ( hAPP @ SY1445 @ ( hAPP @ SV432 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1448 ) @ SY1447 ) @ SY1446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SY1445 ) @ SV432 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6090,plain,
! [SV46: $i,SV149: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
= $false )
| ( ( SV149 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6016]) ).
thf(6091,plain,
! [SV46: $i,SV149: $i] :
( ( ( SV149 = SV46 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV149 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6092,plain,
! [SV47: $i,SV150: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) )
= $false )
| ( ( SV150 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6093,plain,
! [SV47: $i,SV150: $i] :
( ( ( SV150 = SV47 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV150 )
= ( hAPP @ c_Nat_OSuc @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(6094,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i,SV377: $i,SV413: $i,SV433: $i] :
( ( ( SV433 != SV413 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV433 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6020]) ).
thf(6095,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i,SV378: $i,SV414: $i] :
( ( ( ~ ( ( SV414 != SV378 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV414 ) @ SV153 ) ) @ SV378 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV378 ) @ SV50 ) ) @ SV414 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6022]) ).
thf(6096,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6023]) ).
thf(6097,plain,
! [SV324: $i,SV379: $i,SV51: $i,SV154: $i,SV243: $i] :
( ( ~ ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6023]) ).
thf(6098,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i,SV415: $i,SV434: $i] :
( ( ! [SY1449: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1449 @ SV434 @ SV415 @ SV380 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SV434 @ SV415 @ SV158 ) @ SV55 ) )
| ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6025]) ).
thf(6099,plain,
! [SV56: $i,SV159: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) )
= $false )
| ( ( SV159 = SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6100,plain,
! [SV56: $i,SV159: $i] :
( ( ( SV159 = SV56 )
= $false )
| ( ( ( c_Com_Ocom_OBODY @ SV159 )
= ( c_Com_Ocom_OBODY @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6027]) ).
thf(6101,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
| ( SV160 = SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6028]) ).
thf(6102,plain,
! [SV248: $i,SV327: $i,SV57: $i,SV160: $i] :
( ( ( SV160 != SV57 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6029]) ).
thf(6103,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6030]) ).
thf(6104,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ~ ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6030]) ).
thf(6105,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
!= SV61 )
= $true )
| ( ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6031]) ).
thf(6106,plain,
! [SV61: $i,SV251: $i,SV164: $i] :
( ( ( SV164
!= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6032]) ).
thf(6107,plain,
! [SV65: $i,SV168: $i,SV254: $i,SV330: $i,SV382: $i] :
( ( ( ( hAPP @ SV382 @ SV330 )
= SV254 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV168 @ SV65 ) @ SV382 ) @ SV330 ) @ SV254 )
= SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6033]) ).
thf(6108,plain,
! [SV66: $i,SV255: $i,SV331: $i,SV169: $i] :
( ( ( ! [SY1319: $i] :
( ( SV169
!= ( hAPP @ c_Nat_OSuc @ SY1319 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ SY1319 @ SV66 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6034]) ).
thf(6109,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
= $true )
| ( ( SV170 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6035]) ).
thf(6110,plain,
! [SV256: $i,SV67: $i,SV170: $i] :
( ( ( SV170 != SV67 )
= $true )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6036]) ).
thf(6111,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6038]) ).
thf(6112,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ~ ( ~ ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6038]) ).
thf(6113,plain,
! [SV70: $i,SV173: $i,SV259: $i,SV334: $i,SV384: $i,SV416: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV416 @ SV384 @ SV334 @ SV259 @ SV173 ) )
= $true )
| ( ( ( hAPP @ SV259 @ ( hAPP @ SV334 @ SV70 ) )
= SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6039]) ).
thf(6114,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i,SV417: $i,SV435: $i] :
( ( ~ ( ( SV435 != SV417 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV435 ) @ SV175 ) ) @ SV417 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV417 ) @ SV73 ) ) @ SV435 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6115,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6041]) ).
thf(6116,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6042]) ).
thf(6117,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
| ~ ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(6118,plain,
! [SV77: $i,SV179: $i,SV265: $i,SV339: $i,SV387: $i] :
( ( ( ! [SY1401: $i] :
( ( hAPP @ SV387 @ SY1401 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV339 @ SV265 @ SV179 ) @ SY1401 ) ) )
= $false )
| ( ( ( hAPP @ SV387 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SV387 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6119,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
!= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
= $true )
| ( ( SV181 = SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6046]) ).
thf(6120,plain,
! [SV267: $i,SV79: $i,SV181: $i] :
( ( ( SV181 != SV79 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6047]) ).
thf(6121,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV269 @ SV183 @ ( sK5_SY1209 @ SV81 @ SV183 @ SV269 ) @ SV81 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6048]) ).
thf(6122,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
| ( SV184 = SV82 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6049]) ).
thf(6123,plain,
! [SV270: $i,SV340: $i,SV82: $i,SV184: $i] :
( ( ( SV184 != SV82 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6050]) ).
thf(6124,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ~ ( ( SV419 != SV388 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 ) )
| ~ ( ~ ( ( SV419 != SV388 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6051]) ).
thf(6125,plain,
! [SV84: $i,SV186: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
= $false )
| ( ( SV186 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(6126,plain,
! [SV84: $i,SV186: $i] :
( ( ( SV186 = SV84 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV186 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6053]) ).
thf(6127,plain,
! [SV85: $i,SV187: $i,SV272: $i,SV342: $i,SV389: $i,SV420: $i] :
( ( ( SV420 != SV389 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV420 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6054]) ).
thf(6128,plain,
! [SV87: $i,SV188: $i,SV273: $i,SV343: $i,SV390: $i,SV421: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV421 @ SV390 @ SV343 @ SV273 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV421 @ SV188 ) @ SV390 @ SV343 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6055]) ).
thf(6129,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6056]) ).
thf(6130,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ~ ( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6056]) ).
thf(6131,plain,
! [SV90: $i,SV191: $i,SV276: $i,SV345: $i,SV392: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV392 @ SV345 @ SV276 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= ( hAPP @ ( hAPP @ SV276 @ SV191 ) @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6057]) ).
thf(6132,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 ) )
= $true )
| ( ( ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6060]) ).
thf(6133,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ~ ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6061]) ).
thf(6134,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i,SV393: $i,SV422: $i,SV436: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
| ~ ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6062]) ).
thf(6135,plain,
! [SV102: $i,SV202: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
= $false )
| ( ( SV202 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(6136,plain,
! [SV102: $i,SV202: $i] :
( ( ( SV202 = SV102 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV202 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6064]) ).
thf(6137,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i,SV394: $i,SV423: $i] :
( ( ( ~ ( ( SV423 != SV394 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SV394 ) @ SV103 ) @ SV423 )
= ( hAPP @ SV203 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6065]) ).
thf(6138,plain,
! [SV104: $i,SV204: $i,SV288: $i,SV354: $i,SV395: $i,SV424: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV424 @ SV395 @ SV354 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6066]) ).
thf(6139,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i,SV396: $i,SV425: $i,SV437: $i] :
( ( ! [SY1451: $i,SY1452: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1452 @ SY1451 @ SV437 @ SV425 @ SV396 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6140,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i,SV397: $i,SV426: $i,SV438: $i] :
( ( ! [SY1453: $i,SY1454: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1454 @ SY1453 @ SV438 @ SV426 @ SV397 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6068]) ).
thf(6141,plain,
! [SV31: $i,SV309: $i,SV135: $i,SV227: $i,SV368: $i] :
( ( ( ! [SY1369: $i] :
( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ SY1369 )
| ~ ( c_Natural_Oevaln @ SV309 @ SY1369 @ SV135 @ SV31 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6071]) ).
thf(6142,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6072]) ).
thf(6143,plain,
! [SV32: $i,SV136: $i,SV228: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV228 ) ) @ SV136 @ SV32 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV228 ) @ SV136 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6073]) ).
thf(6144,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ~ ( ( SV406 != SV369 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6074]) ).
thf(6145,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ~ ( ~ ( ( SV406 != SV369 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6074]) ).
thf(6146,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i,SV370: $i,SV407: $i,SV429: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV429 @ SV407 @ SV370 @ SV311 ) @ SV230 )
!= SV138 )
= $true )
| ( ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6147,plain,
! [SV35: $i,SV139: $i,SV231: $i,SV312: $i,SV371: $i,SV408: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false )
| ( ( ~ ( ( SV312 != SV139 )
| ( SV231 != SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6076]) ).
thf(6148,plain,
! [SV313: $i,SV439: $i,SV372: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SV439 )
| ( v_Q @ SV313 @ SV439 ) )
= $true )
| ( ( v_P @ SV313 @ SV372 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6079]) ).
thf(6149,plain,
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ sK2_SY1138 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ sK4_SY1288 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6080]) ).
thf(6150,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i,SV430: $i,SV440: $i] :
( ( ! [SY1455: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1455 @ SV440 @ SV430 @ SV409 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SV440 @ SV430 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6082]) ).
thf(6151,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
= $true )
| ( ( SV234 = SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6083]) ).
thf(6152,plain,
! [SV143: $i,SV316: $i,SV39: $i,SV234: $i] :
( ( ( SV234 != SV39 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6084]) ).
thf(6153,plain,
! [SV42: $i,SV145: $i,SV236: $i,SV317: $i,SV374: $i,SV410: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV317 )
= SV236 )
= $false )
| ( ( ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV317 ) @ SV42 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV236 ) @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(6154,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
= $true )
| ( ( SV146 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6086]) ).
thf(6155,plain,
! [SV237: $i,SV318: $i,SV43: $i,SV146: $i] :
( ( ( SV146 != SV43 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6087]) ).
thf(6156,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i,SV375: $i,SV411: $i,SV431: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV431 @ SV411 @ SV375 @ SV319 @ SV238 @ SV147 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV44 ) @ SV44 )
= SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6088]) ).
thf(6157,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i] :
( ( ! [SY1456: $i,SY1457: $i,SY1458: $i] :
( ( ( hAPP @ SY1458 @ ( hAPP @ SY1457 @ SY1456 ) )
!= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1458 ) @ SY1457 ) @ SY1456 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6089]) ).
thf(6158,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i,SV377: $i,SV413: $i,SV433: $i] :
( ( ( SV433 != SV413 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV433 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6094]) ).
thf(6159,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i,SV378: $i,SV414: $i] :
( ( ( SV414 != SV378 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV414 ) @ SV153 ) ) @ SV378 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV378 ) @ SV50 ) ) @ SV414 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6095]) ).
thf(6160,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
| ( ( hAPP @ SV243 @ SV154 )
= SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6096]) ).
thf(6161,plain,
! [SV324: $i,SV379: $i,SV51: $i,SV154: $i,SV243: $i] :
( ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6097]) ).
thf(6162,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i,SV415: $i,SV434: $i,SV442: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV442 @ SV434 @ SV415 @ SV380 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SV434 @ SV415 @ SV158 ) @ SV55 ) )
| ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6098]) ).
thf(6163,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
= $true )
| ( ( SV160 = SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6164,plain,
! [SV248: $i,SV327: $i,SV57: $i,SV160: $i] :
( ( ( SV160 != SV57 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6102]) ).
thf(6165,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
| ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6103]) ).
thf(6166,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6104]) ).
thf(6167,plain,
! [SV61: $i,SV164: $i,SV251: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 )
= $false )
| ( ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6105]) ).
thf(6168,plain,
! [SV61: $i,SV251: $i,SV164: $i] :
( ( ( SV164
= ( hAPP @ ( c_List_Orev @ SV251 ) @ SV61 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV251 ) @ SV164 )
= SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6106]) ).
thf(6169,plain,
! [SV331: $i,SV255: $i,SV66: $i,SV169: $i] :
( ( ( ( SV169
!= ( hAPP @ c_Nat_OSuc @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) @ SV66 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6108]) ).
thf(6170,plain,
! [SV67: $i,SV170: $i,SV256: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
= $false )
| ( ( SV170 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6109]) ).
thf(6171,plain,
! [SV256: $i,SV67: $i,SV170: $i] :
( ( ( SV170 = SV67 )
= $false )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV170 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV256 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6110]) ).
thf(6172,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
| ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6111]) ).
thf(6173,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ~ ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6112]) ).
thf(6174,plain,
! [SV70: $i,SV173: $i,SV259: $i,SV334: $i,SV384: $i,SV416: $i] :
( ( ( c_Typedef_Otype__definition @ SV416 @ SV384 @ SV334 @ SV259 @ SV173 )
= $false )
| ( ( ( hAPP @ SV259 @ ( hAPP @ SV334 @ SV70 ) )
= SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6175,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i,SV417: $i,SV435: $i] :
( ( ( ~ ( ( SV435 != SV417 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV435 ) @ SV175 ) ) @ SV417 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV417 ) @ SV73 ) ) @ SV435 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6114]) ).
thf(6176,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6115]) ).
thf(6177,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6116]) ).
thf(6178,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6117]) ).
thf(6179,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ~ ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6117]) ).
thf(6180,plain,
! [SV339: $i,SV265: $i,SV179: $i,SV77: $i,SV387: $i] :
( ( ( ( hAPP @ SV387 @ ( sK7_SY1401 @ SV77 @ SV179 @ SV265 @ SV339 @ SV387 ) )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV339 @ SV265 @ SV179 ) @ ( sK7_SY1401 @ SV77 @ SV179 @ SV265 @ SV339 @ SV387 ) ) )
= $false )
| ( ( ( hAPP @ SV387 @ ( hAPP @ c_Nat_OSuc @ SV77 ) )
= ( hAPP @ ( hAPP @ SV179 @ SV77 ) @ ( hAPP @ SV387 @ SV77 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6118]) ).
thf(6181,plain,
! [SV79: $i,SV181: $i,SV267: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
= $false )
| ( ( SV181 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6182,plain,
! [SV267: $i,SV79: $i,SV181: $i] :
( ( ( SV181 = SV79 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV267 ) @ SV181 )
= ( hAPP @ ( c_List_Orev @ SV267 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6183,plain,
! [SV81: $i,SV183: $i,SV269: $i] :
( ( ( c_Natural_Oevaln @ SV269 @ SV183 @ ( sK5_SY1209 @ SV81 @ SV183 @ SV269 ) @ SV81 )
= $true )
| ( ( c_Natural_Oevalc @ SV269 @ SV183 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6121]) ).
thf(6184,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
= $true )
| ( ( SV184 = SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6122]) ).
thf(6185,plain,
! [SV270: $i,SV340: $i,SV82: $i,SV184: $i] :
( ( ( SV184 != SV82 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6123]) ).
thf(6186,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ~ ( ( SV419 != SV388 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6124]) ).
thf(6187,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ~ ( ~ ( ( SV419 != SV388 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6124]) ).
thf(6188,plain,
! [SV85: $i,SV187: $i,SV272: $i,SV342: $i,SV389: $i,SV420: $i] :
( ( ( SV420 = SV389 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV420 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV342 @ SV272 @ SV187 ) @ SV85 ) @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(6189,plain,
! [SV87: $i,SV188: $i,SV273: $i,SV343: $i,SV390: $i,SV421: $i] :
( ( ( c_Natural_Oevaln @ SV421 @ SV390 @ SV343 @ SV273 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV421 @ SV188 ) @ SV390 @ SV343 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6128]) ).
thf(6190,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
| ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6129]) ).
thf(6191,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6130]) ).
thf(6192,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $false )
| ( ( ~ ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6132]) ).
thf(6193,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ~ ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6133]) ).
thf(6194,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i,SV393: $i,SV422: $i,SV436: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6195,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i,SV394: $i,SV423: $i] :
( ( ( SV423 != SV394 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SV394 ) @ SV103 ) @ SV423 )
= ( hAPP @ SV203 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6137]) ).
thf(6196,plain,
! [SV104: $i,SV204: $i,SV288: $i,SV354: $i,SV395: $i,SV424: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV424 @ SV395 @ SV354 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ SV104 ) )
= ( hAPP @ ( hAPP @ SV354 @ SV204 ) @ ( hAPP @ ( hAPP @ SV354 @ SV288 ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6138]) ).
thf(6197,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i,SV396: $i,SV425: $i,SV437: $i,SV443: $i] :
( ( ! [SY1460: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1460 @ SV443 @ SV437 @ SV425 @ SV396 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6139]) ).
thf(6198,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i,SV397: $i,SV426: $i,SV438: $i,SV444: $i] :
( ( ! [SY1461: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1461 @ SV444 @ SV438 @ SV426 @ SV397 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6140]) ).
thf(6199,plain,
! [SV309: $i,SV31: $i,SV135: $i,SV227: $i,SV368: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) )
| ~ ( c_Natural_Oevaln @ SV309 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) @ SV135 @ SV31 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6141]) ).
thf(6200,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( SV406 != SV369 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6144]) ).
thf(6201,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ~ ( ( SV406 != SV369 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6145]) ).
thf(6202,plain,
! [SV34: $i,SV138: $i,SV230: $i,SV311: $i,SV370: $i,SV407: $i,SV429: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV429 @ SV407 @ SV370 @ SV311 ) @ SV230 )
= SV138 )
= $false )
| ( ( ( hAPP @ SV311 @ ( hAPP @ SV230 @ SV34 ) )
= ( hAPP @ SV138 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6203,plain,
! [SV371: $i,SV408: $i,SV35: $i,SV231: $i,SV139: $i,SV312: $i] :
( ( ( ( SV312 != SV139 )
| ( SV231 != SV35 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6204,plain,
! [SV313: $i,SV439: $i,SV372: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SV439 ) )
= $true )
| ( ( v_Q @ SV313 @ SV439 )
= $true )
| ( ( v_P @ SV313 @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6148]) ).
thf(6205,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i,SV430: $i,SV440: $i,SV445: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV445 @ SV440 @ SV430 @ SV409 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SV440 @ SV430 @ SV232 ) @ SV141 ) )
| ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6150]) ).
thf(6206,plain,
! [SV39: $i,SV143: $i,SV234: $i,SV316: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
= $false )
| ( ( SV234 = SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(6207,plain,
! [SV143: $i,SV316: $i,SV39: $i,SV234: $i] :
( ( ( SV234 = SV39 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV234 ) @ SV143 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV316 ) @ SV39 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6152]) ).
thf(6208,plain,
! [SV236: $i,SV374: $i,SV42: $i,SV317: $i,SV410: $i,SV145: $i] :
( ( ( SV145
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV317 ) @ SV42 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV236 ) @ SV42 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV317 )
= SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6153]) ).
thf(6209,plain,
! [SV43: $i,SV146: $i,SV237: $i,SV318: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
= $false )
| ( ( SV146 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6154]) ).
thf(6210,plain,
! [SV237: $i,SV318: $i,SV43: $i,SV146: $i] :
( ( ( SV146 = SV43 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV146 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV318 ) @ SV237 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6155]) ).
thf(6211,plain,
! [SV44: $i,SV147: $i,SV238: $i,SV319: $i,SV375: $i,SV411: $i,SV431: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV431 @ SV411 @ SV375 @ SV319 @ SV238 @ SV147 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV44 ) @ SV44 )
= SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6156]) ).
thf(6212,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i,SV446: $i] :
( ( ! [SY1462: $i,SY1463: $i] :
( ( ( hAPP @ SY1463 @ ( hAPP @ SY1462 @ SV446 ) )
!= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1463 ) @ SY1462 ) @ SV446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6157]) ).
thf(6213,plain,
! [SV48: $i,SV151: $i,SV240: $i,SV321: $i,SV377: $i,SV413: $i,SV433: $i] :
( ( ( SV433 = SV413 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV433 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV377 @ SV321 @ SV240 @ SV151 @ SV48 ) @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6158]) ).
thf(6214,plain,
! [SV50: $i,SV153: $i,SV242: $i,SV323: $i,SV378: $i,SV414: $i] :
( ( ( SV414 = SV378 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV414 ) @ SV153 ) ) @ SV378 ) @ SV50 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV323 @ SV242 ) @ SV378 ) @ SV50 ) ) @ SV414 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6159]) ).
thf(6215,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
!= SV243 )
= $true )
| ( ( ( hAPP @ SV243 @ SV154 )
= SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6160]) ).
thf(6216,plain,
! [SV324: $i,SV379: $i,SV51: $i,SV154: $i,SV243: $i] :
( ( ( ( hAPP @ SV243 @ SV154 )
!= SV51 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6161]) ).
thf(6217,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i,SV415: $i,SV434: $i,SV442: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV442 @ SV434 @ SV415 @ SV380 ) @ SV326 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SV434 @ SV415 @ SV158 ) @ SV55 ) )
= $true )
| ( ( ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6162]) ).
thf(6218,plain,
! [SV57: $i,SV160: $i,SV248: $i,SV327: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
= $false )
| ( ( SV160 = SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6163]) ).
thf(6219,plain,
! [SV248: $i,SV327: $i,SV57: $i,SV160: $i] :
( ( ( SV160 = SV57 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV160 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV327 @ SV248 ) @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6164]) ).
thf(6220,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true )
| ( ( ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6165]) ).
thf(6221,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( ~ ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6166]) ).
thf(6222,plain,
! [SV331: $i,SV255: $i,SV66: $i,SV169: $i] :
( ( ( SV169
!= ( hAPP @ c_Nat_OSuc @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6169]) ).
thf(6223,plain,
! [SV169: $i,SV66: $i,SV255: $i,SV331: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) @ SV66 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6169]) ).
thf(6224,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true )
| ( ( ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6172]) ).
thf(6225,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6173]) ).
thf(6226,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i,SV417: $i,SV435: $i] :
( ( ( SV435 != SV417 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV435 ) @ SV175 ) ) @ SV417 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV417 ) @ SV73 ) ) @ SV435 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(6227,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
= $false )
| ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(6228,plain,
! [SV74: $i,SV176: $i,SV262: $i,SV336: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV336 ) ) @ SV262 @ SV176 @ SV74 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV336 ) @ SV262 @ ( hAPP @ c_Nat_OSuc @ SV176 ) @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(6229,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
| ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6178]) ).
thf(6230,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6179]) ).
thf(6231,plain,
! [SV82: $i,SV184: $i,SV270: $i,SV340: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
= $false )
| ( ( SV184 = SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6184]) ).
thf(6232,plain,
! [SV270: $i,SV340: $i,SV82: $i,SV184: $i] :
( ( ( SV184 = SV82 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV184 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV340 @ SV270 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6185]) ).
thf(6233,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( SV419 != SV388 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6186]) ).
thf(6234,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ~ ( ( SV419 != SV388 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6187]) ).
thf(6235,plain,
! [SV390: $i,SV421: $i,SV87: $i,SV343: $i,SV273: $i,SV188: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV421 @ SV188 ) @ SV390 @ SV343 @ SV87 )
= $true )
| ( ( c_Natural_Oevaln @ SV421 @ SV390 @ SV343 @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6189]) ).
thf(6236,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 ) )
= $true )
| ( ( ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6190]) ).
thf(6237,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6191]) ).
thf(6238,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ! [SY1229: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1229 @ SV96 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6192]) ).
thf(6239,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ! [SY1230: $i] :
~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SY1230 @ SV96 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6193]) ).
thf(6240,plain,
! [SV98: $i,SV198: $i,SV283: $i,SV350: $i,SV393: $i,SV422: $i,SV436: $i] :
( ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6194]) ).
thf(6241,plain,
! [SV103: $i,SV203: $i,SV287: $i,SV353: $i,SV394: $i,SV423: $i] :
( ( ( SV423 = SV394 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV353 @ SV287 ) @ SV203 ) @ SV394 ) @ SV103 ) @ SV423 )
= ( hAPP @ SV203 @ SV423 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6195]) ).
thf(6242,plain,
! [SV2: $i,SV106: $i,SV206: $i,SV290: $i,SV355: $i,SV396: $i,SV425: $i,SV437: $i,SV443: $i,SV447: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV447 @ SV443 @ SV437 @ SV425 @ SV396 @ SV355 @ SV290 @ SV206 @ SV106 @ ( c_Com_Ocom_OBODY @ SV2 ) )
= ( hAPP @ SV206 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6197]) ).
thf(6243,plain,
! [SV5: $i,SV109: $i,SV208: $i,SV292: $i,SV356: $i,SV397: $i,SV426: $i,SV438: $i,SV444: $i,SV448: $i] :
( ( ( c_Com_Ocom_Ocom__rec @ SV448 @ SV444 @ SV438 @ SV426 @ SV397 @ SV356 @ SV292 @ SV208 @ SV109 @ ( c_Com_Ocom_OBODY @ SV5 ) )
= ( hAPP @ SV208 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6198]) ).
thf(6244,plain,
! [SV309: $i,SV31: $i,SV135: $i,SV227: $i,SV368: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6199]) ).
thf(6245,plain,
! [SV368: $i,SV227: $i,SV135: $i,SV31: $i,SV309: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV309 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) @ SV135 @ SV31 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6199]) ).
thf(6246,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( SV406 != SV369 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6200]) ).
thf(6247,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( ~ ( ( SV406 != SV369 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6201]) ).
thf(6248,plain,
! [SV35: $i,SV231: $i,SV371: $i,SV408: $i,SV139: $i,SV312: $i] :
( ( ( SV312 != SV139 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6203]) ).
thf(6249,plain,
! [SV139: $i,SV312: $i,SV371: $i,SV408: $i,SV35: $i,SV231: $i] :
( ( ( SV231 != SV35 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6203]) ).
thf(6250,plain,
! [SV313: $i,SV439: $i,SV372: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SV372 @ v_n @ SV439 )
= $false )
| ( ( v_Q @ SV313 @ SV439 )
= $true )
| ( ( v_P @ SV313 @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6204]) ).
thf(6251,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i,SV430: $i,SV440: $i,SV445: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV445 @ SV440 @ SV430 @ SV409 ) @ SV373 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SV440 @ SV430 @ SV232 ) @ SV141 ) )
= $true )
| ( ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6205]) ).
thf(6252,plain,
! [SV236: $i,SV374: $i,SV42: $i,SV317: $i,SV410: $i,SV145: $i] :
( ( ( SV145
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV317 ) @ SV42 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV145 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV236 ) @ SV42 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV410 ) @ SV374 ) @ SV317 )
= SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6208]) ).
thf(6253,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i,SV446: $i,SV449: $i] :
( ( ! [SY1464: $i] :
( ( ( hAPP @ SY1464 @ ( hAPP @ SV449 @ SV446 ) )
!= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SY1464 ) @ SV449 ) @ SV446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6212]) ).
thf(6254,plain,
! [SV51: $i,SV154: $i,SV243: $i,SV324: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 )
= $false )
| ( ( ( hAPP @ SV243 @ SV154 )
= SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6215]) ).
thf(6255,plain,
! [SV324: $i,SV379: $i,SV51: $i,SV154: $i,SV243: $i] :
( ( ( ( hAPP @ SV243 @ SV154 )
= SV51 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV379 @ SV324 ) @ SV243 ) @ SV154 ) @ SV51 )
= SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6256,plain,
! [SV55: $i,SV158: $i,SV247: $i,SV326: $i,SV380: $i,SV415: $i,SV434: $i,SV442: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV442 @ SV434 @ SV415 @ SV380 ) @ SV326 )
= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SV434 @ SV415 @ SV158 ) @ SV55 ) )
= $false )
| ( ( ! [SY1394: $i] :
( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SY1394 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SY1394 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6217]) ).
thf(6257,plain,
! [SV60: $i,SV163: $i,SV250: $i,SV328: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false )
| ( ( ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6220]) ).
thf(6258,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( ~ ( ( SV328 != SV163 )
| ( SV250 != SV60 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6221]) ).
thf(6259,plain,
! [SV331: $i,SV255: $i,SV66: $i,SV169: $i] :
( ( ( SV169
= ( hAPP @ c_Nat_OSuc @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6222]) ).
thf(6260,plain,
! [SV169: $i,SV66: $i,SV255: $i,SV331: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV331 ) ) @ SV255 @ ( sK6_SY1319 @ SV66 @ SV255 @ SV331 @ SV169 ) @ SV66 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV331 ) @ SV255 @ SV169 @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6223]) ).
thf(6261,plain,
! [SV69: $i,SV172: $i,SV258: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false )
| ( ( ~ ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6224]) ).
thf(6262,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6225]) ).
thf(6263,plain,
! [SV73: $i,SV175: $i,SV261: $i,SV335: $i,SV385: $i,SV417: $i,SV435: $i] :
( ( ( SV435 = SV417 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV435 ) @ SV175 ) ) @ SV417 ) @ SV73 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV385 @ SV335 ) @ SV261 ) @ SV417 ) @ SV73 ) ) @ SV435 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6226]) ).
thf(6264,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true )
| ( ( ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6229]) ).
thf(6265,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( ~ ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6230]) ).
thf(6266,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( SV419 != SV388 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6233]) ).
thf(6267,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( ~ ( ( SV419 != SV388 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6234]) ).
thf(6268,plain,
! [SV390: $i,SV421: $i,SV87: $i,SV343: $i,SV273: $i,SV188: $i] :
( ( ( c_Natural_Oevaln @ SV188 @ SV273 @ SV343 @ SV87 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV421 @ SV188 ) @ SV390 @ SV343 @ SV87 )
= $true )
| ( ( c_Natural_Oevaln @ SV421 @ SV390 @ SV343 @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6235]) ).
thf(6269,plain,
! [SV89: $i,SV190: $i,SV275: $i,SV344: $i,SV391: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false )
| ( ( ~ ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6236]) ).
thf(6270,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6237]) ).
thf(6271,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV281 @ SV196 @ ( sK9_SY1229 @ SV96 @ SV196 @ SV281 ) @ SV96 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6238]) ).
thf(6272,plain,
! [SV96: $i,SV450: $i,SV196: $i,SV281: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV281 @ SV196 @ SV450 @ SV96 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6239]) ).
thf(6273,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV98: $i,SV198: $i,SV393: $i] :
( ( ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
| ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6274,plain,
! [SV309: $i,SV31: $i,SV135: $i,SV227: $i,SV368: $i] :
( ( ( c_Natural_Oevaln @ SV368 @ SV227 @ SV135 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6244]) ).
thf(6275,plain,
! [SV368: $i,SV227: $i,SV135: $i,SV31: $i,SV309: $i] :
( ( ( c_Natural_Oevaln @ SV309 @ ( sK8_SY1369 @ SV31 @ SV309 @ SV135 @ SV227 @ SV368 ) @ SV135 @ SV31 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV368 @ SV309 ) @ SV227 @ SV135 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6245]) ).
thf(6276,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( SV406 = SV369 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(6277,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( SV406 != SV369 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6247]) ).
thf(6278,plain,
! [SV35: $i,SV231: $i,SV371: $i,SV408: $i,SV139: $i,SV312: $i] :
( ( ( SV312 = SV139 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6248]) ).
thf(6279,plain,
! [SV139: $i,SV312: $i,SV371: $i,SV408: $i,SV35: $i,SV231: $i] :
( ( ( SV231 = SV35 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV312 ) @ SV231 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV408 @ SV371 ) @ SV139 ) @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6249]) ).
thf(6280,plain,
! [SV37: $i,SV141: $i,SV232: $i,SV314: $i,SV373: $i,SV409: $i,SV430: $i,SV440: $i,SV445: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV445 @ SV440 @ SV430 @ SV409 ) @ SV373 )
= ( hAPP @ ( c_Fun_Ocomp @ SV314 @ SV440 @ SV430 @ SV232 ) @ SV141 ) )
= $false )
| ( ( ( hAPP @ SV409 @ ( hAPP @ SV373 @ SV37 ) )
= ( hAPP @ SV232 @ ( hAPP @ SV141 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6251]) ).
thf(6281,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i,SV446: $i,SV449: $i,SV451: $i] :
( ( ( ( hAPP @ SV451 @ ( hAPP @ SV449 @ SV446 ) )
!= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SV451 ) @ SV449 ) @ SV446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6253]) ).
thf(6282,plain,
! [SV247: $i,SV415: $i,SV434: $i,SV442: $i,SV55: $i,SV158: $i,SV452: $i,SV326: $i,SV380: $i] :
( ( ( ( hAPP @ SV380 @ ( hAPP @ SV326 @ SV452 ) )
= ( hAPP @ SV158 @ ( hAPP @ SV55 @ SV452 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV442 @ SV434 @ SV415 @ SV380 ) @ SV326 )
= ( hAPP @ ( c_Fun_Ocomp @ SV247 @ SV434 @ SV415 @ SV158 ) @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6256]) ).
thf(6283,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6284,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( ( SV328 != SV163 )
| ( SV250 != SV60 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6258]) ).
thf(6285,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ! [SY1395: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1395 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1395 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1395 ) @ SV69 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6261]) ).
thf(6286,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ! [SY1396: $i] :
~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SY1396 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SY1396 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SY1396 ) @ SV69 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6262]) ).
thf(6287,plain,
! [SV76: $i,SV178: $i,SV264: $i,SV338: $i,SV386: $i,SV418: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false )
| ( ( ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6264]) ).
thf(6288,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( ~ ( ( SV338 != SV178 )
| ( SV264 != SV76 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(6289,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( SV419 = SV388 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6266]) ).
thf(6290,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( SV419 != SV388 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6267]) ).
thf(6291,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ! [SY1405: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1405 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1405 @ SV190 @ SV89 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6269]) ).
