%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:01:09 AM UTC 2026
% Result : Theorem 106.06s 21.42s
% Output : CNFRefutation 106.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 151
% Syntax : Number of formulae : 2238 (1292 unt; 0 typ; 0 def)
% Number of atoms : 13761 (5892 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 48937 (5711 ~;4269 |; 45 &;38419 @)
% ( 153 <=>; 340 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 545 ( 542 usr; 49 con; 0-7 aty)
% Number of variables : 10374 ( 0 ^;10344 !; 30 ?;10374 :)
% 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_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_Oenum__class_Oenum__all,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(tp_c_Enum_Oenum__class_Oenum__ex,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(tp_c_Enum_Oenum__the,type,
c_Enum_Oenum__the: $i > $i > $i ).
thf(tp_c_Enum_On__lists,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(tp_c_Enum_Oproduct,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Enum_Osublists,type,
c_Enum_Osublists: $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequivp,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Opart__equivp,type,
c_Equiv__Relations_Opart__equivp: $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_OTHE__default,type,
c_FunDef_OTHE__default: $i > $i > $i > $i ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_Ois__measure,type,
c_FunDef_Ois__measure: $i > $i > $o ).
thf(tp_c_FunDef_Omax__strict,type,
c_FunDef_Omax__strict: $i ).
thf(tp_c_FunDef_Omax__weak,type,
c_FunDef_Omax__weak: $i ).
thf(tp_c_FunDef_Omin__strict,type,
c_FunDef_Omin__strict: $i ).
thf(tp_c_FunDef_Omin__weak,type,
c_FunDef_Omin__weak: $i ).
thf(tp_c_FunDef_Opair__leq,type,
c_FunDef_Opair__leq: $i ).
thf(tp_c_FunDef_Opair__less,type,
c_FunDef_Opair__less: $i ).
thf(tp_c_FunDef_Oreduction__pair,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(tp_c_FunDef_Orp__inv__image,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: $i > $i > $i > $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_Othe__inv__into,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tp_c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tp_c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(tp_c_Groups_Osgn__class_Osgn,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(tp_c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(tp_c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_HOL_OAll,type,
c_HOL_OAll: $i > $i ).
thf(tp_c_HOL_OEx,type,
c_HOL_OEx: $i > $i ).
thf(tp_c_HOL_OLet,type,
c_HOL_OLet: $i > $i > $i ).
thf(tp_c_HOL_