thf(6292,plain,
! [SV89: $i,SV344: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ! [SY1406: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SY1406 )
| ~ ( c_Natural_Oevaln @ SV344 @ SY1406 @ SV190 @ SV89 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6270]) ).
thf(6293,plain,
! [SV96: $i,SV196: $i,SV281: $i] :
( ( ( c_Natural_Oevaln @ SV281 @ SV196 @ ( sK9_SY1229 @ SV96 @ SV196 @ SV281 ) @ SV96 )
= $true )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6271]) ).
thf(6294,plain,
! [SV96: $i,SV450: $i,SV196: $i,SV281: $i] :
( ( ( c_Natural_Oevaln @ SV281 @ SV196 @ SV450 @ SV96 )
= $false )
| ( ( c_Natural_Oevalc @ SV281 @ SV196 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6272]) ).
thf(6295,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV98: $i,SV198: $i,SV393: $i] :
( ( ( ~ ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6273]) ).
thf(6296,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV393: $i,SV98: $i,SV198: $i] :
( ( ( ~ ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6273]) ).
thf(6297,plain,
! [SV33: $i,SV137: $i,SV229: $i,SV310: $i,SV369: $i,SV406: $i] :
( ( ( SV406 = SV369 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV310 @ SV229 ) @ SV137 ) @ SV369 ) @ SV33 ) @ SV406 )
= ( hAPP @ SV137 @ SV406 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6277]) ).
thf(6298,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i,SV446: $i,SV449: $i,SV451: $i] :
( ( ( ( hAPP @ SV451 @ ( hAPP @ SV449 @ SV446 ) )
!= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SV451 ) @ SV449 ) @ SV446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6281]) ).
thf(6299,plain,
! [SV60: $i,SV250: $i,SV381: $i,SV163: $i,SV328: $i] :
( ( ( SV328 != SV163 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6283]) ).
thf(6300,plain,
! [SV163: $i,SV328: $i,SV381: $i,SV60: $i,SV250: $i] :
( ( ( SV250 != SV60 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6283]) ).
thf(6301,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( SV328 != SV163 )
= $true )
| ( ( SV250 != SV60 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6284]) ).
thf(6302,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6285]) ).
thf(6303,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6286]) ).
thf(6304,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(6305,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( ( SV338 != SV178 )
| ( SV264 != SV76 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6288]) ).
thf(6306,plain,
! [SV83: $i,SV185: $i,SV271: $i,SV341: $i,SV388: $i,SV419: $i] :
( ( ( SV419 = SV388 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV341 @ SV271 ) @ SV185 ) @ SV388 ) @ SV83 ) @ SV419 )
= ( hAPP @ SV185 @ SV419 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6290]) ).
thf(6307,plain,
! [SV344: $i,SV89: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) )
| ~ ( c_Natural_Oevaln @ SV344 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) @ SV190 @ SV89 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6291]) ).
thf(6308,plain,
! [SV89: $i,SV344: $i,SV454: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 )
| ~ ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6292]) ).
thf(6309,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV98: $i,SV198: $i,SV393: $i] :
( ( ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
| ( SV198 = SV98 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6295]) ).
thf(6310,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV393: $i,SV98: $i,SV198: $i] :
( ( ( ( SV198 != SV98 )
| ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6296]) ).
thf(6311,plain,
! [SV45: $i,SV148: $i,SV239: $i,SV320: $i,SV376: $i,SV412: $i,SV432: $i,SV441: $i,SV446: $i,SV449: $i,SV451: $i] :
( ( ( ( hAPP @ SV451 @ ( hAPP @ SV449 @ SV446 ) )
= ( hAPP @ SV441 @ ( hAPP @ SV432 @ SV412 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV376 @ SV320 @ SV239 @ SV451 ) @ SV449 ) @ SV446 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV148 @ SV320 @ SV45 @ SV441 ) @ SV432 ) @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6298]) ).
thf(6312,plain,
! [SV60: $i,SV250: $i,SV381: $i,SV163: $i,SV328: $i] :
( ( ( SV328 = SV163 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6299]) ).
thf(6313,plain,
! [SV163: $i,SV328: $i,SV381: $i,SV60: $i,SV250: $i] :
( ( ( SV250 = SV60 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6300]) ).
thf(6314,plain,
! [SV381: $i,SV60: $i,SV250: $i,SV163: $i,SV328: $i] :
( ( ( SV328 = SV163 )
= $false )
| ( ( SV250 != SV60 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6301]) ).
thf(6315,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6302]) ).
thf(6316,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6303]) ).
thf(6317,plain,
! [SV76: $i,SV264: $i,SV386: $i,SV418: $i,SV178: $i,SV338: $i] :
( ( ( SV338 != SV178 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6304]) ).
thf(6318,plain,
! [SV178: $i,SV338: $i,SV386: $i,SV418: $i,SV76: $i,SV264: $i] :
( ( ( SV264 != SV76 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6304]) ).
thf(6319,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( SV338 != SV178 )
= $true )
| ( ( SV264 != SV76 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6305]) ).
thf(6320,plain,
! [SV344: $i,SV89: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) )
| ~ ( c_Natural_Oevaln @ SV344 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) @ SV190 @ SV89 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6307]) ).
thf(6321,plain,
! [SV89: $i,SV344: $i,SV454: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 )
| ~ ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6308]) ).
thf(6322,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV98: $i,SV198: $i,SV393: $i] :
( ( ( ( hAPP @ SV393 @ SV198 )
!= ( hAPP @ SV393 @ SV98 ) )
= $true )
| ( ( SV198 = SV98 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6309]) ).
thf(6323,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV393: $i,SV98: $i,SV198: $i] :
( ( ( SV198 != SV98 )
= $true )
| ( ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6310]) ).
thf(6324,plain,
! [SV381: $i,SV163: $i,SV328: $i,SV60: $i,SV250: $i] :
( ( ( SV250 = SV60 )
= $false )
| ( ( SV328 = SV163 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV328 ) @ SV250 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV381 ) @ SV163 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(6325,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
!= SV69 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6315]) ).
thf(6326,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ~ ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6316]) ).
thf(6327,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV453: $i,SV333: $i,SV383: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6316]) ).
thf(6328,plain,
! [SV76: $i,SV264: $i,SV386: $i,SV418: $i,SV178: $i,SV338: $i] :
( ( ( SV338 = SV178 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6317]) ).
thf(6329,plain,
! [SV178: $i,SV338: $i,SV386: $i,SV418: $i,SV76: $i,SV264: $i] :
( ( ( SV264 = SV76 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6318]) ).
thf(6330,plain,
! [SV386: $i,SV418: $i,SV76: $i,SV264: $i,SV178: $i,SV338: $i] :
( ( ( SV338 = SV178 )
= $false )
| ( ( SV264 != SV76 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6319]) ).
thf(6331,plain,
! [SV344: $i,SV89: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) )
| ~ ( c_Natural_Oevaln @ SV344 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) @ SV190 @ SV89 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6320]) ).
thf(6332,plain,
! [SV89: $i,SV344: $i,SV454: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 )
| ~ ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6321]) ).
thf(6333,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV98: $i,SV198: $i,SV393: $i] :
( ( ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) )
= $false )
| ( ( SV198 = SV98 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6322]) ).
thf(6334,plain,
! [SV283: $i,SV350: $i,SV422: $i,SV436: $i,SV393: $i,SV98: $i,SV198: $i] :
( ( ( SV198 = SV98 )
= $false )
| ( ( ( hAPP @ SV393 @ SV198 )
= ( hAPP @ SV393 @ SV98 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV436 @ SV422 @ SV393 @ SV350 @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6323]) ).
thf(6335,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
!= SV69 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6325]) ).
thf(6336,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6326]) ).
thf(6337,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV453: $i,SV333: $i,SV383: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6327]) ).
thf(6338,plain,
! [SV386: $i,SV418: $i,SV178: $i,SV338: $i,SV76: $i,SV264: $i] :
( ( ( SV264 = SV76 )
= $false )
| ( ( SV338 = SV178 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV338 ) @ SV264 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV418 @ SV386 ) @ SV178 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6330]) ).
thf(6339,plain,
! [SV344: $i,SV89: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6331]) ).
thf(6340,plain,
! [SV391: $i,SV275: $i,SV190: $i,SV89: $i,SV344: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV344 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) @ SV190 @ SV89 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6331]) ).
thf(6341,plain,
! [SV89: $i,SV344: $i,SV454: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6332]) ).
thf(6342,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6335]) ).
thf(6343,plain,
! [SV333: $i,SV172: $i,SV258: $i,SV69: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
!= SV69 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6335]) ).
thf(6344,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( SV333
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6336]) ).
thf(6345,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV453: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
!= SV172 )
= $true )
| ( ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6337]) ).
thf(6346,plain,
! [SV344: $i,SV89: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6339]) ).
thf(6347,plain,
! [SV391: $i,SV275: $i,SV190: $i,SV89: $i,SV344: $i] :
( ( ( c_Natural_Oevaln @ SV344 @ ( sK11_SY1405 @ SV89 @ SV344 @ SV190 @ SV275 @ SV391 ) @ SV190 @ SV89 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6340]) ).
thf(6348,plain,
! [SV89: $i,SV344: $i,SV454: $i,SV190: $i,SV275: $i,SV391: $i] :
( ( ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6341]) ).
thf(6349,plain,
! [SV258: $i,SV69: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6342]) ).
thf(6350,plain,
! [SV333: $i,SV172: $i,SV258: $i,SV69: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6343]) ).
thf(6351,plain,
! [SV69: $i,SV258: $i,SV453: $i,SV172: $i,SV383: $i,SV333: $i] :
( ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
!= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(6352,plain,
! [SV69: $i,SV258: $i,SV172: $i,SV453: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
= SV172 )
= $false )
| ( ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6345]) ).
thf(6353,plain,
! [SV275: $i,SV391: $i,SV89: $i,SV190: $i,SV454: $i,SV344: $i] :
( ( ( c_Natural_Oevaln @ SV344 @ SV454 @ SV190 @ SV89 )
= $false )
| ( ( c_Natural_Oevaln @ SV391 @ SV275 @ SV190 @ SV454 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV391 @ SV344 ) @ SV275 @ SV190 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6348]) ).
thf(6354,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) )
= $false )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6349]) ).
thf(6355,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
| ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6350]) ).
thf(6356,plain,
! [SV172: $i,SV333: $i,SV69: $i,SV258: $i,SV453: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV258 )
= SV69 )
= $false )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV453 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(6357,plain,
! [SV172: $i,SV333: $i,SV69: $i,SV453: $i,SV383: $i,SV258: $i] :
( ( ( SV258
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV453 ) @ SV69 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV453 )
= SV172 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6352]) ).
thf(6358,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
= $false )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6354]) ).
thf(6359,plain,
! [SV333: $i,SV172: $i,SV69: $i,SV383: $i,SV258: $i] :
( ( ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) )
= $false )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6354]) ).
thf(6360,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
!= SV172 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6355]) ).
thf(6361,plain,
! [SV333: $i,SV172: $i,SV69: $i,SV383: $i,SV258: $i] :
( ( ( SV258
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6355]) ).
thf(6362,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
= SV172 )
= $true )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6358]) ).
thf(6363,plain,
! [SV333: $i,SV172: $i,SV69: $i,SV383: $i,SV258: $i] :
( ( ( SV258
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) )
= $true )
| ( ( SV333
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6359]) ).
thf(6364,plain,
! [SV172: $i,SV258: $i,SV69: $i,SV333: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) )
= SV172 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6360]) ).
thf(6365,plain,
! [SV333: $i,SV172: $i,SV69: $i,SV383: $i,SV258: $i] :
( ( ( SV258
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ ( sK10_SY1395 @ SV69 @ SV258 @ SV172 @ SV383 @ SV333 ) ) @ SV258 )
= SV69 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV333 ) @ SV258 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV383 ) @ SV172 ) @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6361]) ).
thf(6366,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5603,6365,6364,6363,6362,6357,6356,6353,6347,6346,6338,6334,6333,6329,6328,6324,6313,6312,6311,6306,6297,6294,6293,6289,6282,6280,6279,6278,6276,6275,6274,6268,6263,6260,6259,6255,6254,6252,6250,6243,6242,6241,6232,6231,6228,6227,6219,6218,6214,6213,6211,6210,6209,6207,6206,6202,6196,6188,6183,6182,6181,6180,6174,6171,6170,6168,6167,6149,6143,6142,6136,6135,6131,6126,6125,6107,6100,6099,6093,6092,6091,6090,6081,6078,6077,6070,6069,6059,6058,6043,6037,6024,6021,6006,5996,5995,5994,5991,5990,5989,5982,5981,5980,5978,5973,5949,5948,5940,5938,5924,5908,5903,5901,5885,5882,5874,5872,5866,5858,5854,5853,5833,5817,5816,5814,5807,5806,5803,5801,5721,5712,5696,5688,5674,5642,5626,5625,5619,5618,5617,5607,5606]) ).
thf(6367,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)],[5311]) ).
thf(6368,plain,
( ( ! [V_s1: $i,V_n: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5310]) ).
thf(6369,plain,
( ( ! [V_a4_2: $i,V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ ( hAPP @ c_Nat_OSuc @ V_a3_2 ) @ V_a4_2 )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 @ V_a4_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5309]) ).
thf(6370,plain,
( ( ! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[5308]) ).
thf(6371,plain,
( ( ! [V_s1: $i,V_n: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 )
=> ~ ! [B_n: $i] :
( ( V_n
= ( hAPP @ c_Nat_OSuc @ B_n ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ B_n @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(6372,plain,
( ( ! [V_pname_H_2: $i,V_pname_2: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname_2 )
= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) )
<=> ( V_pname_2 = V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5306]) ).
thf(6373,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5305]) ).
thf(6374,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5304]) ).
thf(6375,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)],[5303]) ).
thf(6376,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)],[5302]) ).
thf(6377,plain,
( ( ! [V_s1: $i,V_s: $i,V_P: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5301]) ).
thf(6378,plain,
( ( ! [V_s1: $i,V_s0: $i,V_pn: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[5300]) ).
thf(6379,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t )
=> ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(6380,plain,
( ( ! [V_t_2: $i,V_s_2: $i,V_c_2: $i] :
( ( c_Natural_Oevalc @ V_c_2 @ V_s_2 @ V_t_2 )
<=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c_2 @ V_s_2 @ B_n @ V_t_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5298]) ).
thf(6381,plain,
( ( ! [V_a3_2: $i,V_a2_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_a1_2 ) @ V_a2_2 @ V_a3_2 )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_a1_2 ) ) @ V_a2_2 @ V_a3_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(6382,plain,
( ( ! [V_t: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
=> ? [B_n: $i] : ( c_Natural_Oevaln @ V_c @ V_s @ B_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[5296]) ).
thf(6383,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(6384,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__case @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(6385,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[5293]) ).
thf(6386,plain,
( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[5292]) ).
thf(6387,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5291]) ).
thf(6388,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5290]) ).
thf(6389,plain,
( ( ! [V_pname_2: $i,V_f8_2: $i,V_f7_2: $i,V_f6_2: $i,V_f5_2: $i,V_f4_2: $i,V_f3_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Com_Ocom_Ocom__rec @ T_b @ V_f1_2 @ V_f2_2 @ V_f3_2 @ V_f4_2 @ V_f5_2 @ V_f6_2 @ V_f7_2 @ V_f8_2 @ ( c_Com_Ocom_OBODY @ V_pname_2 ) )
= ( hAPP @ V_f7_2 @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(6390,plain,
( ( ! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(6391,plain,
( ( ! [V_com2: $i,V_com1: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(6392,plain,
( ( ! [V_pname_H: $i,V_com2: $i,V_com1: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(6393,plain,
( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(6394,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(6395,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(6396,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5282]) ).
thf(6397,plain,
( ( ! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(6398,plain,
( ( ! [V_pname_H_2: $i,V_com2_2: $i,V_com1_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5280]) ).
thf(6399,plain,
( ( ! [V_com2_2: $i,V_com1_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OCond @ V_fun_2 @ V_com1_2 @ V_com2_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(6400,plain,
( ( ! [V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i,V_pname_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_2 )
!= ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(6401,plain,
( ( ! [V_pname_2: $i,V_fun_H_2: $i,V_pname_H_2: $i,V_vname_H_2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H_2 @ V_pname_H_2 @ V_fun_H_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(6402,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( hAPP @ ( c_Option_Ooption_OSome @ T_a ) @ V_x ) )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(6403,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_2 )
= ( hAPP @ ( c_Option_Ooption_OSome @ T_b ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(6404,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_loc_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5274]) ).
thf(6405,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i,V_loc_2: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_2 @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5273]) ).
thf(6406,plain,
( ( ! [V_pname_H_2: $i,V_com_2: $i,V_fun_2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5272]) ).
thf(6407,plain,
( ( ! [V_com_2: $i,V_fun_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OWhile @ V_fun_2 @ V_com_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5271]) ).
thf(6408,plain,
( ( ! [V_fun_2: $i,V_vname_2: $i,V_pname_H_2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H_2 )
!= ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5270]) ).
thf(6409,plain,
( ( ! [V_pname_H_2: $i,V_fun_2: $i,V_vname_2: $i] :
( ( c_Com_Ocom_OAss @ V_vname_2 @ V_fun_2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5269]) ).
thf(6410,plain,
( ( ! [V_b_H_2: $i,V_b_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_2 )
= ( hAPP @ ( c_Sum__Type_OInr @ T_c @ T_b ) @ V_b_H_2 ) )
<=> ( V_b_2 = V_b_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5268]) ).
thf(6411,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInr @ T_b @ T_a ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5267]) ).
thf(6412,plain,
( ( ! [V_a_H_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_2 )
= ( hAPP @ ( c_Sum__Type_OInl @ T_b @ T_c ) @ V_a_H_2 ) )
<=> ( V_a_2 = V_a_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(6413,plain,
( ( ! [V_y: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_x )
= ( hAPP @ ( c_Sum__Type_OInl @ T_a @ T_b ) @ V_y ) )
=> ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[5265]) ).
thf(6414,plain,
( ( ! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5264]) ).
thf(6415,plain,
( ( ! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5263]) ).
thf(6416,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)],[5262]) ).
thf(6417,plain,
( ( ! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5261]) ).
thf(6418,plain,
( ( ! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5260]) ).
thf(6419,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)],[5259]) ).
thf(6420,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)],[5258]) ).
thf(6421,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_c: $i,T_d: $i,T_b: $i,V_t_2: $i,V_s_2: $i] :
( ( V_s_2 = V_t_2 )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_s_2 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ T_b @ T_d @ T_c @ V_f_2 @ V_g_2 ) @ V_t_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(6422,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5256]) ).
thf(6423,plain,
( ( ! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5255]) ).
thf(6424,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)],[5254]) ).
thf(6425,plain,
( ( ! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(6426,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5252]) ).
thf(6427,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(6428,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ) )
= $true ),
inference(copy,[status(thm)],[5250]) ).
thf(6429,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(6430,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) ) @ V_x_2 ) @ V_z_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5248]) ).
thf(6431,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_x_2 )
= V_y_2 ) )
= $true ),
inference(copy,[status(thm)],[5247]) ).
thf(6432,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5246]) ).
thf(6433,plain,
( ( ! [V_d_2: $i,V_b_2: $i,V_m_2: $i,T_c: $i,T_b: $i,V_c_2: $i,V_a_2: $i] :
( ( V_a_2 != V_c_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_a_2 ) @ V_b_2 ) ) @ V_c_2 ) @ V_d_2 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_m_2 ) @ V_c_2 ) @ V_d_2 ) ) @ V_a_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(6434,plain,
( ( ! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(6435,plain,
( ( ! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b ) @ V_f_2 ) @ V_x_2 ) @ V_y_2 )
= V_f_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(6436,plain,
( ( ! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c ) @ V_f_2 ) @ V_a_2 ) @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(6437,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(6438,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(6439,plain,
( ( ! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(6440,plain,
( ( ! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(6441,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(6442,plain,
( ( ! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(6443,plain,
( ( ! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(6444,plain,
( ( ! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(6445,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ) )
= $true ),
inference(copy,[status(thm)],[5233]) ).
thf(6446,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)],[5232]) ).
thf(6447,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5231]) ).
thf(6448,plain,
( ( ! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5230]) ).
thf(6449,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5229]) ).
thf(6450,plain,
( ( ! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ) )
= $true ),
inference(copy,[status(thm)],[5228]) ).
thf(6451,plain,
( ( ! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5227]) ).
thf(6452,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5226]) ).
thf(6453,plain,
( ( ! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5225]) ).
thf(6454,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)],[5224]) ).
thf(6455,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)],[5223]) ).
thf(6456,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)],[5222]) ).
thf(6457,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)],[5221]) ).
thf(6458,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)],[5220]) ).
thf(6459,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5219]) ).
thf(6460,plain,
( ( ! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5218]) ).
thf(6461,plain,
( ( ! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5217]) ).
thf(6462,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)],[5216]) ).
thf(6463,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)],[5215]) ).
thf(6464,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5214]) ).
thf(6465,plain,
( ( ! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5213]) ).
thf(6466,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5212]) ).
thf(6467,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)],[5211]) ).
thf(6468,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5210]) ).
thf(6469,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Qa_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5209]) ).
thf(6470,plain,
( ( ! [V_R_2: $i,V_Qa_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Qa_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Qa_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5208]) ).
thf(6471,plain,
( ( ~ ( ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_P @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B_s @ v_n @ B_s_H )
=> ( v_Q @ B_Z @ B_s_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5315]) ).
thf(6472,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)],[6437]) ).
thf(6473,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)],[6418]) ).
thf(6474,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)],[6427]) ).
thf(6475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6377]) ).
thf(6476,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OWhile @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6407]) ).
thf(6477,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6378]) ).
thf(6478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6411]) ).
thf(6479,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)],[6403]) ).
thf(6480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SX4 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SX3 @ SX2 @ SX1 ) @ SX5 ) )
| ( ( hAPP @ SX4 @ ( hAPP @ c_Nat_OSuc @ SX0 ) )
= ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ ( hAPP @ SX4 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6397]) ).
thf(6481,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)],[6421]) ).
thf(6482,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)],[6456]) ).
thf(6483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OAss @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6408]) ).
thf(6484,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)],[6375]) ).
thf(6485,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)],[6416]) ).
thf(6486,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)],[6453]) ).
thf(6487,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)],[6439]) ).
thf(6488,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ SX3 @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6379]) ).
thf(6489,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ SX3 @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ SX3 @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6370]) ).
thf(6490,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)],[6440]) ).
thf(6491,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)],[6444]) ).
thf(6492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( c_Natural_Oevaln @ SX1 @ SX2 @ SX3 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX5 @ SX1 ) @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6388]) ).
thf(6493,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OWhile @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6406]) ).
thf(6494,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)],[6420]) ).
thf(6495,plain,
( ( ! [SX0: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6394]) ).
thf(6496,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6382]) ).
thf(6497,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SX5 @ SX4 @ SX3 )
| ( ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
= ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6449]) ).
thf(6498,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OSemi @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6392]) ).
thf(6499,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OCond @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6399]) ).
thf(6500,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX1 )
= ( hAPP @ ( c_Sum__Type_OInr @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6410]) ).
thf(6501,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( c_Com_Ocom_OBODY @ SX1 )
= ( c_Com_Ocom_OBODY @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6372]) ).
thf(6502,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6471]) ).
thf(6503,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OCond @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6398]) ).
thf(6504,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)],[6415]) ).
thf(6505,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ ( hAPP @ SX4 @ SX0 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6452]) ).
thf(6506,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6413]) ).
thf(6507,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)],[6424]) ).
thf(6508,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)],[6426]) ).
thf(6509,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)],[6432]) ).
thf(6510,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)],[6462]) ).
thf(6511,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX2 ) ) @ SX1 @ SX0 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SX2 ) @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6381]) ).
thf(6512,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)],[6425]) ).
thf(6513,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6373]) ).
thf(6514,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)],[6429]) ).
thf(6515,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX2 )
!= ( c_Com_Ocom_OSemi @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6391]) ).
thf(6516,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6396]) ).
thf(6517,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[6454]) ).
thf(6518,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OLocal @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6404]) ).
thf(6519,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)],[6465]) ).
thf(6520,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OAss @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6409]) ).
thf(6521,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)],[6433]) ).
thf(6522,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( c_Natural_Oevaln @ SX2 @ SX1 @ SX3 @ SX0 )
| ( c_Natural_Oevalc @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6380]) ).
thf(6523,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)],[6436]) ).
thf(6524,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)],[6434]) ).
thf(6525,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX4: $i] :
( ( SX1
!= ( hAPP @ c_Nat_OSuc @ SX4 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX4 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6371]) ).
thf(6526,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6369]) ).
thf(6527,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)],[6460]) ).
thf(6528,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)],[6417]) ).
thf(6529,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)],[6461]) ).
thf(6530,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6455]) ).
thf(6531,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[6374]) ).
thf(6532,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX1 )
= ( hAPP @ ( c_Sum__Type_OInl @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6412]) ).
thf(6533,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)],[6443]) ).
thf(6534,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SX3 ) ) @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SX3 ) @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6368]) ).
thf(6535,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)],[6435]) ).
thf(6536,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)],[6459]) ).
thf(6537,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)],[6419]) ).
thf(6538,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OBODY @ SX3 )
!= ( c_Com_Ocom_OCall @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6400]) ).
thf(6539,plain,
( ( ! [SX0: $i] :
( ( c_Com_Ocom_OBODY @ SX0 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[6395]) ).
thf(6540,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OCall @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6401]) ).
thf(6541,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SX2 @ SX1 @ SX0 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6385]) ).
thf(6542,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)],[6464]) ).
thf(6543,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6390]) ).
thf(6544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6376]) ).
thf(6545,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Com_Ocom_OLocal @ SX3 @ SX2 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6405]) ).
thf(6546,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6367]) ).
thf(6547,plain,
! [SV455: $i] :
( ( ! [SY1465: $i,SY1466: $i,SY1467: $i] :
( ( c_Nat_Onat_Onat__case @ SY1467 @ SY1466 @ SY1465 @ ( hAPP @ c_Nat_OSuc @ SV455 ) )
= ( hAPP @ SY1465 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6383]) ).
thf(6548,plain,
! [SV456: $i] :
( ( ! [SY1468: $i,SY1469: $i,SY1470: $i,SY1471: $i,SY1472: $i,SY1473: $i,SY1474: $i,SY1475: $i,SY1476: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1476 @ SY1475 @ SY1474 @ SY1473 @ SY1472 @ SY1471 @ SY1470 @ SY1469 @ SY1468 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SY1469 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6384]) ).
thf(6549,plain,
! [SV457: $i] :
( ( ! [SY1477: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY1477 @ SV457 @ SY1477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6386]) ).
thf(6550,plain,
! [SV458: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1480 @ SY1479 @ SY1478 ) @ ( hAPP @ c_Nat_OSuc @ SV458 ) )
= ( hAPP @ ( hAPP @ SY1478 @ SV458 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1480 @ SY1479 @ SY1478 ) @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6387]) ).
thf(6551,plain,
! [SV459: $i] :
( ( ! [SY1481: $i,SY1482: $i,SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i,SY1487: $i,SY1488: $i,SY1489: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1489 @ SY1488 @ SY1487 @ SY1486 @ SY1485 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SY1482 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6389]) ).
thf(6552,plain,
! [SV460: $i] :
( ( ! [SY1490: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY1490 @ SV460 @ SY1490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6393]) ).
thf(6553,plain,
! [SV461: $i] :
( ( ! [SY1491: $i] :
( ( hAPP @ ( c_Option_Othe @ SY1491 ) @ ( hAPP @ ( c_Option_Ooption_OSome @ SY1491 ) @ SV461 ) )
= SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6402]) ).
thf(6554,plain,
! [SV462: $i] :
( ( ! [SY1492: $i,SY1493: $i,SY1494: $i,SY1495: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1495 @ SY1494 @ SY1493 ) @ SY1492 ) @ ( hAPP @ c_Nat_OSuc @ SV462 ) )
= ( hAPP @ ( hAPP @ SY1493 @ SY1492 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1495 @ SY1494 @ SY1493 ) @ SY1492 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6414]) ).
thf(6555,plain,
! [SV463: $i] :
( ( ! [SY1496: $i,SY1497: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1497 ) @ SY1496 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1497 ) @ SY1496 ) @ SV463 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1497 ) @ SY1496 ) @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6422]) ).
thf(6556,plain,
! [SV464: $i] :
( ( ! [SY1498: $i,SY1499: $i,SY1500: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1500 ) @ SY1499 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1500 ) @ SY1498 ) @ SV464 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1500 ) @ SY1498 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1500 ) @ SY1499 ) @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6423]) ).
thf(6557,plain,
! [SV465: $i] :
( ( ! [SY1501: $i,SY1502: $i,SY1503: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1503 @ SY1502 ) @ SY1501 ) @ SV465 ) @ ( hAPP @ SY1501 @ SV465 ) )
= SY1501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6428]) ).
thf(6558,plain,
! [SV466: $i] :
( ( ! [SY1504: $i,SY1505: $i,SY1506: $i,SY1507: $i,SY1508: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1508 @ SY1507 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1508 @ SY1507 ) @ SY1506 ) @ SY1505 ) @ SY1504 ) ) @ SY1505 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1508 @ SY1507 ) @ SY1506 ) @ SY1505 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6430]) ).
thf(6559,plain,
! [SV467: $i] :
( ( ! [SY1509: $i,SY1510: $i,SY1511: $i,SY1512: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1512 @ SY1511 ) @ SY1510 ) @ SY1509 ) @ SV467 ) @ SY1509 )
= SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6431]) ).
thf(6560,plain,
! [SV468: $i] :
( ( ! [SY1513: $i,SY1514: $i,SY1515: $i,SY1516: $i,SY1517: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1517 @ SY1516 @ SY1515 @ SY1514 ) @ SY1513 ) @ SV468 )
= ( hAPP @ SY1514 @ ( hAPP @ SY1513 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6438]) ).
thf(6561,plain,
! [SV469: $i] :
( ( ! [SY1518: $i,SY1519: $i,SY1520: $i,SY1521: $i,SY1522: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1522 @ SY1521 @ SY1520 @ SY1519 ) @ SY1518 ) @ SV469 )
= ( hAPP @ SY1519 @ ( hAPP @ SY1518 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6441]) ).
thf(6562,plain,
! [SV470: $i] :
( ( ! [SY1523: $i,SY1524: $i,SY1525: $i,SY1526: $i,SY1527: $i,SY1528: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1528 @ SY1527 @ SY1526 @ SY1525 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1524 @ SY1528 @ SY1526 @ SY1523 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY1524 @ SY1527 @ SY1526 @ ( hAPP @ ( c_Fun_Ocomp @ SY1528 @ SY1527 @ SY1524 @ SY1525 ) @ SY1523 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6442]) ).
thf(6563,plain,
! [SV471: $i] :
( ( ! [SY1529: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY1529 ) @ SV471 )
= SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6445]) ).
thf(6564,plain,
! [SV472: $i] :
( ( ! [SY1530: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY1530 ) @ SV472 )
= SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6446]) ).
thf(6565,plain,
! [SV473: $i] :
( ( ! [SY1531: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY1531 ) @ SV473 )
= SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6447]) ).
thf(6566,plain,
! [SV474: $i] :
( ( ! [SY1532: $i,SY1533: $i,SY1534: $i,SY1535: $i,SY1536: $i,SY1537: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1537 @ SY1536 @ SY1535 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1537 @ SY1534 @ SY1536 ) @ SY1533 ) @ SY1532 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1537 @ SY1534 @ SY1535 ) @ SY1533 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1534 @ SY1536 @ SY1535 ) @ SY1532 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6448]) ).
thf(6567,plain,
! [SV475: $i] :
( ( ! [SY1538: $i,SY1539: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1539 @ SY1538 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY1538 @ SY1539 ) @ SV475 ) )
= SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6450]) ).
thf(6568,plain,
! [SV476: $i] :
( ( ! [SY1540: $i,SY1541: $i,SY1542: $i] :
( ( hAPP @ SY1542 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1541 @ SY1541 ) @ SY1540 ) @ SY1542 ) @ SV476 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1541 @ SY1541 ) @ SY1540 ) @ SY1542 ) @ ( hAPP @ SY1542 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6451]) ).
thf(6569,plain,
! [SV477: $i] :
( ( ! [SY1543: $i,SY1544: $i,SY1545: $i,SY1546: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1546 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1546 @ SY1545 ) @ SY1544 ) @ SY1543 ) ) @ SY1544 ) @ SV477 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1546 @ SY1545 ) @ SY1544 ) @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6457]) ).
thf(6570,plain,
! [SV478: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1549 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1549 ) @ SY1548 ) @ SY1547 ) ) @ SV478 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1549 ) @ SY1548 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1549 ) @ SY1547 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6458]) ).
thf(6571,plain,
! [SV479: $i] :
( ( ! [SY1550: $i] :
( ( hAPP @ ( c_List_Orev @ SY1550 ) @ ( hAPP @ ( c_List_Orev @ SY1550 ) @ SV479 ) )
= SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6463]) ).
thf(6572,plain,
! [SV480: $i] :
( ( ! [SY1551: $i] :
( ( hAPP @ ( c_COMBI @ SY1551 ) @ SV480 )
= SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6466]) ).
thf(6573,plain,
! [SV481: $i] :
( ( ! [SY1552: $i,SY1553: $i,SY1554: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1554 @ SY1553 ) @ SY1552 ) @ SV481 )
= SY1552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6467]) ).
thf(6574,plain,
! [SV482: $i] :
( ( ! [SY1555: $i,SY1556: $i,SY1557: $i,SY1558: $i,SY1559: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1559 @ SY1558 @ SY1557 ) @ SY1556 ) @ SY1555 ) @ SV482 )
= ( hAPP @ SY1556 @ ( hAPP @ SY1555 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6468]) ).
thf(6575,plain,
! [SV483: $i] :
( ( ! [SY1560: $i,SY1561: $i,SY1562: $i,SY1563: $i,SY1564: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1564 @ SY1563 @ SY1562 ) @ SY1561 ) @ SY1560 ) @ SV483 )
= ( hAPP @ ( hAPP @ SY1561 @ SV483 ) @ SY1560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6469]) ).
thf(6576,plain,
! [SV484: $i] :
( ( ! [SY1565: $i,SY1566: $i,SY1567: $i,SY1568: $i,SY1569: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1569 @ SY1568 @ SY1567 ) @ SY1566 ) @ SY1565 ) @ SV484 )
= ( hAPP @ ( hAPP @ SY1566 @ SV484 ) @ ( hAPP @ SY1565 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6470]) ).
thf(6577,plain,
! [SV485: $i] :
( ( ! [SY1570: $i,SY1571: $i,SY1572: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1572 @ SY1571 @ SY1570 )
| ( ( hAPP @ ( hAPP @ SY1571 @ SV485 ) @ SV485 )
= SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6472]) ).
thf(6578,plain,
! [SV486: $i] :
( ( ! [SY1573: $i,SY1574: $i,SY1575: $i,SY1576: $i,SY1577: $i] :
( ( SY1577 != SY1576 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1575 @ SY1574 @ SY1573 ) @ SV486 ) @ SY1577 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1575 @ SY1574 @ SY1573 ) @ SV486 ) @ SY1576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6473]) ).
thf(6579,plain,
! [SV487: $i] :
( ( ! [SY1578: $i,SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i,SY1583: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1583 @ SY1582 @ SY1581 @ SY1580 @ SY1579 )
| ~ ( ~ ( ( ( hAPP @ SY1581 @ SY1578 )
!= ( hAPP @ SY1581 @ SV487 ) )
| ( SY1578 = SV487 ) )
| ~ ( ( SY1578 != SV487 )
| ( ( hAPP @ SY1581 @ SY1578 )
= ( hAPP @ SY1581 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6474]) ).
thf(6580,plain,
! [SV488: $i] :
( ( ! [SY1584: $i,SY1585: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1585 ) @ SY1584 @ SV488 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1585 ) ) @ SY1584 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6475]) ).
thf(6581,plain,
! [SV489: $i] :
( ( ! [SY1586: $i,SY1587: $i] :
( ( c_Com_Ocom_OBODY @ SY1587 )
!= ( c_Com_Ocom_OWhile @ SY1586 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6476]) ).
thf(6582,plain,
! [SV490: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1589 ) ) @ SY1588 @ SV490 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1589 ) @ SY1588 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6477]) ).
thf(6583,plain,
! [SV491: $i] :
( ( ! [SY1590: $i,SY1591: $i,SY1592: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1592 @ SY1591 ) @ SY1590 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1592 @ SY1591 ) @ SV491 ) )
| ( SY1590 = SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6478]) ).
thf(6584,plain,
! [SV492: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1594 ) @ SY1593 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY1594 ) @ SV492 ) )
| ( SY1593 = SV492 ) )
| ~ ( ( SY1593 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1594 ) @ SY1593 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY1594 ) @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6479]) ).
thf(6585,plain,
! [SV493: $i] :
( ( ! [SY1595: $i,SY1596: $i,SY1597: $i,SY1598: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SY1598 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1597 @ SY1596 @ SY1595 ) @ SX5 ) )
| ( ( hAPP @ SY1598 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SY1595 @ SV493 ) @ ( hAPP @ SY1598 @ SV493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6480]) ).
thf(6586,plain,
! [SV494: $i] :
( ( ! [SY1600: $i,SY1601: $i,SY1602: $i,SY1603: $i,SY1604: $i,SY1605: $i] :
( ( SY1605 != SY1604 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1603 @ SY1602 @ SY1601 @ SY1600 @ SV494 ) @ SY1605 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1603 @ SY1602 @ SY1601 @ SY1600 @ SV494 ) @ SY1604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6481]) ).
thf(6587,plain,
! [SV495: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i,SY1609: $i,SY1610: $i] :
( ~ ( ( SY1610 != SY1609 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1608 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1608 @ SY1607 ) @ SY1610 ) @ SY1606 ) ) @ SY1609 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1608 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1608 @ SY1607 ) @ SY1609 ) @ SV495 ) ) @ SY1610 ) @ SY1606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6482]) ).
thf(6588,plain,
! [SV496: $i] :
( ( ! [SY1611: $i,SY1612: $i] :
( ( c_Com_Ocom_OBODY @ SY1612 )
!= ( c_Com_Ocom_OAss @ SY1611 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6483]) ).
thf(6589,plain,
! [SV497: $i] :
( ( ! [SY1613: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY1613 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
| ( SY1613 = SV497 ) )
| ~ ( ( SY1613 != SV497 )
| ( ( hAPP @ c_Nat_OSuc @ SY1613 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6484]) ).
thf(6590,plain,
! [SV498: $i] :
( ( ! [SY1614: $i,SY1615: $i,SY1616: $i,SY1617: $i,SY1618: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1618 @ SY1617 ) @ SY1616 ) @ SY1615 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1618 @ SY1617 ) @ SY1614 ) @ SV498 ) )
| ~ ( ( SY1616 != SY1614 )
| ( SY1615 != SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6485]) ).
thf(6591,plain,
! [SV499: $i] :
( ( ! [SY1619: $i,SY1620: $i,SY1621: $i,SY1622: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1622 ) @ SY1621 ) @ SY1620 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1622 ) @ SY1619 ) @ SV499 ) )
| ~ ( ( SY1621 != SY1619 )
| ( SY1620 != SV499 ) ) )
| ~ ( ~ ~ ( ( SY1621 != SY1619 )
| ( SY1620 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1622 ) @ SY1621 ) @ SY1620 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1622 ) @ SY1619 ) @ SV499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6486]) ).
thf(6592,plain,
! [SV500: $i] :
( ( ! [SY1623: $i,SY1624: $i,SY1625: $i,SY1626: $i,SY1627: $i,SY1628: $i,SY1629: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1629 @ SY1628 @ SY1627 @ SY1626 ) @ SY1625 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1624 @ SY1628 @ SY1627 @ SY1623 ) @ SV500 ) )
| ! [SY1630: $i] :
( ( hAPP @ SY1626 @ ( hAPP @ SY1625 @ SY1630 ) )
= ( hAPP @ SY1623 @ ( hAPP @ SV500 @ SY1630 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6487]) ).
thf(6593,plain,
! [SV501: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ~ ( c_Natural_Oevaln @ SY1633 @ SY1632 @ SY1631 @ SV501 )
| ( c_Natural_Oevalc @ SY1633 @ SY1632 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6488]) ).
thf(6594,plain,
! [SV502: $i] :
( ( ! [SY1634: $i,SY1635: $i,SY1636: $i] :
( ~ ( c_Natural_Oevaln @ SY1636 @ SY1635 @ SY1634 @ SV502 )
| ( c_Natural_Oevaln @ SY1636 @ SY1635 @ ( hAPP @ c_Nat_OSuc @ SY1634 ) @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6489]) ).
thf(6595,plain,
! [SV503: $i] :
( ( ! [SY1637: $i,SY1638: $i,SY1639: $i,SY1640: $i,SY1641: $i,SY1642: $i,SY1643: $i,SY1644: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1644 @ SY1643 @ SY1642 @ SY1641 ) @ SY1640 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1639 @ SY1643 @ SY1642 @ SY1638 ) @ SY1637 ) )
| ( ( hAPP @ SY1641 @ ( hAPP @ SY1640 @ SV503 ) )
= ( hAPP @ SY1638 @ ( hAPP @ SY1637 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6490]) ).
thf(6596,plain,
! [SV504: $i] :
( ( ! [SY1645: $i,SY1646: $i,SY1647: $i,SY1648: $i,SY1649: $i,SY1650: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1650 @ SY1649 @ SY1648 @ SY1647 ) @ SY1646 )
!= SY1645 )
| ( ( hAPP @ SY1647 @ ( hAPP @ SY1646 @ SV504 ) )
= ( hAPP @ SY1645 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6491]) ).
thf(6597,plain,
! [SV505: $i] :
( ( ! [SY1651: $i,SY1652: $i,SY1653: $i,SY1654: $i,SY1655: $i] :
( ~ ( c_Natural_Oevaln @ SY1655 @ SY1654 @ SY1653 @ SY1652 )
| ~ ( c_Natural_Oevaln @ SY1651 @ SY1652 @ SY1653 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1655 @ SY1651 ) @ SY1654 @ SY1653 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6492]) ).
thf(6598,plain,
! [SV506: $i] :
( ( ! [SY1656: $i,SY1657: $i] :
( ( c_Com_Ocom_OWhile @ SY1657 @ SY1656 )
!= ( c_Com_Ocom_OBODY @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6493]) ).
thf(6599,plain,
! [SV507: $i] :
( ( ! [SY1658: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1658 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
| ( SY1658 = SV507 ) )
| ~ ( ( SY1658 != SV507 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1658 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6494]) ).
thf(6600,plain,
! [SV508: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6495]) ).
thf(6601,plain,
! [SV509: $i] :
( ( ! [SY1659: $i,SY1660: $i] :
( ~ ( c_Natural_Oevalc @ SY1660 @ SY1659 @ SV509 )
| ~ ! [SY1661: $i] :
~ ( c_Natural_Oevaln @ SY1660 @ SY1659 @ SY1661 @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6496]) ).
thf(6602,plain,
! [SV510: $i] :
( ( ! [SY1662: $i,SY1663: $i,SY1664: $i,SY1665: $i,SY1666: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1666 @ SY1665 @ SY1664 )
| ( ( hAPP @ ( hAPP @ SY1664 @ SY1663 ) @ ( hAPP @ ( hAPP @ SY1664 @ SY1662 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SY1664 @ SY1662 ) @ ( hAPP @ ( hAPP @ SY1664 @ SY1663 ) @ SV510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6497]) ).
thf(6603,plain,
! [SV511: $i] :
( ( ! [SY1667: $i,SY1668: $i] :
( ( c_Com_Ocom_OSemi @ SY1668 @ SY1667 )
!= ( c_Com_Ocom_OBODY @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6498]) ).
thf(6604,plain,
! [SV512: $i] :
( ( ! [SY1669: $i,SY1670: $i,SY1671: $i] :
( ( c_Com_Ocom_OBODY @ SY1671 )
!= ( c_Com_Ocom_OCond @ SY1670 @ SY1669 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6499]) ).
thf(6605,plain,
! [SV513: $i] :
( ( ! [SY1672: $i,SY1673: $i,SY1674: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1674 @ SY1673 ) @ SY1672 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1674 @ SY1673 ) @ SV513 ) )
| ( SY1672 = SV513 ) )
| ~ ( ( SY1672 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY1674 @ SY1673 ) @ SY1672 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY1674 @ SY1673 ) @ SV513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6500]) ).
thf(6606,plain,
! [SV514: $i] :
( ( ! [SY1675: $i] :
~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SY1675 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
| ( SY1675 = SV514 ) )
| ~ ( ( SY1675 != SV514 )
| ( ( c_Com_Ocom_OBODY @ SY1675 )
= ( c_Com_Ocom_OBODY @ SV514 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6501]) ).
thf(6607,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(6608,plain,
! [SV515: $i] :
( ( ! [SY1676: $i,SY1677: $i,SY1678: $i] :
( ( c_Com_Ocom_OCond @ SY1678 @ SY1677 @ SY1676 )
!= ( c_Com_Ocom_OBODY @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6503]) ).
thf(6609,plain,
! [SV516: $i] :
( ( ! [SY1679: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1679 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
| ( SY1679 = SV516 ) )
| ~ ( ( SY1679 != SV516 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1679 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6504]) ).
thf(6610,plain,
! [SV517: $i] :
( ( ! [SY1680: $i,SY1681: $i,SY1682: $i,SY1683: $i,SY1684: $i,SY1685: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1685 @ SY1684 @ SY1683 @ SY1682 @ SY1681 @ SY1680 )
| ( ( hAPP @ ( hAPP @ SY1683 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6505]) ).
thf(6611,plain,
! [SV518: $i] :
( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1688 @ SY1687 ) @ SY1686 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1688 @ SY1687 ) @ SV518 ) )
| ( SY1686 = SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6506]) ).
thf(6612,plain,
! [SV519: $i] :
( ( ! [SY1689: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY1689 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
| ( SY1689 = SV519 ) )
| ~ ( ( SY1689 != SV519 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY1689 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6507]) ).
thf(6613,plain,
! [SV520: $i] :
( ( ! [SY1690: $i,SY1691: $i,SY1692: $i,SY1693: $i,SY1694: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1694 @ SY1693 @ SY1692 @ SY1691 @ SY1690 )
| ( ( hAPP @ SY1691 @ ( hAPP @ SY1692 @ SV520 ) )
= SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6508]) ).
thf(6614,plain,
! [SV521: $i] :
( ( ! [SY1695: $i,SY1696: $i,SY1697: $i,SY1698: $i,SY1699: $i] :
~ ( ~ ( ( SY1699 != SY1698 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1697 @ SY1696 ) @ SY1695 ) @ SY1698 ) @ SV521 ) @ SY1699 )
= SV521 ) )
| ~ ( ~ ( ( SY1699 != SY1698 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1697 @ SY1696 ) @ SY1695 ) @ SY1698 ) @ SV521 ) @ SY1699 )
= ( hAPP @ SY1695 @ SY1699 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6509]) ).
thf(6615,plain,
! [SV522: $i] :
( ( ! [SY1700: $i,SY1701: $i,SY1702: $i,SY1703: $i,SY1704: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1704 ) @ SY1703 ) @ SY1702 )
!= SY1701 )
| ( SY1700
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1704 ) @ SY1702 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1704 ) @ SY1703 ) @ SY1700 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1704 ) @ SY1701 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6510]) ).
thf(6616,plain,
! [SV523: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1706 ) @ SY1705 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1706 ) ) @ SY1705 @ SV523 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1706 ) ) @ SY1705 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1706 ) @ SY1705 @ SV523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6511]) ).
thf(6617,plain,
! [SV524: $i] :
( ( ! [SY1707: $i,SY1708: $i,SY1709: $i,SY1710: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1710 @ SY1709 @ SY1708 )
| ( ( hAPP @ ( hAPP @ SY1708 @ SY1707 ) @ ( hAPP @ ( hAPP @ SY1708 @ SY1707 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SY1708 @ SY1707 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6512]) ).
thf(6618,plain,
! [SV525: $i] :
( ( SV525
!= ( hAPP @ c_Nat_OSuc @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6513]) ).
thf(6619,plain,
! [SV526: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i,SY1714: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1714 @ SY1713 ) @ SY1712 ) @ SY1711 ) @ SV526 )
!= SY1712 )
| ( ( hAPP @ SY1712 @ SY1711 )
= SV526 ) )
| ~ ( ( ( hAPP @ SY1712 @ SY1711 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1714 @ SY1713 ) @ SY1712 ) @ SY1711 ) @ SV526 )
= SY1712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6514]) ).
thf(6620,plain,
! [SV527: $i] :
( ( ! [SY1715: $i,SY1716: $i] :
( ( c_Com_Ocom_OBODY @ SY1716 )
!= ( c_Com_Ocom_OSemi @ SY1715 @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6515]) ).
thf(6621,plain,
! [SV528: $i] :
( ( ! [SY1717: $i,SY1718: $i,SY1719: $i,SY1720: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1720 @ SY1719 ) @ SY1718 @ SY1717 @ SV528 )
| ~ ! [SY1721: $i] :
( ~ ( c_Natural_Oevaln @ SY1720 @ SY1718 @ SY1717 @ SY1721 )
| ~ ( c_Natural_Oevaln @ SY1719 @ SY1721 @ SY1717 @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6516]) ).
thf(6622,plain,
! [SV529: $i] :
( ( ! [SY1722: $i,SY1723: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1723 ) @ SY1722 ) @ SV529 )
!= SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6517]) ).
thf(6623,plain,
! [SV530: $i] :
( ( ! [SY1724: $i,SY1725: $i,SY1726: $i] :
( ( c_Com_Ocom_OBODY @ SY1726 )
!= ( c_Com_Ocom_OLocal @ SY1725 @ SY1724 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6518]) ).
thf(6624,plain,
! [SV531: $i] :
( ( ! [SY1727: $i,SY1728: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1728 ) @ SY1727 )
!= ( hAPP @ ( c_List_Orev @ SY1728 ) @ SV531 ) )
| ( SY1727 = SV531 ) )
| ~ ( ( SY1727 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SY1728 ) @ SY1727 )
= ( hAPP @ ( c_List_Orev @ SY1728 ) @ SV531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6519]) ).
thf(6625,plain,
! [SV532: $i] :
( ( ! [SY1729: $i,SY1730: $i] :
( ( c_Com_Ocom_OAss @ SY1730 @ SY1729 )
!= ( c_Com_Ocom_OBODY @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6520]) ).
thf(6626,plain,
! [SV533: $i] :
( ( ! [SY1731: $i,SY1732: $i,SY1733: $i,SY1734: $i,SY1735: $i,SY1736: $i] :
( ~ ( ( SY1736 != SY1735 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1734 @ SY1733 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1734 @ SY1733 ) @ SY1732 ) @ SY1736 ) @ SY1731 ) ) @ SY1735 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1734 @ SY1733 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1734 @ SY1733 ) @ SY1732 ) @ SY1735 ) @ SV533 ) ) @ SY1736 ) @ SY1731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6521]) ).
thf(6627,plain,
! [SV534: $i] :
( ( ! [SY1737: $i,SY1738: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SY1738 @ SY1737 @ SV534 )
| ~ ! [SY1739: $i] :
~ ( c_Natural_Oevaln @ SY1738 @ SY1737 @ SY1739 @ SV534 ) )
| ~ ( ~ ~ ! [SY1740: $i] :
~ ( c_Natural_Oevaln @ SY1738 @ SY1737 @ SY1740 @ SV534 )
| ( c_Natural_Oevalc @ SY1738 @ SY1737 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6522]) ).
thf(6628,plain,
! [SV535: $i] :
( ( ! [SY1741: $i,SY1742: $i,SY1743: $i,SY1744: $i,SY1745: $i] :
~ ( ~ ( ( SY1745 != SY1744 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1743 @ SY1742 ) @ SY1741 ) @ SY1744 ) @ SV535 ) @ SY1745 )
= SV535 ) )
| ~ ( ~ ( ( SY1745 != SY1744 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1743 @ SY1742 ) @ SY1741 ) @ SY1744 ) @ SV535 ) @ SY1745 )
= ( hAPP @ SY1741 @ SY1745 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6523]) ).
thf(6629,plain,
! [SV536: $i] :
( ( ! [SY1746: $i,SY1747: $i,SY1748: $i,SY1749: $i,SY1750: $i] :
( ~ ( ( SY1750 != SY1749 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1748 @ SY1747 ) @ SY1746 ) @ SY1749 ) @ SV536 ) @ SY1750 )
= ( hAPP @ SY1746 @ SY1750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6524]) ).
thf(6630,plain,
! [SV537: $i] :
( ( ! [SY1751: $i,SY1752: $i,SY1753: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1753 ) @ SY1752 @ SY1751 @ SV537 )
| ~ ! [SY1754: $i] :
( ( SY1751
!= ( hAPP @ c_Nat_OSuc @ SY1754 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1753 ) ) @ SY1752 @ SY1754 @ SV537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6525]) ).
thf(6631,plain,
! [SV538: $i] :
( ( ! [SY1755: $i,SY1756: $i,SY1757: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1757 ) @ SY1756 @ ( hAPP @ c_Nat_OSuc @ SY1755 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1757 ) ) @ SY1756 @ SY1755 @ SV538 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1757 ) ) @ SY1756 @ SY1755 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1757 ) @ SY1756 @ ( hAPP @ c_Nat_OSuc @ SY1755 ) @ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6526]) ).
thf(6632,plain,
! [SV539: $i] :
( ( ! [SY1758: $i,SY1759: $i,SY1760: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1760 ) @ SY1759 ) @ SY1758 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1760 ) @ SY1759 ) @ SV539 ) )
| ( SY1758 = SV539 ) )
| ~ ( ( SY1758 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1760 ) @ SY1759 ) @ SY1758 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1760 ) @ SY1759 ) @ SV539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6527]) ).
thf(6633,plain,
! [SV540: $i] :
( ( ! [SY1761: $i,SY1762: $i,SY1763: $i,SY1764: $i,SY1765: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1765 @ SY1764 ) @ SY1763 ) @ SY1762 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1765 @ SY1764 ) @ SY1761 ) @ SV540 ) )
| ~ ( ( SY1763 != SY1761 )
| ( SY1762 != SV540 ) ) )
| ~ ( ~ ~ ( ( SY1763 != SY1761 )
| ( SY1762 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1765 @ SY1764 ) @ SY1763 ) @ SY1762 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1765 @ SY1764 ) @ SY1761 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6528]) ).
thf(6634,plain,
! [SV541: $i] :
( ( ! [SY1766: $i,SY1767: $i,SY1768: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1768 ) @ SY1767 ) @ SY1766 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1768 ) @ SV541 ) @ SY1766 ) )
| ( SY1767 = SV541 ) )
| ~ ( ( SY1767 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1768 ) @ SY1767 ) @ SY1766 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1768 ) @ SV541 ) @ SY1766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6529]) ).
thf(6635,plain,
! [SV542: $i] :
( ( ! [SY1769: $i,SY1770: $i] :
( SY1770
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1769 ) @ SV542 ) @ SY1770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6530]) ).
thf(6636,plain,
! [SV543: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV543 )
!= SV543 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6531]) ).
thf(6637,plain,
! [SV544: $i] :
( ( ! [SY1771: $i,SY1772: $i,SY1773: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1773 @ SY1772 ) @ SY1771 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1773 @ SY1772 ) @ SV544 ) )
| ( SY1771 = SV544 ) )
| ~ ( ( SY1771 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY1773 @ SY1772 ) @ SY1771 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY1773 @ SY1772 ) @ SV544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6532]) ).
thf(6638,plain,
! [SV545: $i] :
( ( ! [SY1774: $i,SY1775: $i,SY1776: $i,SY1777: $i,SY1778: $i,SY1779: $i,SY1780: $i,SY1781: $i,SY1782: $i,SY1783: $i] :
( ( ( hAPP @ SY1783 @ ( hAPP @ SY1782 @ SY1781 ) )
!= ( hAPP @ SY1780 @ ( hAPP @ SY1779 @ SY1778 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1777 @ SY1776 @ SY1775 @ SY1783 ) @ SY1782 ) @ SY1781 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1774 @ SY1776 @ SV545 @ SY1780 ) @ SY1779 ) @ SY1778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6533]) ).
thf(6639,plain,
! [SV546: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1786 ) ) @ SY1785 @ SY1784 @ SV546 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY1786 ) @ SY1785 @ ( hAPP @ c_Nat_OSuc @ SY1784 ) @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6534]) ).
thf(6640,plain,
! [SV547: $i] :
( ( ! [SY1787: $i,SY1788: $i,SY1789: $i,SY1790: $i] :
( ( ( hAPP @ SY1790 @ SY1789 )
!= SY1788 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1787 @ SV547 ) @ SY1790 ) @ SY1789 ) @ SY1788 )
= SY1790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6535]) ).
thf(6641,plain,
! [SV548: $i] :
( ( ! [SY1791: $i,SY1792: $i,SY1793: $i,SY1794: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1793 ) @ SY1792 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1791 ) @ SV548 ) )
| ~ ! [SY1795: $i] :
~ ( ~ ( ( SY1793
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1791 ) @ SY1795 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1795 ) @ SY1792 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1793 ) @ SY1795 )
!= SY1791 )
| ( SY1792
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1795 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY1796: $i] :
~ ( ~ ( ( SY1793
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1791 ) @ SY1796 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1796 ) @ SY1792 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1793 ) @ SY1796 )
!= SY1791 )
| ( SY1792
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1796 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1793 ) @ SY1792 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1794 ) @ SY1791 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6536]) ).
thf(6642,plain,
! [SV549: $i] :
( ( ! [SY1797: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1797 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
| ( SY1797 = SV549 ) )
| ~ ( ( SY1797 != SV549 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1797 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6537]) ).
thf(6643,plain,
! [SV550: $i] :
( ( ! [SY1798: $i,SY1799: $i,SY1800: $i] :
( ( c_Com_Ocom_OBODY @ SY1800 )
!= ( c_Com_Ocom_OCall @ SY1799 @ SY1798 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6538]) ).
thf(6644,plain,
! [SV551: $i] :
( ( ( c_Com_Ocom_OBODY @ SV551 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6539]) ).
thf(6645,plain,
! [SV552: $i] :
( ( ! [SY1801: $i,SY1802: $i,SY1803: $i] :
( ( c_Com_Ocom_OCall @ SY1803 @ SY1802 @ SY1801 )
!= ( c_Com_Ocom_OBODY @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6540]) ).
thf(6646,plain,
! [SV553: $i] :
( ( ! [SY1804: $i,SY1805: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY1805 @ SY1804 @ SV553 )
| ( SV553 = SY1805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6541]) ).
thf(6647,plain,
! [SV554: $i] :
( ( ! [SY1806: $i,SY1807: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1807 ) @ SY1806 )
!= SV554 )
| ( SY1806
= ( hAPP @ ( c_List_Orev @ SY1807 ) @ SV554 ) ) )
| ~ ( ( SY1806
!= ( hAPP @ ( c_List_Orev @ SY1807 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1807 ) @ SY1806 )
= SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6542]) ).
thf(6648,plain,
! [SV555: $i] :
( ( ! [SY1808: $i,SY1809: $i,SY1810: $i,SY1811: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1811 @ SY1810 ) @ SY1809 @ SY1808 @ SV555 )
| ~ ! [SY1812: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1811 @ SY1809 @ SY1808 @ SY1812 )
| ~ ( c_Natural_Oevaln @ SY1810 @ SY1812 @ SY1808 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY1811 @ SY1809 @ SY1808 @ SY1813 )
| ~ ( c_Natural_Oevaln @ SY1810 @ SY1813 @ SY1808 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1811 @ SY1810 ) @ SY1809 @ SY1808 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6543]) ).
thf(6649,plain,
! [SV556: $i] :
( ( ! [SY1814: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY1814 )
!= ( hAPP @ c_Nat_OSuc @ SV556 ) )
| ( SY1814 = SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6544]) ).
thf(6650,plain,
! [SV557: $i] :
( ( ! [SY1815: $i,SY1816: $i,SY1817: $i] :
( ( c_Com_Ocom_OLocal @ SY1817 @ SY1816 @ SY1815 )
!= ( c_Com_Ocom_OBODY @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6545]) ).
thf(6651,plain,
! [SV558: $i] :
( ( ! [SY1818: $i] :
( ~ ! [SY1819: $i] :
( ( hAPP @ SY1818 @ SY1819 )
= ( hAPP @ SV558 @ SY1819 ) )
| ( SY1818 = SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6546]) ).
thf(6652,plain,
! [SV455: $i,SV559: $i] :
( ( ! [SY1820: $i,SY1821: $i] :
( ( c_Nat_Onat_Onat__case @ SY1821 @ SY1820 @ SV559 @ ( hAPP @ c_Nat_OSuc @ SV455 ) )
= ( hAPP @ SV559 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6547]) ).
thf(6653,plain,
! [SV456: $i,SV560: $i] :
( ( ! [SY1822: $i,SY1823: $i,SY1824: $i,SY1825: $i,SY1826: $i,SY1827: $i,SY1828: $i,SY1829: $i] :
( ( c_Com_Ocom_Ocom__case @ SY1829 @ SY1828 @ SY1827 @ SY1826 @ SY1825 @ SY1824 @ SY1823 @ SY1822 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SY1822 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6548]) ).
thf(6654,plain,
! [SV457: $i,SV561: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV561 @ SV457 @ SV561 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6549]) ).
thf(6655,plain,
! [SV458: $i,SV562: $i] :
( ( ! [SY1830: $i,SY1831: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1831 @ SY1830 @ SV562 ) @ ( hAPP @ c_Nat_OSuc @ SV458 ) )
= ( hAPP @ ( hAPP @ SV562 @ SV458 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1831 @ SY1830 @ SV562 ) @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6550]) ).
thf(6656,plain,
! [SV459: $i,SV563: $i] :
( ( ! [SY1832: $i,SY1833: $i,SY1834: $i,SY1835: $i,SY1836: $i,SY1837: $i,SY1838: $i,SY1839: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY1839 @ SY1838 @ SY1837 @ SY1836 @ SY1835 @ SY1834 @ SY1833 @ SY1832 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SY1832 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6551]) ).
thf(6657,plain,
! [SV460: $i,SV564: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV564 @ SV460 @ SV564 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6552]) ).
thf(6658,plain,
! [SV461: $i,SV565: $i] :
( ( ( hAPP @ ( c_Option_Othe @ SV565 ) @ ( hAPP @ ( c_Option_Ooption_OSome @ SV565 ) @ SV461 ) )
= SV461 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6553]) ).
thf(6659,plain,
! [SV462: $i,SV566: $i] :
( ( ! [SY1840: $i,SY1841: $i,SY1842: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1842 @ SY1841 @ SY1840 ) @ SV566 ) @ ( hAPP @ c_Nat_OSuc @ SV462 ) )
= ( hAPP @ ( hAPP @ SY1840 @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY1842 @ SY1841 @ SY1840 ) @ SV566 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6554]) ).
thf(6660,plain,
! [SV463: $i,SV567: $i] :
( ( ! [SY1843: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1843 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1843 ) @ SV567 ) @ SV463 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1843 ) @ SV567 ) @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6555]) ).
thf(6661,plain,
! [SV464: $i,SV568: $i] :
( ( ! [SY1844: $i,SY1845: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1845 ) @ SY1844 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1845 ) @ SV568 ) @ SV464 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1845 ) @ SV568 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1845 ) @ SY1844 ) @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6556]) ).
thf(6662,plain,
! [SV465: $i,SV569: $i] :
( ( ! [SY1846: $i,SY1847: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1847 @ SY1846 ) @ SV569 ) @ SV465 ) @ ( hAPP @ SV569 @ SV465 ) )
= SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6557]) ).
thf(6663,plain,
! [SV466: $i,SV570: $i] :
( ( ! [SY1848: $i,SY1849: $i,SY1850: $i,SY1851: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1851 @ SY1850 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1851 @ SY1850 ) @ SY1849 ) @ SY1848 ) @ SV570 ) ) @ SY1848 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1851 @ SY1850 ) @ SY1849 ) @ SY1848 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6558]) ).
thf(6664,plain,
! [SV467: $i,SV571: $i] :
( ( ! [SY1852: $i,SY1853: $i,SY1854: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1854 @ SY1853 ) @ SY1852 ) @ SV571 ) @ SV467 ) @ SV571 )
= SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6559]) ).
thf(6665,plain,
! [SV468: $i,SV572: $i] :
( ( ! [SY1855: $i,SY1856: $i,SY1857: $i,SY1858: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1858 @ SY1857 @ SY1856 @ SY1855 ) @ SV572 ) @ SV468 )
= ( hAPP @ SY1855 @ ( hAPP @ SV572 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6560]) ).
thf(6666,plain,
! [SV469: $i,SV573: $i] :
( ( ! [SY1859: $i,SY1860: $i,SY1861: $i,SY1862: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1862 @ SY1861 @ SY1860 @ SY1859 ) @ SV573 ) @ SV469 )
= ( hAPP @ SY1859 @ ( hAPP @ SV573 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6561]) ).
thf(6667,plain,
! [SV470: $i,SV574: $i] :
( ( ! [SY1863: $i,SY1864: $i,SY1865: $i,SY1866: $i,SY1867: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1867 @ SY1866 @ SY1865 @ SY1864 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1863 @ SY1867 @ SY1865 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY1863 @ SY1866 @ SY1865 @ ( hAPP @ ( c_Fun_Ocomp @ SY1867 @ SY1866 @ SY1863 @ SY1864 ) @ SV574 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6562]) ).
thf(6668,plain,
! [SV471: $i,SV575: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV575 ) @ SV471 )
= SV471 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6563]) ).
thf(6669,plain,
! [SV472: $i,SV576: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV576 ) @ SV472 )
= SV472 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6564]) ).
thf(6670,plain,
! [SV473: $i,SV577: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV577 ) @ SV473 )
= SV473 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6565]) ).
thf(6671,plain,
! [SV474: $i,SV578: $i] :
( ( ! [SY1868: $i,SY1869: $i,SY1870: $i,SY1871: $i,SY1872: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1872 @ SY1871 @ SY1870 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1872 @ SY1869 @ SY1871 ) @ SY1868 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1872 @ SY1869 @ SY1870 ) @ SY1868 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1869 @ SY1871 @ SY1870 ) @ SV578 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6566]) ).
thf(6672,plain,
! [SV475: $i,SV579: $i] :
( ( ! [SY1873: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1873 @ SV579 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV579 @ SY1873 ) @ SV475 ) )
= SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6567]) ).
thf(6673,plain,
! [SV476: $i,SV580: $i] :
( ( ! [SY1874: $i,SY1875: $i] :
( ( hAPP @ SY1875 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1874 @ SY1874 ) @ SV580 ) @ SY1875 ) @ SV476 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1874 @ SY1874 ) @ SV580 ) @ SY1875 ) @ ( hAPP @ SY1875 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6568]) ).
thf(6674,plain,
! [SV477: $i,SV581: $i] :
( ( ! [SY1876: $i,SY1877: $i,SY1878: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1878 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1878 @ SY1877 ) @ SY1876 ) @ SV581 ) ) @ SY1876 ) @ SV477 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1878 @ SY1877 ) @ SY1876 ) @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6569]) ).
thf(6675,plain,
! [SV478: $i,SV582: $i] :
( ( ! [SY1879: $i,SY1880: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1880 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1880 ) @ SY1879 ) @ SV582 ) ) @ SV478 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1880 ) @ SY1879 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1880 ) @ SV582 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6570]) ).
thf(6676,plain,
! [SV479: $i,SV583: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV583 ) @ ( hAPP @ ( c_List_Orev @ SV583 ) @ SV479 ) )
= SV479 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6571]) ).
thf(6677,plain,
! [SV480: $i,SV584: $i] :
( ( ( hAPP @ ( c_COMBI @ SV584 ) @ SV480 )
= SV480 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6572]) ).
thf(6678,plain,
! [SV481: $i,SV585: $i] :
( ( ! [SY1881: $i,SY1882: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1882 @ SY1881 ) @ SV585 ) @ SV481 )
= SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6573]) ).
thf(6679,plain,
! [SV482: $i,SV586: $i] :
( ( ! [SY1883: $i,SY1884: $i,SY1885: $i,SY1886: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1886 @ SY1885 @ SY1884 ) @ SY1883 ) @ SV586 ) @ SV482 )
= ( hAPP @ SY1883 @ ( hAPP @ SV586 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6574]) ).
thf(6680,plain,
! [SV483: $i,SV587: $i] :
( ( ! [SY1887: $i,SY1888: $i,SY1889: $i,SY1890: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1890 @ SY1889 @ SY1888 ) @ SY1887 ) @ SV587 ) @ SV483 )
= ( hAPP @ ( hAPP @ SY1887 @ SV483 ) @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6575]) ).
thf(6681,plain,
! [SV484: $i,SV588: $i] :
( ( ! [SY1891: $i,SY1892: $i,SY1893: $i,SY1894: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1894 @ SY1893 @ SY1892 ) @ SY1891 ) @ SV588 ) @ SV484 )
= ( hAPP @ ( hAPP @ SY1891 @ SV484 ) @ ( hAPP @ SV588 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6576]) ).
thf(6682,plain,
! [SV485: $i,SV589: $i] :
( ( ! [SY1895: $i,SY1896: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1896 @ SY1895 @ SV589 )
| ( ( hAPP @ ( hAPP @ SY1895 @ SV485 ) @ SV485 )
= SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6577]) ).
thf(6683,plain,
! [SV486: $i,SV590: $i] :
( ( ! [SY1897: $i,SY1898: $i,SY1899: $i,SY1900: $i] :
( ( SY1900 != SY1899 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1898 @ SY1897 @ SV590 ) @ SV486 ) @ SY1900 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1898 @ SY1897 @ SV590 ) @ SV486 ) @ SY1899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6578]) ).
thf(6684,plain,
! [SV487: $i,SV591: $i] :
( ( ! [SY1901: $i,SY1902: $i,SY1903: $i,SY1904: $i,SY1905: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1905 @ SY1904 @ SY1903 @ SY1902 @ SY1901 )
| ~ ( ~ ( ( ( hAPP @ SY1903 @ SV591 )
!= ( hAPP @ SY1903 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SY1903 @ SV591 )
= ( hAPP @ SY1903 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6579]) ).
thf(6685,plain,
! [SV488: $i,SV592: $i] :
( ( ! [SY1906: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1906 ) @ SV592 @ SV488 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1906 ) ) @ SV592 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6580]) ).
thf(6686,plain,
! [SV489: $i,SV593: $i] :
( ( ! [SY1907: $i] :
( ( c_Com_Ocom_OBODY @ SY1907 )
!= ( c_Com_Ocom_OWhile @ SV593 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6581]) ).
thf(6687,plain,
! [SV490: $i,SV594: $i] :
( ( ! [SY1908: $i] :
( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1908 ) ) @ SV594 @ SV490 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1908 ) @ SV594 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6582]) ).
thf(6688,plain,
! [SV491: $i,SV595: $i] :
( ( ! [SY1909: $i,SY1910: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1910 @ SY1909 ) @ SV595 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1910 @ SY1909 ) @ SV491 ) )
| ( SV595 = SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6583]) ).
thf(6689,plain,
! [SV492: $i,SV596: $i] :
( ( ! [SY1911: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1911 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SY1911 ) @ SV492 ) )
| ( SV596 = SV492 ) )
| ~ ( ( SV596 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SY1911 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SY1911 ) @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6584]) ).
thf(6690,plain,
! [SV493: $i,SV597: $i] :
( ( ! [SY1912: $i,SY1913: $i,SY1914: $i] :
( ~ ! [SY1915: $i] :
( ( hAPP @ SY1914 @ SY1915 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY1913 @ SY1912 @ SV597 ) @ SY1915 ) )
| ( ( hAPP @ SY1914 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SY1914 @ SV493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6585]) ).
thf(6691,plain,
! [SV494: $i,SV598: $i] :
( ( ! [SY1916: $i,SY1917: $i,SY1918: $i,SY1919: $i,SY1920: $i] :
( ( SY1920 != SY1919 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1918 @ SY1917 @ SY1916 @ SV598 @ SV494 ) @ SY1920 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY1918 @ SY1917 @ SY1916 @ SV598 @ SV494 ) @ SY1919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6586]) ).
thf(6692,plain,
! [SV495: $i,SV599: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i,SY1924: $i] :
( ~ ( ( SY1924 != SY1923 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1922 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1922 @ SY1921 ) @ SY1924 ) @ SV599 ) ) @ SY1923 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1922 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1922 @ SY1921 ) @ SY1923 ) @ SV495 ) ) @ SY1924 ) @ SV599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6587]) ).
thf(6693,plain,
! [SV496: $i,SV600: $i] :
( ( ! [SY1925: $i] :
( ( c_Com_Ocom_OBODY @ SY1925 )
!= ( c_Com_Ocom_OAss @ SV600 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6588]) ).
thf(6694,plain,
! [SV497: $i,SV601: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
| ( SV601 = SV497 ) )
| ~ ( ( SV601 != SV497 )
| ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6589]) ).
thf(6695,plain,
! [SV498: $i,SV602: $i] :
( ( ! [SY1926: $i,SY1927: $i,SY1928: $i,SY1929: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1929 @ SY1928 ) @ SY1927 ) @ SY1926 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1929 @ SY1928 ) @ SV602 ) @ SV498 ) )
| ~ ( ( SY1927 != SV602 )
| ( SY1926 != SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6590]) ).
thf(6696,plain,
! [SV499: $i,SV603: $i] :
( ( ! [SY1930: $i,SY1931: $i,SY1932: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1932 ) @ SY1931 ) @ SY1930 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1932 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SY1931 != SV603 )
| ( SY1930 != SV499 ) ) )
| ~ ( ~ ~ ( ( SY1931 != SV603 )
| ( SY1930 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1932 ) @ SY1931 ) @ SY1930 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1932 ) @ SV603 ) @ SV499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6591]) ).
thf(6697,plain,
! [SV500: $i,SV604: $i] :
( ( ! [SY1933: $i,SY1934: $i,SY1935: $i,SY1936: $i,SY1937: $i,SY1938: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1938 @ SY1937 @ SY1936 @ SY1935 ) @ SY1934 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1933 @ SY1937 @ SY1936 @ SV604 ) @ SV500 ) )
| ! [SY1939: $i] :
( ( hAPP @ SY1935 @ ( hAPP @ SY1934 @ SY1939 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY1939 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6592]) ).
thf(6698,plain,
! [SV501: $i,SV605: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ~ ( c_Natural_Oevaln @ SY1941 @ SY1940 @ SV605 @ SV501 )
| ( c_Natural_Oevalc @ SY1941 @ SY1940 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6593]) ).
thf(6699,plain,
! [SV502: $i,SV606: $i] :
( ( ! [SY1942: $i,SY1943: $i] :
( ~ ( c_Natural_Oevaln @ SY1943 @ SY1942 @ SV606 @ SV502 )
| ( c_Natural_Oevaln @ SY1943 @ SY1942 @ ( hAPP @ c_Nat_OSuc @ SV606 ) @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6594]) ).
thf(6700,plain,
! [SV503: $i,SV607: $i] :
( ( ! [SY1944: $i,SY1945: $i,SY1946: $i,SY1947: $i,SY1948: $i,SY1949: $i,SY1950: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1950 @ SY1949 @ SY1948 @ SY1947 ) @ SY1946 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1945 @ SY1949 @ SY1948 @ SY1944 ) @ SV607 ) )
| ( ( hAPP @ SY1947 @ ( hAPP @ SY1946 @ SV503 ) )
= ( hAPP @ SY1944 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6595]) ).
thf(6701,plain,
! [SV504: $i,SV608: $i] :
( ( ! [SY1951: $i,SY1952: $i,SY1953: $i,SY1954: $i,SY1955: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1955 @ SY1954 @ SY1953 @ SY1952 ) @ SY1951 )
!= SV608 )
| ( ( hAPP @ SY1952 @ ( hAPP @ SY1951 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6596]) ).
thf(6702,plain,
! [SV505: $i,SV609: $i] :
( ( ! [SY1956: $i,SY1957: $i,SY1958: $i,SY1959: $i] :
( ~ ( c_Natural_Oevaln @ SY1959 @ SY1958 @ SY1957 @ SY1956 )
| ~ ( c_Natural_Oevaln @ SV609 @ SY1956 @ SY1957 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY1959 @ SV609 ) @ SY1958 @ SY1957 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6597]) ).
thf(6703,plain,
! [SV506: $i,SV610: $i] :
( ( ! [SY1960: $i] :
( ( c_Com_Ocom_OWhile @ SY1960 @ SV610 )
!= ( c_Com_Ocom_OBODY @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6598]) ).
thf(6704,plain,
! [SV507: $i,SV611: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
| ( SV611 = SV507 ) )
| ~ ( ( SV611 != SV507 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6599]) ).
thf(6705,plain,
! [SV508: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OBODY @ SV508 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6600]) ).
thf(6706,plain,
! [SV509: $i,SV612: $i] :
( ( ! [SY1961: $i] :
( ~ ( c_Natural_Oevalc @ SY1961 @ SV612 @ SV509 )
| ~ ! [SY1962: $i] :
~ ( c_Natural_Oevaln @ SY1961 @ SV612 @ SY1962 @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6601]) ).
thf(6707,plain,
! [SV510: $i,SV613: $i] :
( ( ! [SY1963: $i,SY1964: $i,SY1965: $i,SY1966: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1966 @ SY1965 @ SY1964 )
| ( ( hAPP @ ( hAPP @ SY1964 @ SY1963 ) @ ( hAPP @ ( hAPP @ SY1964 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SY1964 @ SV613 ) @ ( hAPP @ ( hAPP @ SY1964 @ SY1963 ) @ SV510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6602]) ).
thf(6708,plain,
! [SV511: $i,SV614: $i] :
( ( ! [SY1967: $i] :
( ( c_Com_Ocom_OSemi @ SY1967 @ SV614 )
!= ( c_Com_Ocom_OBODY @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6603]) ).
thf(6709,plain,
! [SV512: $i,SV615: $i] :
( ( ! [SY1968: $i,SY1969: $i] :
( ( c_Com_Ocom_OBODY @ SY1969 )
!= ( c_Com_Ocom_OCond @ SY1968 @ SV615 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6604]) ).
thf(6710,plain,
! [SV513: $i,SV616: $i] :
( ( ! [SY1970: $i,SY1971: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY1971 @ SY1970 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY1971 @ SY1970 ) @ SV513 ) )
| ( SV616 = SV513 ) )
| ~ ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY1971 @ SY1970 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY1971 @ SY1970 ) @ SV513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6605]) ).
thf(6711,plain,
! [SV514: $i,SV617: $i] :
( ( ~ ( ~ ( ( ( c_Com_Ocom_OBODY @ SV617 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
| ( SV617 = SV514 ) )
| ~ ( ( SV617 != SV514 )
| ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6606]) ).
thf(6712,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6607]) ).
thf(6713,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SX1 @ v_n @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6607]) ).
thf(6714,plain,
! [SV515: $i,SV618: $i] :
( ( ! [SY1972: $i,SY1973: $i] :
( ( c_Com_Ocom_OCond @ SY1973 @ SY1972 @ SV618 )
!= ( c_Com_Ocom_OBODY @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6608]) ).
thf(6715,plain,
! [SV516: $i,SV619: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
| ( SV619 = SV516 ) )
| ~ ( ( SV619 != SV516 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6609]) ).
thf(6716,plain,
! [SV517: $i,SV620: $i] :
( ( ! [SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i,SY1978: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1978 @ SY1977 @ SY1976 @ SY1975 @ SY1974 @ SV620 )
| ( ( hAPP @ ( hAPP @ SY1976 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6610]) ).
thf(6717,plain,
! [SV518: $i,SV621: $i] :
( ( ! [SY1979: $i,SY1980: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY1980 @ SY1979 ) @ SV621 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY1980 @ SY1979 ) @ SV518 ) )
| ( SV621 = SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6611]) ).
thf(6718,plain,
! [SV519: $i,SV622: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
| ( SV622 = SV519 ) )
| ~ ( ( SV622 != SV519 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6612]) ).
thf(6719,plain,
! [SV520: $i,SV623: $i] :
( ( ! [SY1981: $i,SY1982: $i,SY1983: $i,SY1984: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1984 @ SY1983 @ SY1982 @ SY1981 @ SV623 )
| ( ( hAPP @ SY1981 @ ( hAPP @ SY1982 @ SV520 ) )
= SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6613]) ).
thf(6720,plain,
! [SV521: $i,SV624: $i] :
( ( ! [SY1985: $i,SY1986: $i,SY1987: $i,SY1988: $i] :
~ ( ~ ( ( SY1988 != SY1987 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1986 @ SY1985 ) @ SV624 ) @ SY1987 ) @ SV521 ) @ SY1988 )
= SV521 ) )
| ~ ( ~ ( ( SY1988 != SY1987 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1986 @ SY1985 ) @ SV624 ) @ SY1987 ) @ SV521 ) @ SY1988 )
= ( hAPP @ SV624 @ SY1988 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6614]) ).
thf(6721,plain,
! [SV522: $i,SV625: $i] :
( ( ! [SY1989: $i,SY1990: $i,SY1991: $i,SY1992: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1992 ) @ SY1991 ) @ SY1990 )
!= SY1989 )
| ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1992 ) @ SY1990 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1992 ) @ SY1991 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1992 ) @ SY1989 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6615]) ).
thf(6722,plain,
! [SV523: $i,SV626: $i] :
( ( ! [SY1993: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1993 ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1993 ) ) @ SV626 @ SV523 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY1993 ) ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SY1993 ) @ SV626 @ SV523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6616]) ).
thf(6723,plain,
! [SV524: $i,SV627: $i] :
( ( ! [SY1994: $i,SY1995: $i,SY1996: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1996 @ SY1995 @ SY1994 )
| ( ( hAPP @ ( hAPP @ SY1994 @ SV627 ) @ ( hAPP @ ( hAPP @ SY1994 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SY1994 @ SV627 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6617]) ).
thf(6724,plain,
! [SV525: $i] :
( ( SV525
= ( hAPP @ c_Nat_OSuc @ SV525 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6618]) ).
thf(6725,plain,
! [SV526: $i,SV628: $i] :
( ( ! [SY1997: $i,SY1998: $i,SY1999: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1999 @ SY1998 ) @ SY1997 ) @ SV628 ) @ SV526 )
!= SY1997 )
| ( ( hAPP @ SY1997 @ SV628 )
= SV526 ) )
| ~ ( ( ( hAPP @ SY1997 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY1999 @ SY1998 ) @ SY1997 ) @ SV628 ) @ SV526 )
= SY1997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6619]) ).
thf(6726,plain,
! [SV527: $i,SV629: $i] :
( ( ! [SY2000: $i] :
( ( c_Com_Ocom_OBODY @ SY2000 )
!= ( c_Com_Ocom_OSemi @ SV629 @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6620]) ).
thf(6727,plain,
! [SV528: $i,SV630: $i] :
( ( ! [SY2001: $i,SY2002: $i,SY2003: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2003 @ SY2002 ) @ SY2001 @ SV630 @ SV528 )
| ~ ! [SY2004: $i] :
( ~ ( c_Natural_Oevaln @ SY2003 @ SY2001 @ SV630 @ SY2004 )
| ~ ( c_Natural_Oevaln @ SY2002 @ SY2004 @ SV630 @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6621]) ).
thf(6728,plain,
! [SV529: $i,SV631: $i] :
( ( ! [SY2005: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2005 ) @ SV631 ) @ SV529 )
!= SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6622]) ).
thf(6729,plain,
! [SV530: $i,SV632: $i] :
( ( ! [SY2006: $i,SY2007: $i] :
( ( c_Com_Ocom_OBODY @ SY2007 )
!= ( c_Com_Ocom_OLocal @ SY2006 @ SV632 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6623]) ).
thf(6730,plain,
! [SV531: $i,SV633: $i] :
( ( ! [SY2008: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY2008 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SY2008 ) @ SV531 ) )
| ( SV633 = SV531 ) )
| ~ ( ( SV633 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SY2008 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SY2008 ) @ SV531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6624]) ).
thf(6731,plain,
! [SV532: $i,SV634: $i] :
( ( ! [SY2009: $i] :
( ( c_Com_Ocom_OAss @ SY2009 @ SV634 )
!= ( c_Com_Ocom_OBODY @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6625]) ).
thf(6732,plain,
! [SV533: $i,SV635: $i] :
( ( ! [SY2010: $i,SY2011: $i,SY2012: $i,SY2013: $i,SY2014: $i] :
( ~ ( ( SY2014 != SY2013 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2012 @ SY2011 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2012 @ SY2011 ) @ SY2010 ) @ SY2014 ) @ SV635 ) ) @ SY2013 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2012 @ SY2011 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2012 @ SY2011 ) @ SY2010 ) @ SY2013 ) @ SV533 ) ) @ SY2014 ) @ SV635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6626]) ).
thf(6733,plain,
! [SV534: $i,SV636: $i] :
( ( ! [SY2015: $i] :
~ ( ~ ( ~ ( c_Natural_Oevalc @ SY2015 @ SV636 @ SV534 )
| ~ ! [SY2016: $i] :
~ ( c_Natural_Oevaln @ SY2015 @ SV636 @ SY2016 @ SV534 ) )
| ~ ( ~ ~ ! [SY2017: $i] :
~ ( c_Natural_Oevaln @ SY2015 @ SV636 @ SY2017 @ SV534 )
| ( c_Natural_Oevalc @ SY2015 @ SV636 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6627]) ).
thf(6734,plain,
! [SV535: $i,SV637: $i] :
( ( ! [SY2018: $i,SY2019: $i,SY2020: $i,SY2021: $i] :
~ ( ~ ( ( SY2021 != SY2020 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2019 @ SY2018 ) @ SV637 ) @ SY2020 ) @ SV535 ) @ SY2021 )
= SV535 ) )
| ~ ( ~ ( ( SY2021 != SY2020 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2019 @ SY2018 ) @ SV637 ) @ SY2020 ) @ SV535 ) @ SY2021 )
= ( hAPP @ SV637 @ SY2021 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6628]) ).
thf(6735,plain,
! [SV536: $i,SV638: $i] :
( ( ! [SY2022: $i,SY2023: $i,SY2024: $i,SY2025: $i] :
( ~ ( ( SY2025 != SY2024 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2023 @ SY2022 ) @ SV638 ) @ SY2024 ) @ SV536 ) @ SY2025 )
= ( hAPP @ SV638 @ SY2025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6629]) ).
thf(6736,plain,
! [SV537: $i,SV639: $i] :
( ( ! [SY2026: $i,SY2027: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2027 ) @ SY2026 @ SV639 @ SV537 )
| ~ ! [SY2028: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2028 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2027 ) ) @ SY2026 @ SY2028 @ SV537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6630]) ).
thf(6737,plain,
! [SV538: $i,SV640: $i] :
( ( ! [SY2029: $i,SY2030: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2030 ) @ SY2029 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2030 ) ) @ SY2029 @ SV640 @ SV538 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2030 ) ) @ SY2029 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2030 ) @ SY2029 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6631]) ).
thf(6738,plain,
! [SV539: $i,SV641: $i] :
( ( ! [SY2031: $i,SY2032: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2032 ) @ SY2031 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2032 ) @ SY2031 ) @ SV539 ) )
| ( SV641 = SV539 ) )
| ~ ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2032 ) @ SY2031 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2032 ) @ SY2031 ) @ SV539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6632]) ).
thf(6739,plain,
! [SV540: $i,SV642: $i] :
( ( ! [SY2033: $i,SY2034: $i,SY2035: $i,SY2036: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2036 @ SY2035 ) @ SY2034 ) @ SY2033 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2036 @ SY2035 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SY2034 != SV642 )
| ( SY2033 != SV540 ) ) )
| ~ ( ~ ~ ( ( SY2034 != SV642 )
| ( SY2033 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2036 @ SY2035 ) @ SY2034 ) @ SY2033 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2036 @ SY2035 ) @ SV642 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6633]) ).
thf(6740,plain,
! [SV541: $i,SV643: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2038 ) @ SY2037 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2038 ) @ SV541 ) @ SV643 ) )
| ( SY2037 = SV541 ) )
| ~ ( ( SY2037 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2038 ) @ SY2037 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2038 ) @ SV541 ) @ SV643 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6634]) ).
thf(6741,plain,
! [SV542: $i,SV644: $i] :
( ( ! [SY2039: $i] :
( SY2039
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV644 ) @ SV542 ) @ SY2039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6635]) ).
thf(6742,plain,
! [SV543: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV543 )
= SV543 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6636]) ).
thf(6743,plain,
! [SV544: $i,SV645: $i] :
( ( ! [SY2040: $i,SY2041: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY2041 @ SY2040 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY2041 @ SY2040 ) @ SV544 ) )
| ( SV645 = SV544 ) )
| ~ ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY2041 @ SY2040 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY2041 @ SY2040 ) @ SV544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6637]) ).
thf(6744,plain,
! [SV545: $i,SV646: $i] :
( ( ! [SY2042: $i,SY2043: $i,SY2044: $i,SY2045: $i,SY2046: $i,SY2047: $i,SY2048: $i,SY2049: $i,SY2050: $i] :
( ( ( hAPP @ SY2050 @ ( hAPP @ SY2049 @ SY2048 ) )
!= ( hAPP @ SY2047 @ ( hAPP @ SY2046 @ SY2045 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2044 @ SY2043 @ SY2042 @ SY2050 ) @ SY2049 ) @ SY2048 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SY2043 @ SV545 @ SY2047 ) @ SY2046 ) @ SY2045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6638]) ).
thf(6745,plain,
! [SV546: $i,SV647: $i] :
( ( ! [SY2051: $i,SY2052: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2052 ) ) @ SY2051 @ SV647 @ SV546 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2052 ) @ SY2051 @ ( hAPP @ c_Nat_OSuc @ SV647 ) @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6639]) ).
thf(6746,plain,
! [SV547: $i,SV648: $i] :
( ( ! [SY2053: $i,SY2054: $i,SY2055: $i] :
( ( ( hAPP @ SY2055 @ SY2054 )
!= SY2053 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SY2055 ) @ SY2054 ) @ SY2053 )
= SY2055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6640]) ).
thf(6747,plain,
! [SV548: $i,SV649: $i] :
( ( ! [SY2056: $i,SY2057: $i,SY2058: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2057 ) @ SY2056 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2059: $i] :
~ ( ~ ( ( SY2057
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SV649 ) @ SY2059 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2059 ) @ SY2056 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2057 ) @ SY2059 )
!= SV649 )
| ( SY2056
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2059 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY2060: $i] :
~ ( ~ ( ( SY2057
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SV649 ) @ SY2060 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2060 ) @ SY2056 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2057 ) @ SY2060 )
!= SV649 )
| ( SY2056
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2060 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SY2057 ) @ SY2056 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2058 ) @ SV649 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6641]) ).
thf(6748,plain,
! [SV549: $i,SV650: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
| ( SV650 = SV549 ) )
| ~ ( ( SV650 != SV549 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6642]) ).
thf(6749,plain,
! [SV550: $i,SV651: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ( c_Com_Ocom_OBODY @ SY2062 )
!= ( c_Com_Ocom_OCall @ SY2061 @ SV651 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6643]) ).
thf(6750,plain,
! [SV551: $i] :
( ( ( c_Com_Ocom_OBODY @ SV551 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6644]) ).
thf(6751,plain,
! [SV552: $i,SV652: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ( c_Com_Ocom_OCall @ SY2064 @ SY2063 @ SV652 )
!= ( c_Com_Ocom_OBODY @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6645]) ).
thf(6752,plain,
! [SV553: $i,SV653: $i] :
( ( ! [SY2065: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY2065 @ SV653 @ SV553 )
| ( SV553 = SY2065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6646]) ).
thf(6753,plain,
! [SV554: $i,SV654: $i] :
( ( ! [SY2066: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY2066 ) @ SV654 )
!= SV554 )
| ( SV654
= ( hAPP @ ( c_List_Orev @ SY2066 ) @ SV554 ) ) )
| ~ ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SY2066 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SY2066 ) @ SV654 )
= SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6647]) ).
thf(6754,plain,
! [SV555: $i,SV655: $i] :
( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2069 @ SY2068 ) @ SY2067 @ SV655 @ SV555 )
| ~ ! [SY2070: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2069 @ SY2067 @ SV655 @ SY2070 )
| ~ ( c_Natural_Oevaln @ SY2068 @ SY2070 @ SV655 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY2071: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2069 @ SY2067 @ SV655 @ SY2071 )
| ~ ( c_Natural_Oevaln @ SY2068 @ SY2071 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2069 @ SY2068 ) @ SY2067 @ SV655 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6648]) ).
thf(6755,plain,
! [SV556: $i,SV656: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV656 )
!= ( hAPP @ c_Nat_OSuc @ SV556 ) )
| ( SV656 = SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6649]) ).
thf(6756,plain,
! [SV557: $i,SV657: $i] :
( ( ! [SY2072: $i,SY2073: $i] :
( ( c_Com_Ocom_OLocal @ SY2073 @ SY2072 @ SV657 )
!= ( c_Com_Ocom_OBODY @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6650]) ).
thf(6757,plain,
! [SV558: $i,SV658: $i] :
( ( ~ ! [SY2074: $i] :
( ( hAPP @ SV658 @ SY2074 )
= ( hAPP @ SV558 @ SY2074 ) )
| ( SV658 = SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6651]) ).
thf(6758,plain,
! [SV455: $i,SV559: $i,SV659: $i] :
( ( ! [SY2075: $i] :
( ( c_Nat_Onat_Onat__case @ SY2075 @ SV659 @ SV559 @ ( hAPP @ c_Nat_OSuc @ SV455 ) )
= ( hAPP @ SV559 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6652]) ).
thf(6759,plain,
! [SV456: $i,SV560: $i,SV660: $i] :
( ( ! [SY2076: $i,SY2077: $i,SY2078: $i,SY2079: $i,SY2080: $i,SY2081: $i,SY2082: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2082 @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SY2077 @ SY2076 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6653]) ).
thf(6760,plain,
! [SV458: $i,SV562: $i,SV661: $i] :
( ( ! [SY2083: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY2083 @ SV661 @ SV562 ) @ ( hAPP @ c_Nat_OSuc @ SV458 ) )
= ( hAPP @ ( hAPP @ SV562 @ SV458 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY2083 @ SV661 @ SV562 ) @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6655]) ).
thf(6761,plain,
! [SV459: $i,SV563: $i,SV662: $i] :
( ( ! [SY2084: $i,SY2085: $i,SY2086: $i,SY2087: $i,SY2088: $i,SY2089: $i,SY2090: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2090 @ SY2089 @ SY2088 @ SY2087 @ SY2086 @ SY2085 @ SY2084 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6656]) ).
thf(6762,plain,
! [SV462: $i,SV566: $i,SV663: $i] :
( ( ! [SY2091: $i,SY2092: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY2092 @ SY2091 @ SV663 ) @ SV566 ) @ ( hAPP @ c_Nat_OSuc @ SV462 ) )
= ( hAPP @ ( hAPP @ SV663 @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY2092 @ SY2091 @ SV663 ) @ SV566 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6659]) ).
thf(6763,plain,
! [SV463: $i,SV567: $i,SV664: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV664 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV664 ) @ SV567 ) @ SV463 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV664 ) @ SV567 ) @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6660]) ).
thf(6764,plain,
! [SV464: $i,SV568: $i,SV665: $i] :
( ( ! [SY2093: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2093 ) @ SV665 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2093 ) @ SV568 ) @ SV464 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2093 ) @ SV568 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2093 ) @ SV665 ) @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6661]) ).
thf(6765,plain,
! [SV465: $i,SV569: $i,SV666: $i] :
( ( ! [SY2094: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2094 @ SV666 ) @ SV569 ) @ SV465 ) @ ( hAPP @ SV569 @ SV465 ) )
= SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6662]) ).
thf(6766,plain,
! [SV466: $i,SV570: $i,SV667: $i] :
( ( ! [SY2095: $i,SY2096: $i,SY2097: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2097 @ SY2096 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2097 @ SY2096 ) @ SY2095 ) @ SV667 ) @ SV570 ) ) @ SV667 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2097 @ SY2096 ) @ SY2095 ) @ SV667 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6663]) ).
thf(6767,plain,
! [SV467: $i,SV571: $i,SV668: $i] :
( ( ! [SY2098: $i,SY2099: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2099 @ SY2098 ) @ SV668 ) @ SV571 ) @ SV467 ) @ SV571 )
= SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6664]) ).
thf(6768,plain,
! [SV468: $i,SV572: $i,SV669: $i] :
( ( ! [SY2100: $i,SY2101: $i,SY2102: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2102 @ SY2101 @ SY2100 @ SV669 ) @ SV572 ) @ SV468 )
= ( hAPP @ SV669 @ ( hAPP @ SV572 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6665]) ).
thf(6769,plain,
! [SV469: $i,SV573: $i,SV670: $i] :
( ( ! [SY2103: $i,SY2104: $i,SY2105: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2105 @ SY2104 @ SY2103 @ SV670 ) @ SV573 ) @ SV469 )
= ( hAPP @ SV670 @ ( hAPP @ SV573 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6666]) ).
thf(6770,plain,
! [SV470: $i,SV574: $i,SV671: $i] :
( ( ! [SY2106: $i,SY2107: $i,SY2108: $i,SY2109: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2109 @ SY2108 @ SY2107 @ SY2106 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2109 @ SY2107 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2108 @ SY2107 @ ( hAPP @ ( c_Fun_Ocomp @ SY2109 @ SY2108 @ SV671 @ SY2106 ) @ SV574 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6667]) ).
thf(6771,plain,
! [SV474: $i,SV578: $i,SV672: $i] :
( ( ! [SY2110: $i,SY2111: $i,SY2112: $i,SY2113: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2113 @ SY2112 @ SY2111 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2113 @ SY2110 @ SY2112 ) @ SV672 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2113 @ SY2110 @ SY2111 ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2110 @ SY2112 @ SY2111 ) @ SV578 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6671]) ).
thf(6772,plain,
! [SV475: $i,SV579: $i,SV673: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV673 @ SV579 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV579 @ SV673 ) @ SV475 ) )
= SV475 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6672]) ).
thf(6773,plain,
! [SV476: $i,SV580: $i,SV674: $i] :
( ( ! [SY2114: $i] :
( ( hAPP @ SY2114 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV674 @ SV674 ) @ SV580 ) @ SY2114 ) @ SV476 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV674 @ SV674 ) @ SV580 ) @ SY2114 ) @ ( hAPP @ SY2114 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6673]) ).
thf(6774,plain,
! [SV477: $i,SV581: $i,SV675: $i] :
( ( ! [SY2115: $i,SY2116: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2116 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2116 @ SY2115 ) @ SV675 ) @ SV581 ) ) @ SV675 ) @ SV477 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2116 @ SY2115 ) @ SV675 ) @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6674]) ).
thf(6775,plain,
! [SV478: $i,SV582: $i,SV676: $i] :
( ( ! [SY2117: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2117 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2117 ) @ SV676 ) @ SV582 ) ) @ SV478 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2117 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2117 ) @ SV582 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6675]) ).
thf(6776,plain,
! [SV481: $i,SV585: $i,SV677: $i] :
( ( ! [SY2118: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY2118 @ SV677 ) @ SV585 ) @ SV481 )
= SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6678]) ).
thf(6777,plain,
! [SV482: $i,SV586: $i,SV678: $i] :
( ( ! [SY2119: $i,SY2120: $i,SY2121: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2121 @ SY2120 @ SY2119 ) @ SV678 ) @ SV586 ) @ SV482 )
= ( hAPP @ SV678 @ ( hAPP @ SV586 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6679]) ).
thf(6778,plain,
! [SV483: $i,SV587: $i,SV679: $i] :
( ( ! [SY2122: $i,SY2123: $i,SY2124: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2124 @ SY2123 @ SY2122 ) @ SV679 ) @ SV587 ) @ SV483 )
= ( hAPP @ ( hAPP @ SV679 @ SV483 ) @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6680]) ).
thf(6779,plain,
! [SV484: $i,SV588: $i,SV680: $i] :
( ( ! [SY2125: $i,SY2126: $i,SY2127: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2127 @ SY2126 @ SY2125 ) @ SV680 ) @ SV588 ) @ SV484 )
= ( hAPP @ ( hAPP @ SV680 @ SV484 ) @ ( hAPP @ SV588 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6681]) ).
thf(6780,plain,
! [SV485: $i,SV589: $i,SV681: $i] :
( ( ! [SY2128: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY2128 @ SV681 @ SV589 )
| ( ( hAPP @ ( hAPP @ SV681 @ SV485 ) @ SV485 )
= SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6682]) ).
thf(6781,plain,
! [SV486: $i,SV590: $i,SV682: $i] :
( ( ! [SY2129: $i,SY2130: $i,SY2131: $i] :
( ( SY2131 != SY2130 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2129 @ SV682 @ SV590 ) @ SV486 ) @ SY2131 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2129 @ SV682 @ SV590 ) @ SV486 ) @ SY2130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6683]) ).
thf(6782,plain,
! [SV487: $i,SV591: $i,SV683: $i] :
( ( ! [SY2132: $i,SY2133: $i,SY2134: $i,SY2135: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2135 @ SY2134 @ SY2133 @ SY2132 @ SV683 )
| ~ ( ~ ( ( ( hAPP @ SY2133 @ SV591 )
!= ( hAPP @ SY2133 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SY2133 @ SV591 )
= ( hAPP @ SY2133 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6684]) ).
thf(6783,plain,
! [SV488: $i,SV592: $i,SV684: $i] :
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV684 ) @ SV592 @ SV488 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV684 ) ) @ SV592 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6685]) ).
thf(6784,plain,
! [SV489: $i,SV593: $i,SV685: $i] :
( ( ( c_Com_Ocom_OBODY @ SV685 )
!= ( c_Com_Ocom_OWhile @ SV593 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6686]) ).
thf(6785,plain,
! [SV490: $i,SV594: $i,SV686: $i] :
( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV686 ) ) @ SV594 @ SV490 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV686 ) @ SV594 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6687]) ).
thf(6786,plain,
! [SV491: $i,SV595: $i,SV687: $i] :
( ( ! [SY2136: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ SY2136 @ SV687 ) @ SV595 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY2136 @ SV687 ) @ SV491 ) )
| ( SV595 = SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6688]) ).
thf(6787,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
| ( SV596 = SV492 ) )
| ~ ( ( SV596 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6689]) ).
thf(6788,plain,
! [SV493: $i,SV597: $i,SV689: $i] :
( ( ! [SY2137: $i,SY2138: $i] :
( ~ ! [SY2139: $i] :
( ( hAPP @ SY2138 @ SY2139 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY2137 @ SV689 @ SV597 ) @ SY2139 ) )
| ( ( hAPP @ SY2138 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SY2138 @ SV493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6690]) ).
thf(6789,plain,
! [SV494: $i,SV598: $i,SV690: $i] :
( ( ! [SY2140: $i,SY2141: $i,SY2142: $i,SY2143: $i] :
( ( SY2143 != SY2142 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY2141 @ SY2140 @ SV690 @ SV598 @ SV494 ) @ SY2143 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY2141 @ SY2140 @ SV690 @ SV598 @ SV494 ) @ SY2142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6691]) ).
thf(6790,plain,
! [SV495: $i,SV599: $i,SV691: $i] :
( ( ! [SY2144: $i,SY2145: $i,SY2146: $i] :
( ~ ( ( SY2146 != SY2145 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2144 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2144 @ SV691 ) @ SY2146 ) @ SV599 ) ) @ SY2145 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2144 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2144 @ SV691 ) @ SY2145 ) @ SV495 ) ) @ SY2146 ) @ SV599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6692]) ).
thf(6791,plain,
! [SV496: $i,SV600: $i,SV692: $i] :
( ( ( c_Com_Ocom_OBODY @ SV692 )
!= ( c_Com_Ocom_OAss @ SV600 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(6792,plain,
! [SV497: $i,SV601: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
| ( SV601 = SV497 ) )
| ~ ( ( SV601 != SV497 )
| ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6694]) ).
thf(6793,plain,
! [SV498: $i,SV602: $i,SV693: $i] :
( ( ! [SY2147: $i,SY2148: $i,SY2149: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2149 @ SY2148 ) @ SY2147 ) @ SV693 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2149 @ SY2148 ) @ SV602 ) @ SV498 ) )
| ~ ( ( SY2147 != SV602 )
| ( SV693 != SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6695]) ).
thf(6794,plain,
! [SV499: $i,SV603: $i,SV694: $i] :
( ( ! [SY2150: $i,SY2151: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2151 ) @ SY2150 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2151 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SY2150 != SV603 )
| ( SV694 != SV499 ) ) )
| ~ ( ~ ~ ( ( SY2150 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2151 ) @ SY2150 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2151 ) @ SV603 ) @ SV499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6696]) ).
thf(6795,plain,
! [SV500: $i,SV604: $i,SV695: $i] :
( ( ! [SY2152: $i,SY2153: $i,SY2154: $i,SY2155: $i,SY2156: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2156 @ SY2155 @ SY2154 @ SY2153 ) @ SY2152 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SY2155 @ SY2154 @ SV604 ) @ SV500 ) )
| ! [SY1939: $i] :
( ( hAPP @ SY2153 @ ( hAPP @ SY2152 @ SY1939 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY1939 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6697]) ).
thf(6796,plain,
! [SV501: $i,SV605: $i,SV696: $i] :
( ( ! [SY2158: $i] :
( ~ ( c_Natural_Oevaln @ SY2158 @ SV696 @ SV605 @ SV501 )
| ( c_Natural_Oevalc @ SY2158 @ SV696 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6698]) ).
thf(6797,plain,
! [SV502: $i,SV606: $i,SV697: $i] :
( ( ! [SY2159: $i] :
( ~ ( c_Natural_Oevaln @ SY2159 @ SV697 @ SV606 @ SV502 )
| ( c_Natural_Oevaln @ SY2159 @ SV697 @ ( hAPP @ c_Nat_OSuc @ SV606 ) @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6699]) ).
thf(6798,plain,
! [SV503: $i,SV607: $i,SV698: $i] :
( ( ! [SY2160: $i,SY2161: $i,SY2162: $i,SY2163: $i,SY2164: $i,SY2165: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2165 @ SY2164 @ SY2163 @ SY2162 ) @ SY2161 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY2160 @ SY2164 @ SY2163 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SY2162 @ ( hAPP @ SY2161 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6700]) ).
thf(6799,plain,
! [SV504: $i,SV608: $i,SV699: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i,SY2169: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2169 @ SY2168 @ SY2167 @ SY2166 ) @ SV699 )
!= SV608 )
| ( ( hAPP @ SY2166 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6701]) ).
thf(6800,plain,
! [SV505: $i,SV609: $i,SV700: $i] :
( ( ! [SY2170: $i,SY2171: $i,SY2172: $i] :
( ~ ( c_Natural_Oevaln @ SY2172 @ SY2171 @ SY2170 @ SV700 )
| ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SY2170 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2172 @ SV609 ) @ SY2171 @ SY2170 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6702]) ).
thf(6801,plain,
! [SV506: $i,SV610: $i,SV701: $i] :
( ( ( c_Com_Ocom_OWhile @ SV701 @ SV610 )
!= ( c_Com_Ocom_OBODY @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6703]) ).
thf(6802,plain,
! [SV507: $i,SV611: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
| ( SV611 = SV507 ) )
| ~ ( ( SV611 != SV507 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6704]) ).
thf(6803,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ~ ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 )
| ~ ! [SY2173: $i] :
~ ( c_Natural_Oevaln @ SV702 @ SV612 @ SY2173 @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6706]) ).
thf(6804,plain,
! [SV510: $i,SV613: $i,SV703: $i] :
( ( ! [SY2174: $i,SY2175: $i,SY2176: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2176 @ SY2175 @ SY2174 )
| ( ( hAPP @ ( hAPP @ SY2174 @ SV703 ) @ ( hAPP @ ( hAPP @ SY2174 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SY2174 @ SV613 ) @ ( hAPP @ ( hAPP @ SY2174 @ SV703 ) @ SV510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6707]) ).
thf(6805,plain,
! [SV511: $i,SV614: $i,SV704: $i] :
( ( ( c_Com_Ocom_OSemi @ SV704 @ SV614 )
!= ( c_Com_Ocom_OBODY @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6708]) ).
thf(6806,plain,
! [SV512: $i,SV615: $i,SV705: $i] :
( ( ! [SY2177: $i] :
( ( c_Com_Ocom_OBODY @ SY2177 )
!= ( c_Com_Ocom_OCond @ SV705 @ SV615 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6709]) ).
thf(6807,plain,
! [SV513: $i,SV616: $i,SV706: $i] :
( ( ! [SY2178: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SY2178 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SY2178 @ SV706 ) @ SV513 ) )
| ( SV616 = SV513 ) )
| ~ ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SY2178 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SY2178 @ SV706 ) @ SV513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6710]) ).
thf(6808,plain,
! [SV514: $i,SV617: $i] :
( ( ~ ( ( ( c_Com_Ocom_OBODY @ SV617 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
| ( SV617 = SV514 ) )
| ~ ( ( SV617 != SV514 )
| ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6711]) ).
thf(6809,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_P @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_Q @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6712]) ).
thf(6810,plain,
( ( ! [SY2179: $i] :
( ~ ( v_P @ sK12_SX0 @ SY2179 )
| ! [SY2180: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ SY2179 @ v_n @ SY2180 )
| ( v_Q @ sK12_SX0 @ SY2180 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6713]) ).
thf(6811,plain,
! [SV515: $i,SV618: $i,SV707: $i] :
( ( ! [SY2181: $i] :
( ( c_Com_Ocom_OCond @ SY2181 @ SV707 @ SV618 )
!= ( c_Com_Ocom_OBODY @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6714]) ).
thf(6812,plain,
! [SV516: $i,SV619: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
| ( SV619 = SV516 ) )
| ~ ( ( SV619 != SV516 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6715]) ).
thf(6813,plain,
! [SV517: $i,SV620: $i,SV708: $i] :
( ( ! [SY2182: $i,SY2183: $i,SY2184: $i,SY2185: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2185 @ SY2184 @ SY2183 @ SY2182 @ SV708 @ SV620 )
| ( ( hAPP @ ( hAPP @ SY2183 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6716]) ).
thf(6814,plain,
! [SV518: $i,SV621: $i,SV709: $i] :
( ( ! [SY2186: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ SY2186 @ SV709 ) @ SV621 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY2186 @ SV709 ) @ SV518 ) )
| ( SV621 = SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6717]) ).
thf(6815,plain,
! [SV519: $i,SV622: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
| ( SV622 = SV519 ) )
| ~ ( ( SV622 != SV519 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6718]) ).
thf(6816,plain,
! [SV520: $i,SV623: $i,SV710: $i] :
( ( ! [SY2187: $i,SY2188: $i,SY2189: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2189 @ SY2188 @ SY2187 @ SV710 @ SV623 )
| ( ( hAPP @ SV710 @ ( hAPP @ SY2187 @ SV520 ) )
= SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6719]) ).
thf(6817,plain,
! [SV521: $i,SV624: $i,SV711: $i] :
( ( ! [SY2190: $i,SY2191: $i,SY2192: $i] :
~ ( ~ ( ( SY2192 != SY2191 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2190 @ SV711 ) @ SV624 ) @ SY2191 ) @ SV521 ) @ SY2192 )
= SV521 ) )
| ~ ( ~ ( ( SY2192 != SY2191 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2190 @ SV711 ) @ SV624 ) @ SY2191 ) @ SV521 ) @ SY2192 )
= ( hAPP @ SV624 @ SY2192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6720]) ).
thf(6818,plain,
! [SV522: $i,SV625: $i,SV712: $i] :
( ( ! [SY2193: $i,SY2194: $i,SY2195: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2195 ) @ SY2194 ) @ SY2193 )
!= SV712 )
| ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2195 ) @ SY2193 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2195 ) @ SY2194 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2195 ) @ SV712 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6721]) ).
thf(6819,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6722]) ).
thf(6820,plain,
! [SV524: $i,SV627: $i,SV714: $i] :
( ( ! [SY2196: $i,SY2197: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2197 @ SY2196 @ SV714 )
| ( ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6723]) ).
thf(6821,plain,
! [SV526: $i,SV628: $i,SV715: $i] :
( ( ! [SY2198: $i,SY2199: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2199 @ SY2198 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) )
| ~ ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2199 @ SY2198 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6725]) ).
thf(6822,plain,
! [SV527: $i,SV629: $i,SV716: $i] :
( ( ( c_Com_Ocom_OBODY @ SV716 )
!= ( c_Com_Ocom_OSemi @ SV629 @ SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6726]) ).
thf(6823,plain,
! [SV528: $i,SV630: $i,SV717: $i] :
( ( ! [SY2200: $i,SY2201: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2201 @ SY2200 ) @ SV717 @ SV630 @ SV528 )
| ~ ! [SY2202: $i] :
( ~ ( c_Natural_Oevaln @ SY2201 @ SV717 @ SV630 @ SY2202 )
| ~ ( c_Natural_Oevaln @ SY2200 @ SY2202 @ SV630 @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6727]) ).
thf(6824,plain,
! [SV529: $i,SV631: $i,SV718: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV718 ) @ SV631 ) @ SV529 )
!= SV529 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6728]) ).
thf(6825,plain,
! [SV530: $i,SV632: $i,SV719: $i] :
( ( ! [SY2203: $i] :
( ( c_Com_Ocom_OBODY @ SY2203 )
!= ( c_Com_Ocom_OLocal @ SV719 @ SV632 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6729]) ).
thf(6826,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
| ( SV633 = SV531 ) )
| ~ ( ( SV633 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6730]) ).
thf(6827,plain,
! [SV532: $i,SV634: $i,SV721: $i] :
( ( ( c_Com_Ocom_OAss @ SV721 @ SV634 )
!= ( c_Com_Ocom_OBODY @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6731]) ).
thf(6828,plain,
! [SV533: $i,SV635: $i,SV722: $i] :
( ( ! [SY2204: $i,SY2205: $i,SY2206: $i,SY2207: $i] :
( ~ ( ( SY2207 != SY2206 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2205 @ SY2204 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2205 @ SY2204 ) @ SV722 ) @ SY2207 ) @ SV635 ) ) @ SY2206 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2205 @ SY2204 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2205 @ SY2204 ) @ SV722 ) @ SY2206 ) @ SV533 ) ) @ SY2207 ) @ SV635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6732]) ).
thf(6829,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
| ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
| ~ ( ~ ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 )
| ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6733]) ).
thf(6830,plain,
! [SV535: $i,SV637: $i,SV724: $i] :
( ( ! [SY2210: $i,SY2211: $i,SY2212: $i] :
~ ( ~ ( ( SY2212 != SY2211 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2210 @ SV724 ) @ SV637 ) @ SY2211 ) @ SV535 ) @ SY2212 )
= SV535 ) )
| ~ ( ~ ( ( SY2212 != SY2211 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2210 @ SV724 ) @ SV637 ) @ SY2211 ) @ SV535 ) @ SY2212 )
= ( hAPP @ SV637 @ SY2212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6734]) ).
thf(6831,plain,
! [SV536: $i,SV638: $i,SV725: $i] :
( ( ! [SY2213: $i,SY2214: $i,SY2215: $i] :
( ~ ( ( SY2215 != SY2214 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2213 @ SV725 ) @ SV638 ) @ SY2214 ) @ SV536 ) @ SY2215 )
= ( hAPP @ SV638 @ SY2215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6735]) ).
thf(6832,plain,
! [SV537: $i,SV639: $i,SV726: $i] :
( ( ! [SY2216: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2216 ) @ SV726 @ SV639 @ SV537 )
| ~ ! [SY2217: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2217 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2216 ) ) @ SV726 @ SY2217 @ SV537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6736]) ).
thf(6833,plain,
! [SV538: $i,SV640: $i,SV727: $i] :
( ( ! [SY2218: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2218 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2218 ) ) @ SV727 @ SV640 @ SV538 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2218 ) ) @ SV727 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2218 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6737]) ).
thf(6834,plain,
! [SV539: $i,SV641: $i,SV728: $i] :
( ( ! [SY2219: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2219 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2219 ) @ SV728 ) @ SV539 ) )
| ( SV641 = SV539 ) )
| ~ ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2219 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2219 ) @ SV728 ) @ SV539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6738]) ).
thf(6835,plain,
! [SV540: $i,SV642: $i,SV729: $i] :
( ( ! [SY2220: $i,SY2221: $i,SY2222: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2222 @ SY2221 ) @ SY2220 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2222 @ SY2221 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SY2220 != SV642 )
| ( SV729 != SV540 ) ) )
| ~ ( ~ ~ ( ( SY2220 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2222 @ SY2221 ) @ SY2220 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2222 @ SY2221 ) @ SV642 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6739]) ).
thf(6836,plain,
! [SV541: $i,SV643: $i,SV730: $i] :
( ( ! [SY2223: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2223 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2223 ) @ SV541 ) @ SV643 ) )
| ( SV730 = SV541 ) )
| ~ ( ( SV730 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2223 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2223 ) @ SV541 ) @ SV643 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6740]) ).
thf(6837,plain,
! [SV542: $i,SV644: $i,SV731: $i] :
( ( SV731
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV644 ) @ SV542 ) @ SV731 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6741]) ).
thf(6838,plain,
! [SV544: $i,SV645: $i,SV732: $i] :
( ( ! [SY2224: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SY2224 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SY2224 @ SV732 ) @ SV544 ) )
| ( SV645 = SV544 ) )
| ~ ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SY2224 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SY2224 @ SV732 ) @ SV544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6743]) ).
thf(6839,plain,
! [SV545: $i,SV646: $i,SV733: $i] :
( ( ! [SY2225: $i,SY2226: $i,SY2227: $i,SY2228: $i,SY2229: $i,SY2230: $i,SY2231: $i,SY2232: $i] :
( ( ( hAPP @ SY2232 @ ( hAPP @ SY2231 @ SY2230 ) )
!= ( hAPP @ SY2229 @ ( hAPP @ SY2228 @ SY2227 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2226 @ SY2225 @ SV733 @ SY2232 ) @ SY2231 ) @ SY2230 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SY2225 @ SV545 @ SY2229 ) @ SY2228 ) @ SY2227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6744]) ).
thf(6840,plain,
! [SV546: $i,SV647: $i,SV734: $i] :
( ( ! [SY2233: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY2233 ) ) @ SV734 @ SV647 @ SV546 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY2233 ) @ SV734 @ ( hAPP @ c_Nat_OSuc @ SV647 ) @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6745]) ).
thf(6841,plain,
! [SV547: $i,SV648: $i,SV735: $i] :
( ( ! [SY2234: $i,SY2235: $i] :
( ( ( hAPP @ SY2235 @ SY2234 )
!= SV735 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SY2235 ) @ SY2234 ) @ SV735 )
= SY2235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6746]) ).
thf(6842,plain,
! [SV548: $i,SV649: $i,SV736: $i] :
( ( ! [SY2236: $i,SY2237: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2236 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2238: $i] :
~ ( ~ ( ( SY2236
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SV649 ) @ SY2238 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2238 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2236 ) @ SY2238 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2238 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY2239: $i] :
~ ( ~ ( ( SY2236
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SV649 ) @ SY2239 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2239 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2236 ) @ SY2239 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2239 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SY2236 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2237 ) @ SV649 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6747]) ).
thf(6843,plain,
! [SV549: $i,SV650: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
| ( SV650 = SV549 ) )
| ~ ( ( SV650 != SV549 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6748]) ).
thf(6844,plain,
! [SV550: $i,SV651: $i,SV737: $i] :
( ( ! [SY2240: $i] :
( ( c_Com_Ocom_OBODY @ SY2240 )
!= ( c_Com_Ocom_OCall @ SV737 @ SV651 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6749]) ).
thf(6845,plain,
! [SV552: $i,SV652: $i,SV738: $i] :
( ( ! [SY2241: $i] :
( ( c_Com_Ocom_OCall @ SY2241 @ SV738 @ SV652 )
!= ( c_Com_Ocom_OBODY @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6751]) ).
thf(6846,plain,
! [SV553: $i,SV653: $i,SV739: $i] :
( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV739 @ SV653 @ SV553 )
| ( SV553 = SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6752]) ).
thf(6847,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
!= SV554 )
| ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) ) )
| ~ ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6753]) ).
thf(6848,plain,
! [SV555: $i,SV655: $i,SV741: $i] :
( ( ! [SY2242: $i,SY2243: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2243 @ SY2242 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2244: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2243 @ SV741 @ SV655 @ SY2244 )
| ~ ( c_Natural_Oevaln @ SY2242 @ SY2244 @ SV655 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY2245: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2243 @ SV741 @ SV655 @ SY2245 )
| ~ ( c_Natural_Oevaln @ SY2242 @ SY2245 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2243 @ SY2242 ) @ SV741 @ SV655 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6754]) ).
thf(6849,plain,
! [SV556: $i,SV656: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV656 )
!= ( hAPP @ c_Nat_OSuc @ SV556 ) )
= $true )
| ( ( SV656 = SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6755]) ).
thf(6850,plain,
! [SV557: $i,SV657: $i,SV742: $i] :
( ( ! [SY2246: $i] :
( ( c_Com_Ocom_OLocal @ SY2246 @ SV742 @ SV657 )
!= ( c_Com_Ocom_OBODY @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6756]) ).
thf(6851,plain,
! [SV558: $i,SV658: $i] :
( ( ( ~ ! [SY2074: $i] :
( ( hAPP @ SV658 @ SY2074 )
= ( hAPP @ SV558 @ SY2074 ) ) )
= $true )
| ( ( SV658 = SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6757]) ).
thf(6852,plain,
! [SV455: $i,SV559: $i,SV659: $i,SV743: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV743 @ SV659 @ SV559 @ ( hAPP @ c_Nat_OSuc @ SV455 ) )
= ( hAPP @ SV559 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6758]) ).
thf(6853,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i] :
( ( ! [SY2247: $i,SY2248: $i,SY2249: $i,SY2250: $i,SY2251: $i,SY2252: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2252 @ SY2251 @ SY2250 @ SY2249 @ SY2248 @ SY2247 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6759]) ).
thf(6854,plain,
! [SV458: $i,SV562: $i,SV661: $i,SV745: $i] :
( ( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV745 @ SV661 @ SV562 ) @ ( hAPP @ c_Nat_OSuc @ SV458 ) )
= ( hAPP @ ( hAPP @ SV562 @ SV458 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV745 @ SV661 @ SV562 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6760]) ).
thf(6855,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i] :
( ( ! [SY2253: $i,SY2254: $i,SY2255: $i,SY2256: $i,SY2257: $i,SY2258: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2258 @ SY2257 @ SY2256 @ SY2255 @ SY2254 @ SY2253 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6761]) ).
thf(6856,plain,
! [SV462: $i,SV566: $i,SV663: $i,SV747: $i] :
( ( ! [SY2259: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY2259 @ SV747 @ SV663 ) @ SV566 ) @ ( hAPP @ c_Nat_OSuc @ SV462 ) )
= ( hAPP @ ( hAPP @ SV663 @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY2259 @ SV747 @ SV663 ) @ SV566 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6762]) ).
thf(6857,plain,
! [SV464: $i,SV568: $i,SV665: $i,SV748: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV748 ) @ SV665 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV748 ) @ SV568 ) @ SV464 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV748 ) @ SV568 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV748 ) @ SV665 ) @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6764]) ).
thf(6858,plain,
! [SV465: $i,SV569: $i,SV666: $i,SV749: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV749 @ SV666 ) @ SV569 ) @ SV465 ) @ ( hAPP @ SV569 @ SV465 ) )
= SV569 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6765]) ).
thf(6859,plain,
! [SV466: $i,SV570: $i,SV667: $i,SV750: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2261 @ SY2260 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2261 @ SY2260 ) @ SV750 ) @ SV667 ) @ SV570 ) ) @ SV667 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2261 @ SY2260 ) @ SV750 ) @ SV667 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6766]) ).
thf(6860,plain,
! [SV467: $i,SV571: $i,SV668: $i,SV751: $i] :
( ( ! [SY2262: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2262 @ SV751 ) @ SV668 ) @ SV571 ) @ SV467 ) @ SV571 )
= SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6767]) ).
thf(6861,plain,
! [SV468: $i,SV572: $i,SV669: $i,SV752: $i] :
( ( ! [SY2263: $i,SY2264: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2264 @ SY2263 @ SV752 @ SV669 ) @ SV572 ) @ SV468 )
= ( hAPP @ SV669 @ ( hAPP @ SV572 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6768]) ).
thf(6862,plain,
! [SV469: $i,SV573: $i,SV670: $i,SV753: $i] :
( ( ! [SY2265: $i,SY2266: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2266 @ SY2265 @ SV753 @ SV670 ) @ SV573 ) @ SV469 )
= ( hAPP @ SV670 @ ( hAPP @ SV573 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6769]) ).
thf(6863,plain,
! [SV470: $i,SV574: $i,SV671: $i,SV754: $i] :
( ( ! [SY2267: $i,SY2268: $i,SY2269: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2269 @ SY2268 @ SY2267 @ SV754 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2269 @ SY2267 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2268 @ SY2267 @ ( hAPP @ ( c_Fun_Ocomp @ SY2269 @ SY2268 @ SV671 @ SV754 ) @ SV574 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6770]) ).
thf(6864,plain,
! [SV474: $i,SV578: $i,SV672: $i,SV755: $i] :
( ( ! [SY2270: $i,SY2271: $i,SY2272: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2272 @ SY2271 @ SY2270 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2272 @ SV755 @ SY2271 ) @ SV672 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2272 @ SV755 @ SY2270 ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV755 @ SY2271 @ SY2270 ) @ SV578 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6771]) ).
thf(6865,plain,
! [SV476: $i,SV580: $i,SV674: $i,SV756: $i] :
( ( ( hAPP @ SV756 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV674 @ SV674 ) @ SV580 ) @ SV756 ) @ SV476 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV674 @ SV674 ) @ SV580 ) @ SV756 ) @ ( hAPP @ SV756 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6773]) ).
thf(6866,plain,
! [SV477: $i,SV581: $i,SV675: $i,SV757: $i] :
( ( ! [SY2273: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2273 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2273 @ SV757 ) @ SV675 ) @ SV581 ) ) @ SV675 ) @ SV477 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2273 @ SV757 ) @ SV675 ) @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6774]) ).
thf(6867,plain,
! [SV478: $i,SV582: $i,SV676: $i,SV758: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV758 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV758 ) @ SV676 ) @ SV582 ) ) @ SV478 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV758 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV758 ) @ SV582 ) @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6775]) ).
thf(6868,plain,
! [SV481: $i,SV585: $i,SV677: $i,SV759: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV759 @ SV677 ) @ SV585 ) @ SV481 )
= SV585 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6776]) ).
thf(6869,plain,
! [SV482: $i,SV586: $i,SV678: $i,SV760: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2275 @ SY2274 @ SV760 ) @ SV678 ) @ SV586 ) @ SV482 )
= ( hAPP @ SV678 @ ( hAPP @ SV586 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6777]) ).
thf(6870,plain,
! [SV483: $i,SV587: $i,SV679: $i,SV761: $i] :
( ( ! [SY2276: $i,SY2277: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2277 @ SY2276 @ SV761 ) @ SV679 ) @ SV587 ) @ SV483 )
= ( hAPP @ ( hAPP @ SV679 @ SV483 ) @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6778]) ).
thf(6871,plain,
! [SV484: $i,SV588: $i,SV680: $i,SV762: $i] :
( ( ! [SY2278: $i,SY2279: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2279 @ SY2278 @ SV762 ) @ SV680 ) @ SV588 ) @ SV484 )
= ( hAPP @ ( hAPP @ SV680 @ SV484 ) @ ( hAPP @ SV588 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6779]) ).
thf(6872,plain,
! [SV485: $i,SV589: $i,SV681: $i,SV763: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV763 @ SV681 @ SV589 )
| ( ( hAPP @ ( hAPP @ SV681 @ SV485 ) @ SV485 )
= SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6780]) ).
thf(6873,plain,
! [SV486: $i,SV590: $i,SV682: $i,SV764: $i] :
( ( ! [SY2280: $i,SY2281: $i] :
( ( SY2281 != SY2280 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SY2281 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SY2280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6781]) ).
thf(6874,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i] :
( ( ! [SY2282: $i,SY2283: $i,SY2284: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2284 @ SY2283 @ SY2282 @ SV765 @ SV683 )
| ~ ( ~ ( ( ( hAPP @ SY2282 @ SV591 )
!= ( hAPP @ SY2282 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SY2282 @ SV591 )
= ( hAPP @ SY2282 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6782]) ).
thf(6875,plain,
! [SV488: $i,SV592: $i,SV684: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV684 ) @ SV592 @ SV488 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV684 ) ) @ SV592 @ SV488 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6783]) ).
thf(6876,plain,
! [SV489: $i,SV593: $i,SV685: $i] :
( ( ( c_Com_Ocom_OBODY @ SV685 )
= ( c_Com_Ocom_OWhile @ SV593 @ SV489 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6784]) ).
thf(6877,plain,
! [SV490: $i,SV594: $i,SV686: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV686 ) ) @ SV594 @ SV490 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV686 ) @ SV594 @ SV490 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6785]) ).
thf(6878,plain,
! [SV491: $i,SV595: $i,SV687: $i,SV766: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV595 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV491 ) )
| ( SV595 = SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6786]) ).
thf(6879,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
| ( SV596 = SV492 ) )
| ~ ( ( SV596 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6787]) ).
thf(6880,plain,
! [SV493: $i,SV597: $i,SV689: $i,SV767: $i] :
( ( ! [SY2285: $i] :
( ~ ! [SY2286: $i] :
( ( hAPP @ SY2285 @ SY2286 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV767 @ SV689 @ SV597 ) @ SY2286 ) )
| ( ( hAPP @ SY2285 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SY2285 @ SV493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6788]) ).
thf(6881,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i] :
( ( ! [SY2287: $i,SY2288: $i,SY2289: $i] :
( ( SY2289 != SY2288 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY2287 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SY2289 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SY2287 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SY2288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6789]) ).
thf(6882,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i] :
( ( ! [SY2290: $i,SY2291: $i] :
( ~ ( ( SY2291 != SY2290 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SY2291 ) @ SV599 ) ) @ SY2290 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SY2290 ) @ SV495 ) ) @ SY2291 ) @ SV599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6790]) ).
thf(6883,plain,
! [SV496: $i,SV600: $i,SV692: $i] :
( ( ( c_Com_Ocom_OBODY @ SV692 )
= ( c_Com_Ocom_OAss @ SV600 @ SV496 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6791]) ).
thf(6884,plain,
! [SV497: $i,SV601: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
| ( SV601 = SV497 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6792]) ).
thf(6885,plain,
! [SV497: $i,SV601: $i] :
( ( ~ ( ( SV601 != SV497 )
| ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6792]) ).
thf(6886,plain,
! [SV498: $i,SV602: $i,SV693: $i,SV770: $i] :
( ( ! [SY2292: $i,SY2293: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2293 @ SY2292 ) @ SV770 ) @ SV693 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2293 @ SY2292 ) @ SV602 ) @ SV498 ) )
| ~ ( ( SV770 != SV602 )
| ( SV693 != SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6793]) ).
thf(6887,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i] :
( ( ! [SY2294: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2294 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2294 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
| ~ ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2294 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2294 ) @ SV603 ) @ SV499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6794]) ).
thf(6888,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i,SY2298: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2298 @ SY2297 @ SY2296 @ SY2295 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SY2297 @ SY2296 @ SV604 ) @ SV500 ) )
| ! [SY2299: $i] :
( ( hAPP @ SY2295 @ ( hAPP @ SV772 @ SY2299 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6795]) ).
thf(6889,plain,
! [SV501: $i,SV605: $i,SV696: $i,SV773: $i] :
( ( ~ ( c_Natural_Oevaln @ SV773 @ SV696 @ SV605 @ SV501 )
| ( c_Natural_Oevalc @ SV773 @ SV696 @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6796]) ).
thf(6890,plain,
! [SV502: $i,SV606: $i,SV697: $i,SV774: $i] :
( ( ~ ( c_Natural_Oevaln @ SV774 @ SV697 @ SV606 @ SV502 )
| ( c_Natural_Oevaln @ SV774 @ SV697 @ ( hAPP @ c_Nat_OSuc @ SV606 ) @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6797]) ).
thf(6891,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i] :
( ( ! [SY2300: $i,SY2301: $i,SY2302: $i,SY2303: $i,SY2304: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2304 @ SY2303 @ SY2302 @ SY2301 ) @ SY2300 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SY2303 @ SY2302 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SY2301 @ ( hAPP @ SY2300 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6798]) ).
thf(6892,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2307 @ SY2306 @ SY2305 @ SV776 ) @ SV699 )
!= SV608 )
| ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6799]) ).
thf(6893,plain,
! [SV505: $i,SV609: $i,SV700: $i,SV777: $i] :
( ( ! [SY2308: $i,SY2309: $i] :
( ~ ( c_Natural_Oevaln @ SY2309 @ SY2308 @ SV777 @ SV700 )
| ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2309 @ SV609 ) @ SY2308 @ SV777 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6800]) ).
thf(6894,plain,
! [SV506: $i,SV610: $i,SV701: $i] :
( ( ( c_Com_Ocom_OWhile @ SV701 @ SV610 )
= ( c_Com_Ocom_OBODY @ SV506 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6801]) ).
thf(6895,plain,
! [SV507: $i,SV611: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
| ( SV611 = SV507 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6802]) ).
thf(6896,plain,
! [SV507: $i,SV611: $i] :
( ( ~ ( ( SV611 != SV507 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6802]) ).
thf(6897,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 ) )
= $true )
| ( ( ~ ! [SY2173: $i] :
~ ( c_Natural_Oevaln @ SV702 @ SV612 @ SY2173 @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6803]) ).
thf(6898,plain,
! [SV510: $i,SV613: $i,SV703: $i,SV778: $i] :
( ( ! [SY2310: $i,SY2311: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2311 @ SY2310 @ SV778 )
| ( ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ SV510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6804]) ).
thf(6899,plain,
! [SV511: $i,SV614: $i,SV704: $i] :
( ( ( c_Com_Ocom_OSemi @ SV704 @ SV614 )
= ( c_Com_Ocom_OBODY @ SV511 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6805]) ).
thf(6900,plain,
! [SV512: $i,SV615: $i,SV705: $i,SV779: $i] :
( ( ( c_Com_Ocom_OBODY @ SV779 )
!= ( c_Com_Ocom_OCond @ SV705 @ SV615 @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6806]) ).
thf(6901,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
| ( SV616 = SV513 ) )
| ~ ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6807]) ).
thf(6902,plain,
! [SV514: $i,SV617: $i] :
( ( ~ ( ( ( c_Com_Ocom_OBODY @ SV617 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
| ( SV617 = SV514 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6808]) ).
thf(6903,plain,
! [SV514: $i,SV617: $i] :
( ( ~ ( ( SV617 != SV514 )
| ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6808]) ).
thf(6904,plain,
! [SV781: $i] :
( ( ! [SY2312: $i] :
( ~ ( v_P @ SV781 @ SY2312 )
| ! [SY2313: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SY2312 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY2313 )
| ( v_Q @ SV781 @ SY2313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6809]) ).
thf(6905,plain,
( ( ~ ( v_P @ sK12_SX0 @ sK13_SY2179 )
| ! [SY2314: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ sK13_SY2179 @ v_n @ SY2314 )
| ( v_Q @ sK12_SX0 @ SY2314 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6810]) ).
thf(6906,plain,
! [SV515: $i,SV618: $i,SV707: $i,SV782: $i] :
( ( ( c_Com_Ocom_OCond @ SV782 @ SV707 @ SV618 )
!= ( c_Com_Ocom_OBODY @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6811]) ).
thf(6907,plain,
! [SV516: $i,SV619: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
| ( SV619 = SV516 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6812]) ).
thf(6908,plain,
! [SV516: $i,SV619: $i] :
( ( ~ ( ( SV619 != SV516 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6812]) ).
thf(6909,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i] :
( ( ! [SY2315: $i,SY2316: $i,SY2317: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2317 @ SY2316 @ SY2315 @ SV783 @ SV708 @ SV620 )
| ( ( hAPP @ ( hAPP @ SY2315 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6813]) ).
thf(6910,plain,
! [SV518: $i,SV621: $i,SV709: $i,SV784: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV621 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV518 ) )
| ( SV621 = SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6814]) ).
thf(6911,plain,
! [SV519: $i,SV622: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
| ( SV622 = SV519 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6815]) ).
thf(6912,plain,
! [SV519: $i,SV622: $i] :
( ( ~ ( ( SV622 != SV519 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6815]) ).
thf(6913,plain,
! [SV520: $i,SV623: $i,SV710: $i,SV785: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2319 @ SY2318 @ SV785 @ SV710 @ SV623 )
| ( ( hAPP @ SV710 @ ( hAPP @ SV785 @ SV520 ) )
= SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6816]) ).
thf(6914,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i] :
( ( ! [SY2320: $i,SY2321: $i] :
~ ( ~ ( ( SY2321 != SY2320 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SY2320 ) @ SV521 ) @ SY2321 )
= SV521 ) )
| ~ ( ~ ( ( SY2321 != SY2320 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SY2320 ) @ SV521 ) @ SY2321 )
= ( hAPP @ SV624 @ SY2321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6817]) ).
thf(6915,plain,
! [SV522: $i,SV625: $i,SV712: $i,SV787: $i] :
( ( ! [SY2322: $i,SY2323: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2323 ) @ SY2322 ) @ SV787 )
!= SV712 )
| ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2323 ) @ SV787 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2323 ) @ SY2322 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2323 ) @ SV712 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6818]) ).
thf(6916,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 ) )
| ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6819]) ).
thf(6917,plain,
! [SV524: $i,SV627: $i,SV714: $i,SV788: $i] :
( ( ! [SY2324: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2324 @ SV788 @ SV714 )
| ( ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6820]) ).
thf(6918,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i] :
( ( ! [SY2325: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2325 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) )
| ~ ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2325 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6821]) ).
thf(6919,plain,
! [SV527: $i,SV629: $i,SV716: $i] :
( ( ( c_Com_Ocom_OBODY @ SV716 )
= ( c_Com_Ocom_OSemi @ SV629 @ SV527 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(6920,plain,
! [SV528: $i,SV630: $i,SV717: $i,SV790: $i] :
( ( ! [SY2326: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2326 @ SV790 ) @ SV717 @ SV630 @ SV528 )
| ~ ! [SY2327: $i] :
( ~ ( c_Natural_Oevaln @ SY2326 @ SV717 @ SV630 @ SY2327 )
| ~ ( c_Natural_Oevaln @ SV790 @ SY2327 @ SV630 @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6823]) ).
thf(6921,plain,
! [SV529: $i,SV631: $i,SV718: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV718 ) @ SV631 ) @ SV529 )
= SV529 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6824]) ).
thf(6922,plain,
! [SV530: $i,SV632: $i,SV719: $i,SV791: $i] :
( ( ( c_Com_Ocom_OBODY @ SV791 )
!= ( c_Com_Ocom_OLocal @ SV719 @ SV632 @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6825]) ).
thf(6923,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
| ( SV633 = SV531 ) )
| ~ ( ( SV633 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6826]) ).
thf(6924,plain,
! [SV532: $i,SV634: $i,SV721: $i] :
( ( ( c_Com_Ocom_OAss @ SV721 @ SV634 )
= ( c_Com_Ocom_OBODY @ SV532 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6827]) ).
thf(6925,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i] :
( ( ! [SY2328: $i,SY2329: $i,SY2330: $i] :
( ~ ( ( SY2330 != SY2329 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2328 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2328 @ SV792 ) @ SV722 ) @ SY2330 ) @ SV635 ) ) @ SY2329 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2328 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2328 @ SV792 ) @ SV722 ) @ SY2329 ) @ SV533 ) ) @ SY2330 ) @ SV635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6828]) ).
thf(6926,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
| ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
| ~ ( ~ ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 )
| ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6829]) ).
thf(6927,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i] :
( ( ! [SY2331: $i,SY2332: $i] :
~ ( ~ ( ( SY2332 != SY2331 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SY2331 ) @ SV535 ) @ SY2332 )
= SV535 ) )
| ~ ( ~ ( ( SY2332 != SY2331 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SY2331 ) @ SV535 ) @ SY2332 )
= ( hAPP @ SV637 @ SY2332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6830]) ).
thf(6928,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i] :
( ( ! [SY2333: $i,SY2334: $i] :
( ~ ( ( SY2334 != SY2333 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SY2333 ) @ SV536 ) @ SY2334 )
= ( hAPP @ SV638 @ SY2334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6831]) ).
thf(6929,plain,
! [SV537: $i,SV639: $i,SV726: $i,SV795: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
| ~ ! [SY2335: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2335 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ SY2335 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6832]) ).
thf(6930,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6833]) ).
thf(6931,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
| ( SV641 = SV539 ) )
| ~ ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6834]) ).
thf(6932,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i] :
( ( ! [SY2336: $i,SY2337: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2337 @ SY2336 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2337 @ SY2336 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
| ~ ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2337 @ SY2336 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2337 @ SY2336 ) @ SV642 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6835]) ).
thf(6933,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
| ( SV730 = SV541 ) )
| ~ ( ( SV730 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6836]) ).
thf(6934,plain,
! [SV542: $i,SV644: $i,SV731: $i] :
( ( SV731
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV644 ) @ SV542 ) @ SV731 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6837]) ).
thf(6935,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
| ( SV645 = SV544 ) )
| ~ ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6838]) ).
thf(6936,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i] :
( ( ! [SY2338: $i,SY2339: $i,SY2340: $i,SY2341: $i,SY2342: $i,SY2343: $i,SY2344: $i] :
( ( ( hAPP @ SY2344 @ ( hAPP @ SY2343 @ SY2342 ) )
!= ( hAPP @ SY2341 @ ( hAPP @ SY2340 @ SY2339 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2338 @ SV801 @ SV733 @ SY2344 ) @ SY2343 ) @ SY2342 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SY2341 ) @ SY2340 ) @ SY2339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6839]) ).
thf(6937,plain,
! [SV546: $i,SV647: $i,SV734: $i,SV802: $i] :
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV802 ) ) @ SV734 @ SV647 @ SV546 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV802 ) @ SV734 @ ( hAPP @ c_Nat_OSuc @ SV647 ) @ SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6840]) ).
thf(6938,plain,
! [SV547: $i,SV648: $i,SV735: $i,SV803: $i] :
( ( ! [SY2345: $i] :
( ( ( hAPP @ SY2345 @ SV803 )
!= SV735 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SY2345 ) @ SV803 ) @ SV735 )
= SY2345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6841]) ).
thf(6939,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i] :
( ( ! [SY2346: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2347: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV649 ) @ SY2347 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SY2347 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV804 ) @ SY2347 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SY2347 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY2348: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV649 ) @ SY2348 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SY2348 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV804 ) @ SY2348 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SY2348 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2346 ) @ SV649 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6842]) ).
thf(6940,plain,
! [SV549: $i,SV650: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
| ( SV650 = SV549 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6843]) ).
thf(6941,plain,
! [SV549: $i,SV650: $i] :
( ( ~ ( ( SV650 != SV549 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6843]) ).
thf(6942,plain,
! [SV550: $i,SV651: $i,SV737: $i,SV805: $i] :
( ( ( c_Com_Ocom_OBODY @ SV805 )
!= ( c_Com_Ocom_OCall @ SV737 @ SV651 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6844]) ).
thf(6943,plain,
! [SV552: $i,SV652: $i,SV738: $i,SV806: $i] :
( ( ( c_Com_Ocom_OCall @ SV806 @ SV738 @ SV652 )
!= ( c_Com_Ocom_OBODY @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6845]) ).
thf(6944,plain,
! [SV553: $i,SV653: $i,SV739: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV739 @ SV653 @ SV553 ) )
= $true )
| ( ( SV553 = SV739 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6846]) ).
thf(6945,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
!= SV554 )
| ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) ) )
| ~ ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(6946,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i] :
( ( ! [SY2349: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2349 @ SV807 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2350: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2349 @ SV741 @ SV655 @ SY2350 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2350 @ SV655 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY2351: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY2349 @ SV741 @ SV655 @ SY2351 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2351 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2349 @ SV807 ) @ SV741 @ SV655 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6848]) ).
thf(6947,plain,
! [SV556: $i,SV656: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV656 )
= ( hAPP @ c_Nat_OSuc @ SV556 ) )
= $false )
| ( ( SV656 = SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6849]) ).
thf(6948,plain,
! [SV557: $i,SV657: $i,SV742: $i,SV808: $i] :
( ( ( c_Com_Ocom_OLocal @ SV808 @ SV742 @ SV657 )
!= ( c_Com_Ocom_OBODY @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6850]) ).
thf(6949,plain,
! [SV558: $i,SV658: $i] :
( ( ( ! [SY2074: $i] :
( ( hAPP @ SV658 @ SY2074 )
= ( hAPP @ SV558 @ SY2074 ) ) )
= $false )
| ( ( SV658 = SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(6950,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i] :
( ( ! [SY2352: $i,SY2353: $i,SY2354: $i,SY2355: $i,SY2356: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2356 @ SY2355 @ SY2354 @ SY2353 @ SY2352 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6853]) ).
thf(6951,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i] :
( ( ! [SY2357: $i,SY2358: $i,SY2359: $i,SY2360: $i,SY2361: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2361 @ SY2360 @ SY2359 @ SY2358 @ SY2357 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6855]) ).
thf(6952,plain,
! [SV462: $i,SV566: $i,SV663: $i,SV747: $i,SV811: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV811 @ SV747 @ SV663 ) @ SV566 ) @ ( hAPP @ c_Nat_OSuc @ SV462 ) )
= ( hAPP @ ( hAPP @ SV663 @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV811 @ SV747 @ SV663 ) @ SV566 ) @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6856]) ).
thf(6953,plain,
! [SV466: $i,SV570: $i,SV667: $i,SV750: $i,SV812: $i] :
( ( ! [SY2362: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2362 @ SV812 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2362 @ SV812 ) @ SV750 ) @ SV667 ) @ SV570 ) ) @ SV667 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SY2362 @ SV812 ) @ SV750 ) @ SV667 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6859]) ).
thf(6954,plain,
! [SV467: $i,SV571: $i,SV668: $i,SV751: $i,SV813: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV813 @ SV751 ) @ SV668 ) @ SV571 ) @ SV467 ) @ SV571 )
= SV467 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6860]) ).
thf(6955,plain,
! [SV468: $i,SV572: $i,SV669: $i,SV752: $i,SV814: $i] :
( ( ! [SY2363: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2363 @ SV814 @ SV752 @ SV669 ) @ SV572 ) @ SV468 )
= ( hAPP @ SV669 @ ( hAPP @ SV572 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6861]) ).
thf(6956,plain,
! [SV469: $i,SV573: $i,SV670: $i,SV753: $i,SV815: $i] :
( ( ! [SY2364: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2364 @ SV815 @ SV753 @ SV670 ) @ SV573 ) @ SV469 )
= ( hAPP @ SV670 @ ( hAPP @ SV573 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6862]) ).
thf(6957,plain,
! [SV470: $i,SV574: $i,SV671: $i,SV754: $i,SV816: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2366 @ SY2365 @ SV816 @ SV754 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2366 @ SV816 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2365 @ SV816 @ ( hAPP @ ( c_Fun_Ocomp @ SY2366 @ SY2365 @ SV671 @ SV754 ) @ SV574 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6863]) ).
thf(6958,plain,
! [SV474: $i,SV578: $i,SV672: $i,SV755: $i,SV817: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2368 @ SY2367 @ SV817 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2368 @ SV755 @ SY2367 ) @ SV672 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2368 @ SV755 @ SV817 ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV755 @ SY2367 @ SV817 ) @ SV578 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6864]) ).
thf(6959,plain,
! [SV477: $i,SV581: $i,SV675: $i,SV757: $i,SV818: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV818 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV818 @ SV757 ) @ SV675 ) @ SV581 ) ) @ SV675 ) @ SV477 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV818 @ SV757 ) @ SV675 ) @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6866]) ).
thf(6960,plain,
! [SV482: $i,SV586: $i,SV678: $i,SV760: $i,SV819: $i] :
( ( ! [SY2369: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2369 @ SV819 @ SV760 ) @ SV678 ) @ SV586 ) @ SV482 )
= ( hAPP @ SV678 @ ( hAPP @ SV586 @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6869]) ).
thf(6961,plain,
! [SV483: $i,SV587: $i,SV679: $i,SV761: $i,SV820: $i] :
( ( ! [SY2370: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2370 @ SV820 @ SV761 ) @ SV679 ) @ SV587 ) @ SV483 )
= ( hAPP @ ( hAPP @ SV679 @ SV483 ) @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6870]) ).
thf(6962,plain,
! [SV484: $i,SV588: $i,SV680: $i,SV762: $i,SV821: $i] :
( ( ! [SY2371: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2371 @ SV821 @ SV762 ) @ SV680 ) @ SV588 ) @ SV484 )
= ( hAPP @ ( hAPP @ SV680 @ SV484 ) @ ( hAPP @ SV588 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6871]) ).
thf(6963,plain,
! [SV485: $i,SV589: $i,SV681: $i,SV763: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV763 @ SV681 @ SV589 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV681 @ SV485 ) @ SV485 )
= SV485 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6872]) ).
thf(6964,plain,
! [SV486: $i,SV590: $i,SV682: $i,SV764: $i,SV822: $i] :
( ( ! [SY2372: $i] :
( ( SY2372 != SV822 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SY2372 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6873]) ).
thf(6965,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i,SV823: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2374 @ SY2373 @ SV823 @ SV765 @ SV683 )
| ~ ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6874]) ).
thf(6966,plain,
! [SV488: $i,SV592: $i,SV684: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV684 ) @ SV592 @ SV488 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV684 ) ) @ SV592 @ SV488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6875]) ).
thf(6967,plain,
! [SV490: $i,SV594: $i,SV686: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV686 ) ) @ SV594 @ SV490 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV686 ) @ SV594 @ SV490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6877]) ).
thf(6968,plain,
! [SV491: $i,SV595: $i,SV687: $i,SV766: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV595 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV491 ) )
= $true )
| ( ( SV595 = SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6878]) ).
thf(6969,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ~ ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
| ( SV596 = SV492 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6879]) ).
thf(6970,plain,
! [SV688: $i,SV492: $i,SV596: $i] :
( ( ~ ( ( SV596 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6879]) ).
thf(6971,plain,
! [SV493: $i,SV597: $i,SV689: $i,SV767: $i,SV824: $i] :
( ( ~ ! [SY2375: $i] :
( ( hAPP @ SV824 @ SY2375 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV767 @ SV689 @ SV597 ) @ SY2375 ) )
| ( ( hAPP @ SV824 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SV824 @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6880]) ).
thf(6972,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i,SV825: $i] :
( ( ! [SY2376: $i,SY2377: $i] :
( ( SY2377 != SY2376 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SY2377 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SY2376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6881]) ).
thf(6973,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i,SV826: $i] :
( ( ! [SY2378: $i] :
( ~ ( ( SY2378 != SV826 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SY2378 ) @ SV599 ) ) @ SV826 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV826 ) @ SV495 ) ) @ SY2378 ) @ SV599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6882]) ).
thf(6974,plain,
! [SV497: $i,SV601: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
| ( SV601 = SV497 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6884]) ).
thf(6975,plain,
! [SV497: $i,SV601: $i] :
( ( ( SV601 != SV497 )
| ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6885]) ).
thf(6976,plain,
! [SV498: $i,SV602: $i,SV693: $i,SV770: $i,SV827: $i] :
( ( ! [SY2379: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2379 @ SV827 ) @ SV770 ) @ SV693 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2379 @ SV827 ) @ SV602 ) @ SV498 ) )
| ~ ( ( SV770 != SV602 )
| ( SV693 != SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6886]) ).
thf(6977,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
| ~ ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6887]) ).
thf(6978,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i] :
( ( ! [SY2380: $i,SY2381: $i,SY2382: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2382 @ SY2381 @ SY2380 @ SV829 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SY2381 @ SY2380 @ SV604 ) @ SV500 ) )
| ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6888]) ).
thf(6979,plain,
! [SV501: $i,SV605: $i,SV696: $i,SV773: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV773 @ SV696 @ SV605 @ SV501 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV773 @ SV696 @ SV501 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6889]) ).
thf(6980,plain,
! [SV502: $i,SV606: $i,SV697: $i,SV774: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV774 @ SV697 @ SV606 @ SV502 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV774 @ SV697 @ ( hAPP @ c_Nat_OSuc @ SV606 ) @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6890]) ).
thf(6981,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i] :
( ( ! [SY2384: $i,SY2385: $i,SY2386: $i,SY2387: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2387 @ SY2386 @ SY2385 @ SY2384 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SY2386 @ SY2385 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SY2384 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6891]) ).
thf(6982,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i,SV831: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2389 @ SY2388 @ SV831 @ SV776 ) @ SV699 )
!= SV608 )
| ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6892]) ).
thf(6983,plain,
! [SV505: $i,SV609: $i,SV700: $i,SV777: $i,SV832: $i] :
( ( ! [SY2390: $i] :
( ~ ( c_Natural_Oevaln @ SY2390 @ SV832 @ SV777 @ SV700 )
| ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY2390 @ SV609 ) @ SV832 @ SV777 @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6893]) ).
thf(6984,plain,
! [SV507: $i,SV611: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
| ( SV611 = SV507 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6895]) ).
thf(6985,plain,
! [SV507: $i,SV611: $i] :
( ( ( SV611 != SV507 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6896]) ).
thf(6986,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 )
= $false )
| ( ( ~ ! [SY2173: $i] :
~ ( c_Natural_Oevaln @ SV702 @ SV612 @ SY2173 @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6897]) ).
thf(6987,plain,
! [SV510: $i,SV613: $i,SV703: $i,SV778: $i,SV833: $i] :
( ( ! [SY2391: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2391 @ SV833 @ SV778 )
| ( ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ SV510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6898]) ).
thf(6988,plain,
! [SV512: $i,SV615: $i,SV705: $i,SV779: $i] :
( ( ( c_Com_Ocom_OBODY @ SV779 )
= ( c_Com_Ocom_OCond @ SV705 @ SV615 @ SV512 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6900]) ).
thf(6989,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
| ( SV616 = SV513 ) )
| ~ ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6901]) ).
thf(6990,plain,
! [SV514: $i,SV617: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV617 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
| ( SV617 = SV514 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6902]) ).
thf(6991,plain,
! [SV514: $i,SV617: $i] :
( ( ( SV617 != SV514 )
| ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6903]) ).
thf(6992,plain,
! [SV834: $i,SV781: $i] :
( ( ~ ( v_P @ SV781 @ SV834 )
| ! [SY2392: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY2392 )
| ( v_Q @ SV781 @ SY2392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6904]) ).
thf(6993,plain,
( ( ~ ( v_P @ sK12_SX0 @ sK13_SY2179 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6905]) ).
thf(6994,plain,
( ( ! [SY2314: $i] :
( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ sK13_SY2179 @ v_n @ SY2314 )
| ( v_Q @ sK12_SX0 @ SY2314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6905]) ).
thf(6995,plain,
! [SV515: $i,SV618: $i,SV707: $i,SV782: $i] :
( ( ( c_Com_Ocom_OCond @ SV782 @ SV707 @ SV618 )
= ( c_Com_Ocom_OBODY @ SV515 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6906]) ).
thf(6996,plain,
! [SV516: $i,SV619: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
| ( SV619 = SV516 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6907]) ).
thf(6997,plain,
! [SV516: $i,SV619: $i] :
( ( ( SV619 != SV516 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6908]) ).
thf(6998,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i,SV835: $i] :
( ( ! [SY2393: $i,SY2394: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2394 @ SY2393 @ SV835 @ SV783 @ SV708 @ SV620 )
| ( ( hAPP @ ( hAPP @ SV835 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6909]) ).
thf(6999,plain,
! [SV518: $i,SV621: $i,SV709: $i,SV784: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV621 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV518 ) )
= $true )
| ( ( SV621 = SV518 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6910]) ).
thf(7000,plain,
! [SV519: $i,SV622: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
| ( SV622 = SV519 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6911]) ).
thf(7001,plain,
! [SV519: $i,SV622: $i] :
( ( ( SV622 != SV519 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6912]) ).
thf(7002,plain,
! [SV520: $i,SV623: $i,SV710: $i,SV785: $i,SV836: $i] :
( ( ! [SY2395: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2395 @ SV836 @ SV785 @ SV710 @ SV623 )
| ( ( hAPP @ SV710 @ ( hAPP @ SV785 @ SV520 ) )
= SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6913]) ).
thf(7003,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i] :
( ( ! [SY2396: $i] :
~ ( ~ ( ( SY2396 != SV837 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SY2396 )
= SV521 ) )
| ~ ( ~ ( ( SY2396 != SV837 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SY2396 )
= ( hAPP @ SV624 @ SY2396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6914]) ).
thf(7004,plain,
! [SV522: $i,SV625: $i,SV712: $i,SV787: $i,SV838: $i] :
( ( ! [SY2397: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2397 ) @ SV838 ) @ SV787 )
!= SV712 )
| ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2397 ) @ SV787 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2397 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2397 ) @ SV712 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6915]) ).
thf(7005,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6916]) ).
thf(7006,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6916]) ).
thf(7007,plain,
! [SV524: $i,SV627: $i,SV714: $i,SV788: $i,SV839: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV839 @ SV788 @ SV714 )
| ( ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6917]) ).
thf(7008,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) )
| ~ ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6918]) ).
thf(7009,plain,
! [SV528: $i,SV630: $i,SV717: $i,SV790: $i,SV841: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
| ~ ! [SY2398: $i] :
( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ SY2398 )
| ~ ( c_Natural_Oevaln @ SV790 @ SY2398 @ SV630 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6920]) ).
thf(7010,plain,
! [SV530: $i,SV632: $i,SV719: $i,SV791: $i] :
( ( ( c_Com_Ocom_OBODY @ SV791 )
= ( c_Com_Ocom_OLocal @ SV719 @ SV632 @ SV530 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6922]) ).
thf(7011,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
| ( SV633 = SV531 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6923]) ).
thf(7012,plain,
! [SV720: $i,SV531: $i,SV633: $i] :
( ( ~ ( ( SV633 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6923]) ).
thf(7013,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i] :
( ( ! [SY2399: $i,SY2400: $i] :
( ~ ( ( SY2400 != SY2399 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SY2400 ) @ SV635 ) ) @ SY2399 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SY2399 ) @ SV533 ) ) @ SY2400 ) @ SV635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6925]) ).
thf(7014,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ( ~ ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
| ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6926]) ).
thf(7015,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ( ~ ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 )
| ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6926]) ).
thf(7016,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i] :
( ( ! [SY2401: $i] :
~ ( ~ ( ( SY2401 != SV843 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SY2401 )
= SV535 ) )
| ~ ( ~ ( ( SY2401 != SV843 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SY2401 )
= ( hAPP @ SV637 @ SY2401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6927]) ).
thf(7017,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i,SV844: $i] :
( ( ! [SY2402: $i] :
( ~ ( ( SY2402 != SV844 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SV844 ) @ SV536 ) @ SY2402 )
= ( hAPP @ SV638 @ SY2402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6928]) ).
thf(7018,plain,
! [SV537: $i,SV639: $i,SV726: $i,SV795: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 ) )
= $true )
| ( ( ~ ! [SY2335: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2335 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ SY2335 @ SV537 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6929]) ).
thf(7019,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 ) )
| ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6930]) ).
thf(7020,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
| ( SV641 = SV539 ) )
| ~ ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6931]) ).
thf(7021,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i] :
( ( ! [SY2403: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2403 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2403 @ SV845 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
| ~ ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2403 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2403 @ SV845 ) @ SV642 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6932]) ).
thf(7022,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
| ( SV730 = SV541 ) )
| ~ ( ( SV730 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6933]) ).
thf(7023,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
| ( SV645 = SV544 ) )
| ~ ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6935]) ).
thf(7024,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i] :
( ( ! [SY2404: $i,SY2405: $i,SY2406: $i,SY2407: $i,SY2408: $i,SY2409: $i] :
( ( ( hAPP @ SY2409 @ ( hAPP @ SY2408 @ SY2407 ) )
!= ( hAPP @ SY2406 @ ( hAPP @ SY2405 @ SY2404 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2409 ) @ SY2408 ) @ SY2407 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SY2406 ) @ SY2405 ) @ SY2404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6936]) ).
thf(7025,plain,
! [SV546: $i,SV647: $i,SV734: $i,SV802: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV802 ) ) @ SV734 @ SV647 @ SV546 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV802 ) @ SV734 @ ( hAPP @ c_Nat_OSuc @ SV647 ) @ SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6937]) ).
thf(7026,plain,
! [SV547: $i,SV648: $i,SV735: $i,SV803: $i,SV847: $i] :
( ( ( ( hAPP @ SV847 @ SV803 )
!= SV735 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SV847 ) @ SV803 ) @ SV735 )
= SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6938]) ).
thf(7027,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6939]) ).
thf(7028,plain,
! [SV549: $i,SV650: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
| ( SV650 = SV549 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6940]) ).
thf(7029,plain,
! [SV549: $i,SV650: $i] :
( ( ( SV650 != SV549 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6941]) ).
thf(7030,plain,
! [SV550: $i,SV651: $i,SV737: $i,SV805: $i] :
( ( ( c_Com_Ocom_OBODY @ SV805 )
= ( c_Com_Ocom_OCall @ SV737 @ SV651 @ SV550 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6942]) ).
thf(7031,plain,
! [SV552: $i,SV652: $i,SV738: $i,SV806: $i] :
( ( ( c_Com_Ocom_OCall @ SV806 @ SV738 @ SV652 )
= ( c_Com_Ocom_OBODY @ SV552 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6943]) ).
thf(7032,plain,
! [SV553: $i,SV653: $i,SV739: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV739 @ SV653 @ SV553 )
= $false )
| ( ( SV553 = SV739 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6944]) ).
thf(7033,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
!= SV554 )
| ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6945]) ).
thf(7034,plain,
! [SV554: $i,SV740: $i,SV654: $i] :
( ( ~ ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6945]) ).
thf(7035,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6946]) ).
thf(7036,plain,
! [SV557: $i,SV657: $i,SV742: $i,SV808: $i] :
( ( ( c_Com_Ocom_OLocal @ SV808 @ SV742 @ SV657 )
= ( c_Com_Ocom_OBODY @ SV557 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6948]) ).
thf(7037,plain,
! [SV558: $i,SV658: $i] :
( ( ( ( hAPP @ SV658 @ ( sK14_SY2074 @ SV558 @ SV658 ) )
= ( hAPP @ SV558 @ ( sK14_SY2074 @ SV558 @ SV658 ) ) )
= $false )
| ( ( SV658 = SV558 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6949]) ).
thf(7038,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i,SV850: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i,SY2417: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2417 @ SY2416 @ SY2415 @ SY2414 @ SV850 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6950]) ).
thf(7039,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i,SV851: $i] :
( ( ! [SY2418: $i,SY2419: $i,SY2420: $i,SY2421: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2421 @ SY2420 @ SY2419 @ SY2418 @ SV851 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6951]) ).
thf(7040,plain,
! [SV466: $i,SV570: $i,SV667: $i,SV750: $i,SV812: $i,SV852: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV852 @ SV812 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV852 @ SV812 ) @ SV750 ) @ SV667 ) @ SV570 ) ) @ SV667 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV852 @ SV812 ) @ SV750 ) @ SV667 ) @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6953]) ).
thf(7041,plain,
! [SV468: $i,SV572: $i,SV669: $i,SV752: $i,SV814: $i,SV853: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV853 @ SV814 @ SV752 @ SV669 ) @ SV572 ) @ SV468 )
= ( hAPP @ SV669 @ ( hAPP @ SV572 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6955]) ).
thf(7042,plain,
! [SV469: $i,SV573: $i,SV670: $i,SV753: $i,SV815: $i,SV854: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV854 @ SV815 @ SV753 @ SV670 ) @ SV573 ) @ SV469 )
= ( hAPP @ SV670 @ ( hAPP @ SV573 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6956]) ).
thf(7043,plain,
! [SV470: $i,SV574: $i,SV671: $i,SV754: $i,SV816: $i,SV855: $i] :
( ( ! [SY2422: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2422 @ SV855 @ SV816 @ SV754 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SY2422 @ SV816 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SV855 @ SV816 @ ( hAPP @ ( c_Fun_Ocomp @ SY2422 @ SV855 @ SV671 @ SV754 ) @ SV574 ) ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6957]) ).
thf(7044,plain,
! [SV474: $i,SV578: $i,SV672: $i,SV755: $i,SV817: $i,SV856: $i] :
( ( ! [SY2423: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2423 @ SV856 @ SV817 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2423 @ SV755 @ SV856 ) @ SV672 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2423 @ SV755 @ SV817 ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV755 @ SV856 @ SV817 ) @ SV578 ) @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6958]) ).
thf(7045,plain,
! [SV482: $i,SV586: $i,SV678: $i,SV760: $i,SV819: $i,SV857: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV857 @ SV819 @ SV760 ) @ SV678 ) @ SV586 ) @ SV482 )
= ( hAPP @ SV678 @ ( hAPP @ SV586 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6960]) ).
thf(7046,plain,
! [SV483: $i,SV587: $i,SV679: $i,SV761: $i,SV820: $i,SV858: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV858 @ SV820 @ SV761 ) @ SV679 ) @ SV587 ) @ SV483 )
= ( hAPP @ ( hAPP @ SV679 @ SV483 ) @ SV587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6961]) ).
thf(7047,plain,
! [SV484: $i,SV588: $i,SV680: $i,SV762: $i,SV821: $i,SV859: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV859 @ SV821 @ SV762 ) @ SV680 ) @ SV588 ) @ SV484 )
= ( hAPP @ ( hAPP @ SV680 @ SV484 ) @ ( hAPP @ SV588 @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6962]) ).
thf(7048,plain,
! [SV485: $i,SV589: $i,SV681: $i,SV763: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV763 @ SV681 @ SV589 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV681 @ SV485 ) @ SV485 )
= SV485 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6963]) ).
thf(7049,plain,
! [SV486: $i,SV590: $i,SV682: $i,SV764: $i,SV822: $i,SV860: $i] :
( ( ( SV860 != SV822 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV860 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6964]) ).
thf(7050,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i,SV823: $i,SV861: $i] :
( ( ! [SY2424: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2424 @ SV861 @ SV823 @ SV765 @ SV683 )
| ~ ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6965]) ).
thf(7051,plain,
! [SV491: $i,SV595: $i,SV687: $i,SV766: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV595 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV766 @ SV687 ) @ SV491 ) )
= $false )
| ( ( SV595 = SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6968]) ).
thf(7052,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
| ( SV596 = SV492 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6969]) ).
thf(7053,plain,
! [SV688: $i,SV492: $i,SV596: $i] :
( ( ( SV596 != SV492 )
| ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6970]) ).
thf(7054,plain,
! [SV493: $i,SV597: $i,SV689: $i,SV767: $i,SV824: $i] :
( ( ( ~ ! [SY2375: $i] :
( ( hAPP @ SV824 @ SY2375 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV767 @ SV689 @ SV597 ) @ SY2375 ) ) )
= $true )
| ( ( ( hAPP @ SV824 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SV824 @ SV493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6971]) ).
thf(7055,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i,SV825: $i,SV862: $i] :
( ( ! [SY2425: $i] :
( ( SY2425 != SV862 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SY2425 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6972]) ).
thf(7056,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i,SV826: $i,SV863: $i] :
( ( ~ ( ( SV863 != SV826 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV863 ) @ SV599 ) ) @ SV826 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV826 ) @ SV495 ) ) @ SV863 ) @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6973]) ).
thf(7057,plain,
! [SV497: $i,SV601: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
!= ( hAPP @ c_Nat_OSuc @ SV497 ) )
= $true )
| ( ( SV601 = SV497 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6974]) ).
thf(7058,plain,
! [SV497: $i,SV601: $i] :
( ( ( SV601 != SV497 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6975]) ).
thf(7059,plain,
! [SV498: $i,SV602: $i,SV693: $i,SV770: $i,SV827: $i,SV864: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
| ~ ( ( SV770 != SV602 )
| ( SV693 != SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6976]) ).
thf(7060,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
| ~ ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6977]) ).
thf(7061,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i,SV865: $i] :
( ( ! [SY2426: $i,SY2427: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2427 @ SY2426 @ SV865 @ SV829 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SY2426 @ SV865 @ SV604 ) @ SV500 ) )
| ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6978]) ).
thf(7062,plain,
! [SV501: $i,SV605: $i,SV696: $i,SV773: $i] :
( ( ( c_Natural_Oevaln @ SV773 @ SV696 @ SV605 @ SV501 )
= $false )
| ( ( c_Natural_Oevalc @ SV773 @ SV696 @ SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6979]) ).
thf(7063,plain,
! [SV502: $i,SV606: $i,SV697: $i,SV774: $i] :
( ( ( c_Natural_Oevaln @ SV774 @ SV697 @ SV606 @ SV502 )
= $false )
| ( ( c_Natural_Oevaln @ SV774 @ SV697 @ ( hAPP @ c_Nat_OSuc @ SV606 ) @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6980]) ).
thf(7064,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i] :
( ( ! [SY2429: $i,SY2430: $i,SY2431: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2431 @ SY2430 @ SY2429 @ SV866 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SY2430 @ SY2429 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6981]) ).
thf(7065,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i,SV831: $i,SV867: $i] :
( ( ! [SY2432: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2432 @ SV867 @ SV831 @ SV776 ) @ SV699 )
!= SV608 )
| ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6982]) ).
thf(7066,plain,
! [SV505: $i,SV609: $i,SV700: $i,SV777: $i,SV832: $i,SV868: $i] :
( ( ~ ( c_Natural_Oevaln @ SV868 @ SV832 @ SV777 @ SV700 )
| ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV868 @ SV609 ) @ SV832 @ SV777 @ SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6983]) ).
thf(7067,plain,
! [SV507: $i,SV611: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
= $true )
| ( ( SV611 = SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6984]) ).
thf(7068,plain,
! [SV507: $i,SV611: $i] :
( ( ( SV611 != SV507 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6985]) ).
thf(7069,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ( ! [SY2173: $i] :
~ ( c_Natural_Oevaln @ SV702 @ SV612 @ SY2173 @ SV509 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6986]) ).
thf(7070,plain,
! [SV510: $i,SV613: $i,SV703: $i,SV778: $i,SV833: $i,SV869: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV869 @ SV833 @ SV778 )
| ( ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6987]) ).
thf(7071,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
| ( SV616 = SV513 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6989]) ).
thf(7072,plain,
! [SV706: $i,SV780: $i,SV513: $i,SV616: $i] :
( ( ~ ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6989]) ).
thf(7073,plain,
! [SV514: $i,SV617: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV617 )
!= ( c_Com_Ocom_OBODY @ SV514 ) )
= $true )
| ( ( SV617 = SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6990]) ).
thf(7074,plain,
! [SV514: $i,SV617: $i] :
( ( ( SV617 != SV514 )
= $true )
| ( ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6991]) ).
thf(7075,plain,
! [SV834: $i,SV781: $i] :
( ( ( ~ ( v_P @ SV781 @ SV834 ) )
= $true )
| ( ( ! [SY2392: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY2392 )
| ( v_Q @ SV781 @ SY2392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6992]) ).
thf(7076,plain,
( ( v_P @ sK12_SX0 @ sK13_SY2179 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6993]) ).
thf(7077,plain,
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ sK13_SY2179 @ v_n @ sK15_SY2314 )
| ( v_Q @ sK12_SX0 @ sK15_SY2314 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6994]) ).
thf(7078,plain,
! [SV516: $i,SV619: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
= $true )
| ( ( SV619 = SV516 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6996]) ).
thf(7079,plain,
! [SV516: $i,SV619: $i] :
( ( ( SV619 != SV516 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6997]) ).
thf(7080,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i,SV835: $i,SV870: $i] :
( ( ! [SY2433: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2433 @ SV870 @ SV835 @ SV783 @ SV708 @ SV620 )
| ( ( hAPP @ ( hAPP @ SV835 @ SV517 ) @ SV517 )
= SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6998]) ).
thf(7081,plain,
! [SV518: $i,SV621: $i,SV709: $i,SV784: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV621 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV784 @ SV709 ) @ SV518 ) )
= $false )
| ( ( SV621 = SV518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6999]) ).
thf(7082,plain,
! [SV519: $i,SV622: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
!= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
= $true )
| ( ( SV622 = SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7000]) ).
thf(7083,plain,
! [SV519: $i,SV622: $i] :
( ( ( SV622 != SV519 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7001]) ).
thf(7084,plain,
! [SV520: $i,SV623: $i,SV710: $i,SV785: $i,SV836: $i,SV871: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV871 @ SV836 @ SV785 @ SV710 @ SV623 )
| ( ( hAPP @ SV710 @ ( hAPP @ SV785 @ SV520 ) )
= SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7002]) ).
thf(7085,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ~ ( ~ ( ( SV872 != SV837 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 ) )
| ~ ( ~ ( ( SV872 != SV837 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7003]) ).
thf(7086,plain,
! [SV522: $i,SV625: $i,SV712: $i,SV787: $i,SV838: $i,SV873: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV787 )
!= SV712 )
| ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV787 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV712 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7004]) ).
thf(7087,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7005]) ).
thf(7088,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
| ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7006]) ).
thf(7089,plain,
! [SV524: $i,SV627: $i,SV714: $i,SV788: $i,SV839: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV839 @ SV788 @ SV714 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7007]) ).
thf(7090,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) )
| ~ ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7008]) ).
thf(7091,plain,
! [SV528: $i,SV630: $i,SV717: $i,SV790: $i,SV841: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 ) )
= $true )
| ( ( ~ ! [SY2398: $i] :
( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ SY2398 )
| ~ ( c_Natural_Oevaln @ SV790 @ SY2398 @ SV630 @ SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7009]) ).
thf(7092,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
| ( SV633 = SV531 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7011]) ).
thf(7093,plain,
! [SV720: $i,SV531: $i,SV633: $i] :
( ( ( SV633 != SV531 )
| ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7012]) ).
thf(7094,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i,SV874: $i] :
( ( ! [SY2434: $i] :
( ~ ( ( SY2434 != SV874 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SY2434 ) @ SV635 ) ) @ SV874 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV874 ) @ SV533 ) ) @ SY2434 ) @ SV635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7013]) ).
thf(7095,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
| ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7014]) ).
thf(7096,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ~ ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 )
| ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7015]) ).
thf(7097,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ~ ( ~ ( ( SV875 != SV843 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 ) )
| ~ ( ~ ( ( SV875 != SV843 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7016]) ).
thf(7098,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i,SV844: $i,SV876: $i] :
( ( ~ ( ( SV876 != SV844 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SV844 ) @ SV536 ) @ SV876 )
= ( hAPP @ SV638 @ SV876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7017]) ).
thf(7099,plain,
! [SV537: $i,SV639: $i,SV726: $i,SV795: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false )
| ( ( ~ ! [SY2335: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2335 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ SY2335 @ SV537 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7018]) ).
thf(7100,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7019]) ).
thf(7101,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7019]) ).
thf(7102,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
| ( SV641 = SV539 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7020]) ).
thf(7103,plain,
! [SV728: $i,SV797: $i,SV539: $i,SV641: $i] :
( ( ~ ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7020]) ).
thf(7104,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
| ~ ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7021]) ).
thf(7105,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
| ( SV730 = SV541 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7022]) ).
thf(7106,plain,
! [SV643: $i,SV799: $i,SV541: $i,SV730: $i] :
( ( ~ ( ( SV730 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7022]) ).
thf(7107,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ~ ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
| ( SV645 = SV544 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7023]) ).
thf(7108,plain,
! [SV732: $i,SV800: $i,SV544: $i,SV645: $i] :
( ( ~ ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7023]) ).
thf(7109,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i] :
( ( ! [SY2435: $i,SY2436: $i,SY2437: $i,SY2438: $i,SY2439: $i] :
( ( ( hAPP @ SY2439 @ ( hAPP @ SY2438 @ SY2437 ) )
!= ( hAPP @ SY2436 @ ( hAPP @ SY2435 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2439 ) @ SY2438 ) @ SY2437 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SY2436 ) @ SY2435 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7024]) ).
thf(7110,plain,
! [SV546: $i,SV647: $i,SV734: $i,SV802: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV802 ) ) @ SV734 @ SV647 @ SV546 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV802 ) @ SV734 @ ( hAPP @ c_Nat_OSuc @ SV647 ) @ SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7025]) ).
thf(7111,plain,
! [SV547: $i,SV648: $i,SV735: $i,SV803: $i,SV847: $i] :
( ( ( ( hAPP @ SV847 @ SV803 )
!= SV735 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SV847 ) @ SV803 ) @ SV735 )
= SV847 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7026]) ).
thf(7112,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
| ~ ( ~ ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7027]) ).
thf(7113,plain,
! [SV549: $i,SV650: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
= $true )
| ( ( SV650 = SV549 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7028]) ).
thf(7114,plain,
! [SV549: $i,SV650: $i] :
( ( ( SV650 != SV549 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7029]) ).
thf(7115,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
!= SV554 )
| ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7033]) ).
thf(7116,plain,
! [SV554: $i,SV740: $i,SV654: $i] :
( ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
| ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7034]) ).
thf(7117,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
| ~ ( ~ ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7035]) ).
thf(7118,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i,SV850: $i,SV879: $i] :
( ( ! [SY2440: $i,SY2441: $i,SY2442: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2442 @ SY2441 @ SY2440 @ SV879 @ SV850 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7038]) ).
thf(7119,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i,SV851: $i,SV880: $i] :
( ( ! [SY2443: $i,SY2444: $i,SY2445: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2445 @ SY2444 @ SY2443 @ SV880 @ SV851 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7039]) ).
thf(7120,plain,
! [SV470: $i,SV574: $i,SV671: $i,SV754: $i,SV816: $i,SV855: $i,SV881: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV881 @ SV855 @ SV816 @ SV754 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SV881 @ SV816 @ SV574 ) @ SV470 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV671 @ SV855 @ SV816 @ ( hAPP @ ( c_Fun_Ocomp @ SV881 @ SV855 @ SV671 @ SV754 ) @ SV574 ) ) @ SV470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7043]) ).
thf(7121,plain,
! [SV474: $i,SV578: $i,SV672: $i,SV755: $i,SV817: $i,SV856: $i,SV882: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV882 @ SV856 @ SV817 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV882 @ SV755 @ SV856 ) @ SV672 ) @ SV578 ) ) @ SV474 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV882 @ SV755 @ SV817 ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV755 @ SV856 @ SV817 ) @ SV578 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7044]) ).
thf(7122,plain,
! [SV486: $i,SV590: $i,SV682: $i,SV764: $i,SV822: $i,SV860: $i] :
( ( ( SV860 != SV822 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV860 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7049]) ).
thf(7123,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i,SV823: $i,SV861: $i,SV883: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
| ~ ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7050]) ).
thf(7124,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
!= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
= $true )
| ( ( SV596 = SV492 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7052]) ).
thf(7125,plain,
! [SV688: $i,SV492: $i,SV596: $i] :
( ( ( SV596 != SV492 )
= $true )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7053]) ).
thf(7126,plain,
! [SV493: $i,SV597: $i,SV689: $i,SV767: $i,SV824: $i] :
( ( ( ! [SY2375: $i] :
( ( hAPP @ SV824 @ SY2375 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV767 @ SV689 @ SV597 ) @ SY2375 ) ) )
= $false )
| ( ( ( hAPP @ SV824 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SV824 @ SV493 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7054]) ).
thf(7127,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i,SV825: $i,SV862: $i,SV884: $i] :
( ( ( SV884 != SV862 )
| ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV884 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7055]) ).
thf(7128,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i,SV826: $i,SV863: $i] :
( ( ( ~ ( ( SV863 != SV826 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV863 ) @ SV599 ) ) @ SV826 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV826 ) @ SV495 ) ) @ SV863 ) @ SV599 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7056]) ).
thf(7129,plain,
! [SV497: $i,SV601: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) )
= $false )
| ( ( SV601 = SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7057]) ).
thf(7130,plain,
! [SV497: $i,SV601: $i] :
( ( ( SV601 = SV497 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV601 )
= ( hAPP @ c_Nat_OSuc @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7058]) ).
thf(7131,plain,
! [SV498: $i,SV602: $i,SV693: $i,SV770: $i,SV827: $i,SV864: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $true )
| ( ( ~ ( ( SV770 != SV602 )
| ( SV693 != SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7059]) ).
thf(7132,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7060]) ).
thf(7133,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ~ ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7060]) ).
thf(7134,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i,SV865: $i,SV885: $i] :
( ( ! [SY2446: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2446 @ SV885 @ SV865 @ SV829 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SV885 @ SV865 @ SV604 ) @ SV500 ) )
| ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7061]) ).
thf(7135,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i,SV886: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2449 @ SY2448 @ SV886 @ SV866 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SY2448 @ SV886 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7064]) ).
thf(7136,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i,SV831: $i,SV867: $i,SV887: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV887 @ SV867 @ SV831 @ SV776 ) @ SV699 )
!= SV608 )
| ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7065]) ).
thf(7137,plain,
! [SV505: $i,SV609: $i,SV700: $i,SV777: $i,SV832: $i,SV868: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV868 @ SV832 @ SV777 @ SV700 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV868 @ SV609 ) @ SV832 @ SV777 @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7066]) ).
thf(7138,plain,
! [SV507: $i,SV611: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
= $false )
| ( ( SV611 = SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7067]) ).
thf(7139,plain,
! [SV507: $i,SV611: $i] :
( ( ( SV611 = SV507 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV611 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7068]) ).
thf(7140,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV702 @ SV612 @ ( sK16_SY2173 @ SV509 @ SV612 @ SV702 ) @ SV509 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7069]) ).
thf(7141,plain,
! [SV510: $i,SV613: $i,SV703: $i,SV778: $i,SV833: $i,SV869: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV869 @ SV833 @ SV778 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7070]) ).
thf(7142,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
| ( SV616 = SV513 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7071]) ).
thf(7143,plain,
! [SV706: $i,SV780: $i,SV513: $i,SV616: $i] :
( ( ( SV616 != SV513 )
| ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7072]) ).
thf(7144,plain,
! [SV514: $i,SV617: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) )
= $false )
| ( ( SV617 = SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7073]) ).
thf(7145,plain,
! [SV514: $i,SV617: $i] :
( ( ( SV617 = SV514 )
= $false )
| ( ( ( c_Com_Ocom_OBODY @ SV617 )
= ( c_Com_Ocom_OBODY @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7074]) ).
thf(7146,plain,
! [SV834: $i,SV781: $i] :
( ( ( v_P @ SV781 @ SV834 )
= $false )
| ( ( ! [SY2392: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY2392 )
| ( v_Q @ SV781 @ SY2392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7075]) ).
thf(7147,plain,
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ sK13_SY2179 @ v_n @ sK15_SY2314 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7077]) ).
thf(7148,plain,
( ( v_Q @ sK12_SX0 @ sK15_SY2314 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7077]) ).
thf(7149,plain,
! [SV516: $i,SV619: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
= $false )
| ( ( SV619 = SV516 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7078]) ).
thf(7150,plain,
! [SV516: $i,SV619: $i] :
( ( ( SV619 = SV516 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV619 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7079]) ).
thf(7151,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i,SV835: $i,SV870: $i,SV888: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV888 @ SV870 @ SV835 @ SV783 @ SV708 @ SV620 )
| ( ( hAPP @ ( hAPP @ SV835 @ SV517 ) @ SV517 )
= SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7080]) ).
thf(7152,plain,
! [SV519: $i,SV622: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
= $false )
| ( ( SV622 = SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7082]) ).
thf(7153,plain,
! [SV519: $i,SV622: $i] :
( ( ( SV622 = SV519 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV622 )
= ( hAPP @ c_Int_ORep__Integ @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7083]) ).
thf(7154,plain,
! [SV520: $i,SV623: $i,SV710: $i,SV785: $i,SV836: $i,SV871: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV871 @ SV836 @ SV785 @ SV710 @ SV623 ) )
= $true )
| ( ( ( hAPP @ SV710 @ ( hAPP @ SV785 @ SV520 ) )
= SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7084]) ).
thf(7155,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ~ ( ( SV872 != SV837 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 ) )
| ~ ( ~ ( ( SV872 != SV837 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7085]) ).
thf(7156,plain,
! [SV522: $i,SV625: $i,SV712: $i,SV787: $i,SV838: $i,SV873: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV787 )
!= SV712 )
= $true )
| ( ( ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV787 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV712 ) @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7086]) ).
thf(7157,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7087]) ).
thf(7158,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7088]) ).
thf(7159,plain,
! [SV524: $i,SV627: $i,SV714: $i,SV788: $i,SV839: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV839 @ SV788 @ SV714 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= ( hAPP @ ( hAPP @ SV714 @ SV627 ) @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7089]) ).
thf(7160,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7090]) ).
thf(7161,plain,
! [SV789: $i,SV840: $i,SV526: $i,SV628: $i,SV715: $i] :
( ( ~ ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7090]) ).
thf(7162,plain,
! [SV528: $i,SV630: $i,SV717: $i,SV790: $i,SV841: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false )
| ( ( ~ ! [SY2398: $i] :
( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ SY2398 )
| ~ ( c_Natural_Oevaln @ SV790 @ SY2398 @ SV630 @ SV528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7091]) ).
thf(7163,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
!= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
= $true )
| ( ( SV633 = SV531 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7092]) ).
thf(7164,plain,
! [SV720: $i,SV531: $i,SV633: $i] :
( ( ( SV633 != SV531 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7093]) ).
thf(7165,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i,SV874: $i,SV889: $i] :
( ( ~ ( ( SV889 != SV874 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV889 ) @ SV635 ) ) @ SV874 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV874 ) @ SV533 ) ) @ SV889 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7094]) ).
thf(7166,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 ) )
= $true )
| ( ( ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7095]) ).
thf(7167,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ~ ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7096]) ).
thf(7168,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ~ ( ( SV875 != SV843 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 ) )
| ~ ( ~ ( ( SV875 != SV843 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7097]) ).
thf(7169,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i,SV844: $i,SV876: $i] :
( ( ( ~ ( ( SV876 != SV844 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SV844 ) @ SV536 ) @ SV876 )
= ( hAPP @ SV638 @ SV876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7098]) ).
thf(7170,plain,
! [SV537: $i,SV726: $i,SV795: $i,SV639: $i] :
( ( ( ! [SY2335: $i] :
( ( SV639
!= ( hAPP @ c_Nat_OSuc @ SY2335 ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ SY2335 @ SV537 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7099]) ).
thf(7171,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
| ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7100]) ).
thf(7172,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7101]) ).
thf(7173,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
| ( SV641 = SV539 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7102]) ).
thf(7174,plain,
! [SV728: $i,SV797: $i,SV539: $i,SV641: $i] :
( ( ( SV641 != SV539 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7103]) ).
thf(7175,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
| ~ ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7104]) ).
thf(7176,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
| ( SV730 = SV541 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7105]) ).
thf(7177,plain,
! [SV643: $i,SV799: $i,SV541: $i,SV730: $i] :
( ( ( SV730 != SV541 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7106]) ).
thf(7178,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
| ( SV645 = SV544 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7107]) ).
thf(7179,plain,
! [SV732: $i,SV800: $i,SV544: $i,SV645: $i] :
( ( ( SV645 != SV544 )
| ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7108]) ).
thf(7180,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i] :
( ( ! [SY2450: $i,SY2451: $i,SY2452: $i,SY2453: $i] :
( ( ( hAPP @ SY2453 @ ( hAPP @ SY2452 @ SY2451 ) )
!= ( hAPP @ SY2450 @ ( hAPP @ SV890 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2453 ) @ SY2452 ) @ SY2451 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SY2450 ) @ SV890 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7109]) ).
thf(7181,plain,
! [SV547: $i,SV648: $i,SV735: $i,SV803: $i,SV847: $i] :
( ( ( ( hAPP @ SV847 @ SV803 )
= SV735 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV648 @ SV547 ) @ SV847 ) @ SV803 ) @ SV735 )
= SV847 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7111]) ).
thf(7182,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7112]) ).
thf(7183,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ~ ( ~ ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7112]) ).
thf(7184,plain,
! [SV549: $i,SV650: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
= $false )
| ( ( SV650 = SV549 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7113]) ).
thf(7185,plain,
! [SV549: $i,SV650: $i] :
( ( ( SV650 = SV549 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV650 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7114]) ).
thf(7186,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
!= SV554 )
= $true )
| ( ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7115]) ).
thf(7187,plain,
! [SV554: $i,SV740: $i,SV654: $i] :
( ( ( SV654
!= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7116]) ).
thf(7188,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7117]) ).
thf(7189,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ~ ( ~ ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7117]) ).
thf(7190,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i,SV850: $i,SV879: $i,SV891: $i] :
( ( ! [SY2454: $i,SY2455: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2455 @ SY2454 @ SV891 @ SV879 @ SV850 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7118]) ).
thf(7191,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i,SV851: $i,SV880: $i,SV892: $i] :
( ( ! [SY2456: $i,SY2457: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2457 @ SY2456 @ SV892 @ SV880 @ SV851 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7119]) ).
thf(7192,plain,
! [SV486: $i,SV590: $i,SV682: $i,SV764: $i,SV822: $i,SV860: $i] :
( ( ( SV860 = SV822 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV860 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV764 @ SV682 @ SV590 ) @ SV486 ) @ SV822 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7122]) ).
thf(7193,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i,SV823: $i,SV861: $i,SV883: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7123]) ).
thf(7194,plain,
! [SV492: $i,SV596: $i,SV688: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
= $false )
| ( ( SV596 = SV492 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7124]) ).
thf(7195,plain,
! [SV688: $i,SV492: $i,SV596: $i] :
( ( ( SV596 = SV492 )
= $false )
| ( ( ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV596 )
= ( hAPP @ ( c_Option_Ooption_OSome @ SV688 ) @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7125]) ).
thf(7196,plain,
! [SV767: $i,SV689: $i,SV597: $i,SV493: $i,SV824: $i] :
( ( ( ( hAPP @ SV824 @ ( sK17_SY2375 @ SV493 @ SV597 @ SV689 @ SV767 @ SV824 ) )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV767 @ SV689 @ SV597 ) @ ( sK17_SY2375 @ SV493 @ SV597 @ SV689 @ SV767 @ SV824 ) ) )
= $false )
| ( ( ( hAPP @ SV824 @ ( hAPP @ c_Nat_OSuc @ SV493 ) )
= ( hAPP @ ( hAPP @ SV597 @ SV493 ) @ ( hAPP @ SV824 @ SV493 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7126]) ).
thf(7197,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i,SV825: $i,SV862: $i,SV884: $i] :
( ( ( SV884 != SV862 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV884 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7127]) ).
thf(7198,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i,SV826: $i,SV863: $i] :
( ( ( SV863 != SV826 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV863 ) @ SV599 ) ) @ SV826 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV826 ) @ SV495 ) ) @ SV863 ) @ SV599 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7128]) ).
thf(7199,plain,
! [SV498: $i,SV602: $i,SV693: $i,SV770: $i,SV827: $i,SV864: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false )
| ( ( ~ ( ( SV770 != SV602 )
| ( SV693 != SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7131]) ).
thf(7200,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
| ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7132]) ).
thf(7201,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7133]) ).
thf(7202,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i,SV865: $i,SV885: $i,SV893: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV893 @ SV885 @ SV865 @ SV829 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SV885 @ SV865 @ SV604 ) @ SV500 ) )
| ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7134]) ).
thf(7203,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i,SV886: $i,SV894: $i] :
( ( ! [SY2459: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2459 @ SV894 @ SV886 @ SV866 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SV894 @ SV886 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7135]) ).
thf(7204,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i,SV831: $i,SV867: $i,SV887: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV887 @ SV867 @ SV831 @ SV776 ) @ SV699 )
!= SV608 )
= $true )
| ( ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7136]) ).
thf(7205,plain,
! [SV505: $i,SV609: $i,SV700: $i,SV777: $i,SV832: $i,SV868: $i] :
( ( ( c_Natural_Oevaln @ SV868 @ SV832 @ SV777 @ SV700 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV868 @ SV609 ) @ SV832 @ SV777 @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7137]) ).
thf(7206,plain,
! [SV509: $i,SV612: $i,SV702: $i] :
( ( ( c_Natural_Oevaln @ SV702 @ SV612 @ ( sK16_SY2173 @ SV509 @ SV612 @ SV702 ) @ SV509 )
= $true )
| ( ( c_Natural_Oevalc @ SV702 @ SV612 @ SV509 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7140]) ).
thf(7207,plain,
! [SV510: $i,SV613: $i,SV703: $i,SV778: $i,SV833: $i,SV869: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV869 @ SV833 @ SV778 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ SV510 ) )
= ( hAPP @ ( hAPP @ SV778 @ SV613 ) @ ( hAPP @ ( hAPP @ SV778 @ SV703 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7141]) ).
thf(7208,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
!= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
= $true )
| ( ( SV616 = SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7142]) ).
thf(7209,plain,
! [SV706: $i,SV780: $i,SV513: $i,SV616: $i] :
( ( ( SV616 != SV513 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7143]) ).
thf(7210,plain,
! [SV781: $i,SV895: $i,SV834: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV895 )
| ( v_Q @ SV781 @ SV895 ) )
= $true )
| ( ( v_P @ SV781 @ SV834 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7146]) ).
thf(7211,plain,
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ sK13_SY2179 @ v_n @ sK15_SY2314 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7147]) ).
thf(7212,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i,SV835: $i,SV870: $i,SV888: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV888 @ SV870 @ SV835 @ SV783 @ SV708 @ SV620 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV835 @ SV517 ) @ SV517 )
= SV517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7151]) ).
thf(7213,plain,
! [SV520: $i,SV623: $i,SV710: $i,SV785: $i,SV836: $i,SV871: $i] :
( ( ( c_Typedef_Otype__definition @ SV871 @ SV836 @ SV785 @ SV710 @ SV623 )
= $false )
| ( ( ( hAPP @ SV710 @ ( hAPP @ SV785 @ SV520 ) )
= SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7154]) ).
thf(7214,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ~ ( ( SV872 != SV837 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7155]) ).
thf(7215,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ~ ( ~ ( ( SV872 != SV837 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7155]) ).
thf(7216,plain,
! [SV522: $i,SV625: $i,SV712: $i,SV787: $i,SV838: $i,SV873: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV787 )
= SV712 )
= $false )
| ( ( ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV787 ) @ SV522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV712 ) @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7156]) ).
thf(7217,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7157]) ).
thf(7218,plain,
! [SV523: $i,SV626: $i,SV713: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV713 ) ) @ SV626 @ SV523 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV713 ) @ SV626 @ SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7158]) ).
thf(7219,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
| ( ( hAPP @ SV715 @ SV628 )
= SV526 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7160]) ).
thf(7220,plain,
! [SV789: $i,SV840: $i,SV526: $i,SV628: $i,SV715: $i] :
( ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7161]) ).
thf(7221,plain,
! [SV528: $i,SV790: $i,SV630: $i,SV717: $i,SV841: $i] :
( ( ( ! [SY2398: $i] :
( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ SY2398 )
| ~ ( c_Natural_Oevaln @ SV790 @ SY2398 @ SV630 @ SV528 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7162]) ).
thf(7222,plain,
! [SV531: $i,SV633: $i,SV720: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
= $false )
| ( ( SV633 = SV531 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7163]) ).
thf(7223,plain,
! [SV720: $i,SV531: $i,SV633: $i] :
( ( ( SV633 = SV531 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV720 ) @ SV633 )
= ( hAPP @ ( c_List_Orev @ SV720 ) @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7164]) ).
thf(7224,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i,SV874: $i,SV889: $i] :
( ( ( ~ ( ( SV889 != SV874 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV889 ) @ SV635 ) ) @ SV874 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV874 ) @ SV533 ) ) @ SV889 ) @ SV635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7165]) ).
thf(7225,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $false )
| ( ( ~ ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7166]) ).
thf(7226,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ~ ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7167]) ).
thf(7227,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ~ ( ( SV875 != SV843 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7168]) ).
thf(7228,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ~ ( ~ ( ( SV875 != SV843 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7168]) ).
thf(7229,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i,SV844: $i,SV876: $i] :
( ( ( SV876 != SV844 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SV844 ) @ SV536 ) @ SV876 )
= ( hAPP @ SV638 @ SV876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7169]) ).
thf(7230,plain,
! [SV795: $i,SV726: $i,SV537: $i,SV639: $i] :
( ( ( ( SV639
!= ( hAPP @ c_Nat_OSuc @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) @ SV537 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7170]) ).
thf(7231,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7171]) ).
thf(7232,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7172]) ).
thf(7233,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
= $true )
| ( ( SV641 = SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7173]) ).
thf(7234,plain,
! [SV728: $i,SV797: $i,SV539: $i,SV641: $i] :
( ( ( SV641 != SV539 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7174]) ).
thf(7235,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7175]) ).
thf(7236,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ~ ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7175]) ).
thf(7237,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
= $true )
| ( ( SV730 = SV541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7176]) ).
thf(7238,plain,
! [SV643: $i,SV799: $i,SV541: $i,SV730: $i] :
( ( ( SV730 != SV541 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7177]) ).
thf(7239,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
!= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
= $true )
| ( ( SV645 = SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7178]) ).
thf(7240,plain,
! [SV732: $i,SV800: $i,SV544: $i,SV645: $i] :
( ( ( SV645 != SV544 )
= $true )
| ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7179]) ).
thf(7241,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i] :
( ( ! [SY2460: $i,SY2461: $i,SY2462: $i] :
( ( ( hAPP @ SY2462 @ ( hAPP @ SY2461 @ SY2460 ) )
!= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2462 ) @ SY2461 ) @ SY2460 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7180]) ).
thf(7242,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
| ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7182]) ).
thf(7243,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ~ ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7183]) ).
thf(7244,plain,
! [SV554: $i,SV654: $i,SV740: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 )
= $false )
| ( ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7186]) ).
thf(7245,plain,
! [SV554: $i,SV740: $i,SV654: $i] :
( ( ( SV654
= ( hAPP @ ( c_List_Orev @ SV740 ) @ SV554 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV740 ) @ SV654 )
= SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7187]) ).
thf(7246,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
| ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7188]) ).
thf(7247,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ~ ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7189]) ).
thf(7248,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i,SV850: $i,SV879: $i,SV891: $i,SV897: $i] :
( ( ! [SY2463: $i] :
( ( c_Com_Ocom_Ocom__case @ SY2463 @ SV897 @ SV891 @ SV879 @ SV850 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7190]) ).
thf(7249,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i,SV851: $i,SV880: $i,SV892: $i,SV898: $i] :
( ( ! [SY2464: $i] :
( ( c_Com_Ocom_Ocom__rec @ SY2464 @ SV898 @ SV892 @ SV880 @ SV851 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7191]) ).
thf(7250,plain,
! [SV487: $i,SV591: $i,SV683: $i,SV765: $i,SV823: $i,SV861: $i,SV883: $i] :
( ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7193]) ).
thf(7251,plain,
! [SV494: $i,SV598: $i,SV690: $i,SV768: $i,SV825: $i,SV862: $i,SV884: $i] :
( ( ( SV884 = SV862 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV884 )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ SV825 @ SV768 @ SV690 @ SV598 @ SV494 ) @ SV862 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7197]) ).
thf(7252,plain,
! [SV495: $i,SV599: $i,SV691: $i,SV769: $i,SV826: $i,SV863: $i] :
( ( ( SV863 = SV826 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV863 ) @ SV599 ) ) @ SV826 ) @ SV495 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV769 @ SV691 ) @ SV826 ) @ SV495 ) ) @ SV863 ) @ SV599 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7198]) ).
thf(7253,plain,
! [SV827: $i,SV864: $i,SV498: $i,SV693: $i,SV602: $i,SV770: $i] :
( ( ( ( SV770 != SV602 )
| ( SV693 != SV498 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7199]) ).
thf(7254,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true )
| ( ( ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7200]) ).
thf(7255,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( ~ ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7201]) ).
thf(7256,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i,SV865: $i,SV885: $i,SV893: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV893 @ SV885 @ SV865 @ SV829 ) @ SV772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SV885 @ SV865 @ SV604 ) @ SV500 ) )
= $true )
| ( ( ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7202]) ).
thf(7257,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i,SV886: $i,SV894: $i,SV899: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV899 @ SV894 @ SV886 @ SV866 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SV894 @ SV886 @ SV698 ) @ SV607 ) )
| ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7203]) ).
thf(7258,plain,
! [SV504: $i,SV608: $i,SV699: $i,SV776: $i,SV831: $i,SV867: $i,SV887: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV887 @ SV867 @ SV831 @ SV776 ) @ SV699 )
= SV608 )
= $false )
| ( ( ( hAPP @ SV776 @ ( hAPP @ SV699 @ SV504 ) )
= ( hAPP @ SV608 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7204]) ).
thf(7259,plain,
! [SV832: $i,SV868: $i,SV505: $i,SV777: $i,SV700: $i,SV609: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV868 @ SV609 ) @ SV832 @ SV777 @ SV505 )
= $true )
| ( ( c_Natural_Oevaln @ SV868 @ SV832 @ SV777 @ SV700 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7205]) ).
thf(7260,plain,
! [SV513: $i,SV616: $i,SV706: $i,SV780: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
= $false )
| ( ( SV616 = SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7208]) ).
thf(7261,plain,
! [SV706: $i,SV780: $i,SV513: $i,SV616: $i] :
( ( ( SV616 = SV513 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV616 )
= ( hAPP @ ( c_Sum__Type_OInr @ SV780 @ SV706 ) @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7209]) ).
thf(7262,plain,
! [SV781: $i,SV895: $i,SV834: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV895 ) )
= $true )
| ( ( v_Q @ SV781 @ SV895 )
= $true )
| ( ( v_P @ SV781 @ SV834 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7210]) ).
thf(7263,plain,
! [SV517: $i,SV620: $i,SV708: $i,SV783: $i,SV835: $i,SV870: $i,SV888: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV888 @ SV870 @ SV835 @ SV783 @ SV708 @ SV620 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV835 @ SV517 ) @ SV517 )
= SV517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7212]) ).
thf(7264,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( SV872 != SV837 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7214]) ).
thf(7265,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ~ ( ( SV872 != SV837 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7215]) ).
thf(7266,plain,
! [SV712: $i,SV838: $i,SV522: $i,SV787: $i,SV873: $i,SV625: $i] :
( ( ( SV625
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV787 ) @ SV522 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV712 ) @ SV522 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV787 )
= SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7216]) ).
thf(7267,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
!= SV715 )
= $true )
| ( ( ( hAPP @ SV715 @ SV628 )
= SV526 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7219]) ).
thf(7268,plain,
! [SV789: $i,SV840: $i,SV526: $i,SV628: $i,SV715: $i] :
( ( ( ( hAPP @ SV715 @ SV628 )
!= SV526 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7220]) ).
thf(7269,plain,
! [SV790: $i,SV528: $i,SV630: $i,SV717: $i,SV841: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) )
| ~ ( c_Natural_Oevaln @ SV790 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) @ SV630 @ SV528 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7221]) ).
thf(7270,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i,SV874: $i,SV889: $i] :
( ( ( SV889 != SV874 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV889 ) @ SV635 ) ) @ SV874 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV874 ) @ SV533 ) ) @ SV889 ) @ SV635 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7224]) ).
thf(7271,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ! [SY2208: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2208 @ SV534 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7225]) ).
thf(7272,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ! [SY2209: $i] :
~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SY2209 @ SV534 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7226]) ).
thf(7273,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( SV875 != SV843 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7227]) ).
thf(7274,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ~ ( ( SV875 != SV843 ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7228]) ).
thf(7275,plain,
! [SV536: $i,SV638: $i,SV725: $i,SV794: $i,SV844: $i,SV876: $i] :
( ( ( SV876 = SV844 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV794 @ SV725 ) @ SV638 ) @ SV844 ) @ SV536 ) @ SV876 )
= ( hAPP @ SV638 @ SV876 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7229]) ).
thf(7276,plain,
! [SV795: $i,SV726: $i,SV537: $i,SV639: $i] :
( ( ( SV639
!= ( hAPP @ c_Nat_OSuc @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7230]) ).
thf(7277,plain,
! [SV639: $i,SV537: $i,SV726: $i,SV795: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) @ SV537 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7230]) ).
thf(7278,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
= $false )
| ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7231]) ).
thf(7279,plain,
! [SV538: $i,SV640: $i,SV727: $i,SV796: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV796 ) ) @ SV727 @ SV640 @ SV538 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV796 ) @ SV727 @ ( hAPP @ c_Nat_OSuc @ SV640 ) @ SV538 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7232]) ).
thf(7280,plain,
! [SV539: $i,SV641: $i,SV728: $i,SV797: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
= $false )
| ( ( SV641 = SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7233]) ).
thf(7281,plain,
! [SV728: $i,SV797: $i,SV539: $i,SV641: $i] :
( ( ( SV641 = SV539 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV797 ) @ SV728 ) @ SV539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7234]) ).
thf(7282,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
| ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7235]) ).
thf(7283,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7236]) ).
thf(7284,plain,
! [SV541: $i,SV643: $i,SV730: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
= $false )
| ( ( SV730 = SV541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7237]) ).
thf(7285,plain,
! [SV643: $i,SV799: $i,SV541: $i,SV730: $i] :
( ( ( SV730 = SV541 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV730 ) @ SV643 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV799 ) @ SV541 ) @ SV643 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7238]) ).
thf(7286,plain,
! [SV544: $i,SV645: $i,SV732: $i,SV800: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
= $false )
| ( ( SV645 = SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7239]) ).
thf(7287,plain,
! [SV732: $i,SV800: $i,SV544: $i,SV645: $i] :
( ( ( SV645 = SV544 )
= $false )
| ( ( ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV645 )
= ( hAPP @ ( c_Sum__Type_OInl @ SV800 @ SV732 ) @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7240]) ).
thf(7288,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i,SV900: $i] :
( ( ! [SY2465: $i,SY2466: $i] :
( ( ( hAPP @ SY2466 @ ( hAPP @ SY2465 @ SV900 ) )
!= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2466 ) @ SY2465 ) @ SV900 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7241]) ).
thf(7289,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true )
| ( ( ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7242]) ).
thf(7290,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7243]) ).
thf(7291,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 ) )
= $true )
| ( ( ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7246]) ).
thf(7292,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7247]) ).
thf(7293,plain,
! [SV456: $i,SV560: $i,SV660: $i,SV744: $i,SV809: $i,SV850: $i,SV879: $i,SV891: $i,SV897: $i,SV901: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV901 @ SV897 @ SV891 @ SV879 @ SV850 @ SV809 @ SV744 @ SV660 @ SV560 @ ( c_Com_Ocom_OBODY @ SV456 ) )
= ( hAPP @ SV660 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7248]) ).
thf(7294,plain,
! [SV459: $i,SV563: $i,SV662: $i,SV746: $i,SV810: $i,SV851: $i,SV880: $i,SV892: $i,SV898: $i,SV902: $i] :
( ( ( c_Com_Ocom_Ocom__rec @ SV902 @ SV898 @ SV892 @ SV880 @ SV851 @ SV810 @ SV746 @ SV662 @ SV563 @ ( c_Com_Ocom_OBODY @ SV459 ) )
= ( hAPP @ SV662 @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7249]) ).
thf(7295,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV487: $i,SV591: $i,SV823: $i] :
( ( ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
| ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7250]) ).
thf(7296,plain,
! [SV498: $i,SV693: $i,SV827: $i,SV864: $i,SV602: $i,SV770: $i] :
( ( ( SV770 != SV602 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7253]) ).
thf(7297,plain,
! [SV602: $i,SV770: $i,SV827: $i,SV864: $i,SV498: $i,SV693: $i] :
( ( ( SV693 != SV498 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7253]) ).
thf(7298,plain,
! [SV499: $i,SV603: $i,SV694: $i,SV771: $i,SV828: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false )
| ( ( ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7254]) ).
thf(7299,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( ~ ( ( SV771 != SV603 )
| ( SV694 != SV499 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7255]) ).
thf(7300,plain,
! [SV500: $i,SV604: $i,SV695: $i,SV772: $i,SV829: $i,SV865: $i,SV885: $i,SV893: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV893 @ SV885 @ SV865 @ SV829 ) @ SV772 )
= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SV885 @ SV865 @ SV604 ) @ SV500 ) )
= $false )
| ( ( ! [SY2383: $i] :
( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SY2383 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SY2383 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7256]) ).
thf(7301,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i,SV886: $i,SV894: $i,SV899: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV899 @ SV894 @ SV886 @ SV866 ) @ SV830 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SV894 @ SV886 @ SV698 ) @ SV607 ) )
= $true )
| ( ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7257]) ).
thf(7302,plain,
! [SV832: $i,SV868: $i,SV505: $i,SV777: $i,SV700: $i,SV609: $i] :
( ( ( c_Natural_Oevaln @ SV609 @ SV700 @ SV777 @ SV505 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV868 @ SV609 ) @ SV832 @ SV777 @ SV505 )
= $true )
| ( ( c_Natural_Oevaln @ SV868 @ SV832 @ SV777 @ SV700 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7259]) ).
thf(7303,plain,
! [SV781: $i,SV895: $i,SV834: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ SV834 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV895 )
= $false )
| ( ( v_Q @ SV781 @ SV895 )
= $true )
| ( ( v_P @ SV781 @ SV834 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7262]) ).
thf(7304,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( SV872 != SV837 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7264]) ).
thf(7305,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( ~ ( ( SV872 != SV837 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7265]) ).
thf(7306,plain,
! [SV712: $i,SV838: $i,SV522: $i,SV787: $i,SV873: $i,SV625: $i] :
( ( ( SV625
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV787 ) @ SV522 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV625 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV712 ) @ SV522 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV873 ) @ SV838 ) @ SV787 )
= SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7266]) ).
thf(7307,plain,
! [SV526: $i,SV628: $i,SV715: $i,SV789: $i,SV840: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 )
= $false )
| ( ( ( hAPP @ SV715 @ SV628 )
= SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7267]) ).
thf(7308,plain,
! [SV789: $i,SV840: $i,SV526: $i,SV628: $i,SV715: $i] :
( ( ( ( hAPP @ SV715 @ SV628 )
= SV526 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV840 @ SV789 ) @ SV715 ) @ SV628 ) @ SV526 )
= SV715 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7268]) ).
thf(7309,plain,
! [SV790: $i,SV528: $i,SV630: $i,SV717: $i,SV841: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7269]) ).
thf(7310,plain,
! [SV841: $i,SV717: $i,SV630: $i,SV528: $i,SV790: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV790 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) @ SV630 @ SV528 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7269]) ).
thf(7311,plain,
! [SV533: $i,SV635: $i,SV722: $i,SV792: $i,SV842: $i,SV874: $i,SV889: $i] :
( ( ( SV889 = SV874 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV889 ) @ SV635 ) ) @ SV874 ) @ SV533 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV842 @ SV792 ) @ SV722 ) @ SV874 ) @ SV533 ) ) @ SV889 ) @ SV635 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7270]) ).
thf(7312,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV723 @ SV636 @ ( sK20_SY2208 @ SV534 @ SV636 @ SV723 ) @ SV534 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7271]) ).
thf(7313,plain,
! [SV534: $i,SV903: $i,SV636: $i,SV723: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV723 @ SV636 @ SV903 @ SV534 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7272]) ).
thf(7314,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( SV875 != SV843 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7273]) ).
thf(7315,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( ~ ( ( SV875 != SV843 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7274]) ).
thf(7316,plain,
! [SV795: $i,SV726: $i,SV537: $i,SV639: $i] :
( ( ( SV639
= ( hAPP @ c_Nat_OSuc @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7276]) ).
thf(7317,plain,
! [SV639: $i,SV537: $i,SV726: $i,SV795: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV795 ) ) @ SV726 @ ( sK18_SY2335 @ SV537 @ SV726 @ SV795 @ SV639 ) @ SV537 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV795 ) @ SV726 @ SV639 @ SV537 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7277]) ).
thf(7318,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true )
| ( ( ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7282]) ).
thf(7319,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( ~ ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7283]) ).
thf(7320,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i,SV900: $i,SV904: $i] :
( ( ! [SY2467: $i] :
( ( ( hAPP @ SY2467 @ ( hAPP @ SV904 @ SV900 ) )
!= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SY2467 ) @ SV904 ) @ SV900 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7288]) ).
thf(7321,plain,
! [SV548: $i,SV649: $i,SV736: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false )
| ( ( ~ ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7289]) ).
thf(7322,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7290]) ).
thf(7323,plain,
! [SV555: $i,SV655: $i,SV741: $i,SV807: $i,SV849: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false )
| ( ( ~ ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7291]) ).
thf(7324,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7292]) ).
thf(7325,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV487: $i,SV591: $i,SV823: $i] :
( ( ( ~ ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7295]) ).
thf(7326,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV823: $i,SV487: $i,SV591: $i] :
( ( ( ~ ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7295]) ).
thf(7327,plain,
! [SV498: $i,SV693: $i,SV827: $i,SV864: $i,SV602: $i,SV770: $i] :
( ( ( SV770 = SV602 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7296]) ).
thf(7328,plain,
! [SV602: $i,SV770: $i,SV827: $i,SV864: $i,SV498: $i,SV693: $i] :
( ( ( SV693 = SV498 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV770 ) @ SV693 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV864 @ SV827 ) @ SV602 ) @ SV498 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7297]) ).
thf(7329,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7298]) ).
thf(7330,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( ( SV771 != SV603 )
| ( SV694 != SV499 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7299]) ).
thf(7331,plain,
! [SV695: $i,SV865: $i,SV885: $i,SV893: $i,SV500: $i,SV604: $i,SV905: $i,SV772: $i,SV829: $i] :
( ( ( ( hAPP @ SV829 @ ( hAPP @ SV772 @ SV905 ) )
= ( hAPP @ SV604 @ ( hAPP @ SV500 @ SV905 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV893 @ SV885 @ SV865 @ SV829 ) @ SV772 )
= ( hAPP @ ( c_Fun_Ocomp @ SV695 @ SV885 @ SV865 @ SV604 ) @ SV500 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7300]) ).
thf(7332,plain,
! [SV503: $i,SV607: $i,SV698: $i,SV775: $i,SV830: $i,SV866: $i,SV886: $i,SV894: $i,SV899: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV899 @ SV894 @ SV886 @ SV866 ) @ SV830 )
= ( hAPP @ ( c_Fun_Ocomp @ SV775 @ SV894 @ SV886 @ SV698 ) @ SV607 ) )
= $false )
| ( ( ( hAPP @ SV866 @ ( hAPP @ SV830 @ SV503 ) )
= ( hAPP @ SV698 @ ( hAPP @ SV607 @ SV503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7301]) ).
thf(7333,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( SV872 = SV837 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= SV521 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7304]) ).
thf(7334,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( SV872 != SV837 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7305]) ).
thf(7335,plain,
! [SV790: $i,SV528: $i,SV630: $i,SV717: $i,SV841: $i] :
( ( ( c_Natural_Oevaln @ SV841 @ SV717 @ SV630 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7309]) ).
thf(7336,plain,
! [SV841: $i,SV717: $i,SV630: $i,SV528: $i,SV790: $i] :
( ( ( c_Natural_Oevaln @ SV790 @ ( sK19_SY2398 @ SV528 @ SV790 @ SV630 @ SV717 @ SV841 ) @ SV630 @ SV528 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV841 @ SV790 ) @ SV717 @ SV630 @ SV528 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7310]) ).
thf(7337,plain,
! [SV534: $i,SV636: $i,SV723: $i] :
( ( ( c_Natural_Oevaln @ SV723 @ SV636 @ ( sK20_SY2208 @ SV534 @ SV636 @ SV723 ) @ SV534 )
= $true )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7312]) ).
thf(7338,plain,
! [SV534: $i,SV903: $i,SV636: $i,SV723: $i] :
( ( ( c_Natural_Oevaln @ SV723 @ SV636 @ SV903 @ SV534 )
= $false )
| ( ( c_Natural_Oevalc @ SV723 @ SV636 @ SV534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7313]) ).
thf(7339,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( SV875 = SV843 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7314]) ).
thf(7340,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( SV875 != SV843 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7315]) ).
thf(7341,plain,
! [SV540: $i,SV642: $i,SV729: $i,SV798: $i,SV845: $i,SV877: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false )
| ( ( ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7318]) ).
thf(7342,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( ~ ( ( SV798 != SV642 )
| ( SV729 != SV540 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7319]) ).
thf(7343,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i,SV900: $i,SV904: $i,SV906: $i] :
( ( ( ( hAPP @ SV906 @ ( hAPP @ SV904 @ SV900 ) )
!= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SV906 ) @ SV904 ) @ SV900 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7320]) ).
thf(7344,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ! [SY2410: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2410 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2410 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2410 ) @ SV548 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7321]) ).
thf(7345,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ! [SY2411: $i] :
~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SY2411 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SY2411 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SY2411 ) @ SV548 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7322]) ).
thf(7346,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ! [SY2412: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2412 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2412 @ SV655 @ SV555 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7323]) ).
thf(7347,plain,
! [SV555: $i,SV807: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ! [SY2413: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SY2413 )
| ~ ( c_Natural_Oevaln @ SV807 @ SY2413 @ SV655 @ SV555 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7324]) ).
thf(7348,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV487: $i,SV591: $i,SV823: $i] :
( ( ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
| ( SV591 = SV487 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7325]) ).
thf(7349,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV823: $i,SV487: $i,SV591: $i] :
( ( ( ( SV591 != SV487 )
| ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7326]) ).
thf(7350,plain,
! [SV499: $i,SV694: $i,SV828: $i,SV603: $i,SV771: $i] :
( ( ( SV771 != SV603 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7329]) ).
thf(7351,plain,
! [SV603: $i,SV771: $i,SV828: $i,SV499: $i,SV694: $i] :
( ( ( SV694 != SV499 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7329]) ).
thf(7352,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( SV771 != SV603 )
= $true )
| ( ( SV694 != SV499 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7330]) ).
thf(7353,plain,
! [SV521: $i,SV624: $i,SV711: $i,SV786: $i,SV837: $i,SV872: $i] :
( ( ( SV872 = SV837 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV786 @ SV711 ) @ SV624 ) @ SV837 ) @ SV521 ) @ SV872 )
= ( hAPP @ SV624 @ SV872 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7334]) ).
thf(7354,plain,
! [SV535: $i,SV637: $i,SV724: $i,SV793: $i,SV843: $i,SV875: $i] :
( ( ( SV875 = SV843 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Fun_Ofun__upd @ SV793 @ SV724 ) @ SV637 ) @ SV843 ) @ SV535 ) @ SV875 )
= ( hAPP @ SV637 @ SV875 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7340]) ).
thf(7355,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7341]) ).
thf(7356,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( ( SV798 != SV642 )
| ( SV729 != SV540 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7342]) ).
thf(7357,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i,SV900: $i,SV904: $i,SV906: $i] :
( ( ( ( hAPP @ SV906 @ ( hAPP @ SV904 @ SV900 ) )
!= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SV906 ) @ SV904 ) @ SV900 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7343]) ).
thf(7358,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7344]) ).
thf(7359,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7345]) ).
thf(7360,plain,
! [SV807: $i,SV555: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) )
| ~ ( c_Natural_Oevaln @ SV807 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) @ SV655 @ SV555 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7346]) ).
thf(7361,plain,
! [SV555: $i,SV807: $i,SV908: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 )
| ~ ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7347]) ).
thf(7362,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV487: $i,SV591: $i,SV823: $i] :
( ( ( ( hAPP @ SV823 @ SV591 )
!= ( hAPP @ SV823 @ SV487 ) )
= $true )
| ( ( SV591 = SV487 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7348]) ).
thf(7363,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV823: $i,SV487: $i,SV591: $i] :
( ( ( SV591 != SV487 )
= $true )
| ( ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7349]) ).
thf(7364,plain,
! [SV499: $i,SV694: $i,SV828: $i,SV603: $i,SV771: $i] :
( ( ( SV771 = SV603 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7350]) ).
thf(7365,plain,
! [SV603: $i,SV771: $i,SV828: $i,SV499: $i,SV694: $i] :
( ( ( SV694 = SV499 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7351]) ).
thf(7366,plain,
! [SV828: $i,SV499: $i,SV694: $i,SV603: $i,SV771: $i] :
( ( ( SV771 = SV603 )
= $false )
| ( ( SV694 != SV499 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7352]) ).
thf(7367,plain,
! [SV540: $i,SV729: $i,SV845: $i,SV877: $i,SV642: $i,SV798: $i] :
( ( ( SV798 != SV642 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7355]) ).
thf(7368,plain,
! [SV642: $i,SV798: $i,SV845: $i,SV877: $i,SV540: $i,SV729: $i] :
( ( ( SV729 != SV540 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7355]) ).
thf(7369,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( SV798 != SV642 )
= $true )
| ( ( SV729 != SV540 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7356]) ).
thf(7370,plain,
! [SV545: $i,SV646: $i,SV733: $i,SV801: $i,SV846: $i,SV878: $i,SV890: $i,SV896: $i,SV900: $i,SV904: $i,SV906: $i] :
( ( ( ( hAPP @ SV906 @ ( hAPP @ SV904 @ SV900 ) )
= ( hAPP @ SV896 @ ( hAPP @ SV890 @ SV878 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV846 @ SV801 @ SV733 @ SV906 ) @ SV904 ) @ SV900 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV646 @ SV801 @ SV545 @ SV896 ) @ SV890 ) @ SV878 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7357]) ).
thf(7371,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7358]) ).
thf(7372,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7359]) ).
thf(7373,plain,
! [SV807: $i,SV555: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) )
| ~ ( c_Natural_Oevaln @ SV807 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) @ SV655 @ SV555 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7360]) ).
thf(7374,plain,
! [SV555: $i,SV807: $i,SV908: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 )
| ~ ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7361]) ).
thf(7375,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV487: $i,SV591: $i,SV823: $i] :
( ( ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) )
= $false )
| ( ( SV591 = SV487 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7362]) ).
thf(7376,plain,
! [SV683: $i,SV765: $i,SV861: $i,SV883: $i,SV823: $i,SV487: $i,SV591: $i] :
( ( ( SV591 = SV487 )
= $false )
| ( ( ( hAPP @ SV823 @ SV591 )
= ( hAPP @ SV823 @ SV487 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV883 @ SV861 @ SV823 @ SV765 @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7363]) ).
thf(7377,plain,
! [SV828: $i,SV603: $i,SV771: $i,SV499: $i,SV694: $i] :
( ( ( SV694 = SV499 )
= $false )
| ( ( SV771 = SV603 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV771 ) @ SV694 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV828 ) @ SV603 ) @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7366]) ).
thf(7378,plain,
! [SV540: $i,SV729: $i,SV845: $i,SV877: $i,SV642: $i,SV798: $i] :
( ( ( SV798 = SV642 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7367]) ).
thf(7379,plain,
! [SV642: $i,SV798: $i,SV845: $i,SV877: $i,SV540: $i,SV729: $i] :
( ( ( SV729 = SV540 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7368]) ).
thf(7380,plain,
! [SV845: $i,SV877: $i,SV540: $i,SV729: $i,SV642: $i,SV798: $i] :
( ( ( SV798 = SV642 )
= $false )
| ( ( SV729 != SV540 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7369]) ).
thf(7381,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
!= SV548 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7371]) ).
thf(7382,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ~ ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7372]) ).
thf(7383,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV907: $i,SV804: $i,SV848: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7372]) ).
thf(7384,plain,
! [SV807: $i,SV555: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) )
| ~ ( c_Natural_Oevaln @ SV807 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) @ SV655 @ SV555 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7373]) ).
thf(7385,plain,
! [SV555: $i,SV807: $i,SV908: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 )
| ~ ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7374]) ).
thf(7386,plain,
! [SV845: $i,SV877: $i,SV642: $i,SV798: $i,SV540: $i,SV729: $i] :
( ( ( SV729 = SV540 )
= $false )
| ( ( SV798 = SV642 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV798 ) @ SV729 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV877 @ SV845 ) @ SV642 ) @ SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7380]) ).
thf(7387,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
!= SV548 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7381]) ).
thf(7388,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7382]) ).
thf(7389,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV907: $i,SV804: $i,SV848: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7383]) ).
thf(7390,plain,
! [SV807: $i,SV555: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7384]) ).
thf(7391,plain,
! [SV849: $i,SV741: $i,SV655: $i,SV555: $i,SV807: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV807 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) @ SV655 @ SV555 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7384]) ).
thf(7392,plain,
! [SV555: $i,SV807: $i,SV908: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7385]) ).
thf(7393,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7387]) ).
thf(7394,plain,
! [SV804: $i,SV649: $i,SV736: $i,SV548: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
!= SV548 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7387]) ).
thf(7395,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( SV804
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7388]) ).
thf(7396,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV907: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
!= SV649 )
= $true )
| ( ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7389]) ).
thf(7397,plain,
! [SV807: $i,SV555: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7390]) ).
thf(7398,plain,
! [SV849: $i,SV741: $i,SV655: $i,SV555: $i,SV807: $i] :
( ( ( c_Natural_Oevaln @ SV807 @ ( sK22_SY2412 @ SV555 @ SV807 @ SV655 @ SV741 @ SV849 ) @ SV655 @ SV555 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7391]) ).
thf(7399,plain,
! [SV555: $i,SV807: $i,SV908: $i,SV655: $i,SV741: $i,SV849: $i] :
( ( ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7392]) ).
thf(7400,plain,
! [SV736: $i,SV548: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7393]) ).
thf(7401,plain,
! [SV804: $i,SV649: $i,SV736: $i,SV548: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7394]) ).
thf(7402,plain,
! [SV548: $i,SV736: $i,SV907: $i,SV649: $i,SV848: $i,SV804: $i] :
( ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
!= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7395]) ).
thf(7403,plain,
! [SV548: $i,SV736: $i,SV649: $i,SV907: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
= SV649 )
= $false )
| ( ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7396]) ).
thf(7404,plain,
! [SV741: $i,SV849: $i,SV555: $i,SV655: $i,SV908: $i,SV807: $i] :
( ( ( c_Natural_Oevaln @ SV807 @ SV908 @ SV655 @ SV555 )
= $false )
| ( ( c_Natural_Oevaln @ SV849 @ SV741 @ SV655 @ SV908 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV849 @ SV807 ) @ SV741 @ SV655 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7399]) ).
thf(7405,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) )
= $false )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7400]) ).
thf(7406,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
| ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7401]) ).
thf(7407,plain,
! [SV649: $i,SV804: $i,SV548: $i,SV736: $i,SV907: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV736 )
= SV548 )
= $false )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV907 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7402]) ).
thf(7408,plain,
! [SV649: $i,SV804: $i,SV548: $i,SV907: $i,SV848: $i,SV736: $i] :
( ( ( SV736
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV907 ) @ SV548 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV907 )
= SV649 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7403]) ).
thf(7409,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
= $false )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7405]) ).
thf(7410,plain,
! [SV804: $i,SV649: $i,SV548: $i,SV848: $i,SV736: $i] :
( ( ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) )
= $false )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7405]) ).
thf(7411,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
!= SV649 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7406]) ).
thf(7412,plain,
! [SV804: $i,SV649: $i,SV548: $i,SV848: $i,SV736: $i] :
( ( ( SV736
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7406]) ).
thf(7413,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
= SV649 )
= $true )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7409]) ).
thf(7414,plain,
! [SV804: $i,SV649: $i,SV548: $i,SV848: $i,SV736: $i] :
( ( ( SV736
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) )
= $true )
| ( ( SV804
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7410]) ).
thf(7415,plain,
! [SV649: $i,SV736: $i,SV548: $i,SV804: $i,SV848: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) )
= SV649 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7411]) ).
thf(7416,plain,
! [SV804: $i,SV649: $i,SV548: $i,SV848: $i,SV736: $i] :
( ( ( SV736
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV548 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ ( sK21_SY2410 @ SV548 @ SV736 @ SV649 @ SV848 @ SV804 ) ) @ SV736 )
= SV548 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV804 ) @ SV736 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV848 ) @ SV649 ) @ SV548 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7412]) ).
thf(7417,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[6654,7416,7415,7414,7413,7408,7407,7404,7398,7397,7386,7379,7378,7377,7376,7375,7370,7365,7364,7354,7353,7339,7338,7337,7336,7335,7333,7332,7331,7328,7327,7317,7316,7311,7308,7307,7306,7303,7302,7294,7293,7287,7286,7285,7284,7281,7280,7279,7278,7275,7263,7261,7260,7258,7252,7251,7245,7244,7223,7222,7218,7217,7213,7211,7207,7206,7196,7195,7194,7192,7185,7184,7181,7159,7153,7152,7150,7149,7148,7145,7144,7139,7138,7130,7129,7121,7120,7110,7081,7076,7063,7062,7051,7048,7047,7046,7045,7042,7041,7040,7037,7036,7032,7031,7030,7010,6995,6988,6967,6966,6959,6954,6952,6947,6934,6924,6921,6919,6899,6894,6883,6876,6868,6867,6865,6858,6857,6854,6852,6772,6763,6750,6742,6724,6705,6677,6676,6670,6669,6668,6658,6657]) ).
thf(7418,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[7417,6366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n018.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 16:56:07 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.64/20.80 ....................................
% 102.64/20.80
% 102.64/20.80 No.of.Axioms: 104
% 102.64/20.80
% 102.64/20.80 Length.of.Defs: 0
% 102.64/20.80
% 102.64/20.80 Contains.Choice.Funs: false
% 102.64/20.80 ..................................................................................................................................................................
% 102.64/20.80
% 102.64/20.80 ********************************
% 102.64/20.80 * All subproblems solved! *
% 102.64/20.80 ********************************
% 102.64/20.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:104,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:289,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7417,loop_count:0,foatp_calls:1,translation:fof_full)
% 102.64/20.80
% 102.64/20.80 %**** Beginning of derivation protocol ****
% 102.64/20.80 % SZS output start CNFRefutation
% See solution above
% 102.64/20.82
% 102.64/20.82 %**** End of derivation protocol ****
% 102.64/20.82 %**** no. of clauses in derivation: 2318 ****
% 102.64/20.82 %**** clause counter: 7417 ****
% 102.64/20.82
% 102.64/20.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:104,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:289,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7417,loop_count:0,foatp_calls:1,translation:fof_full)
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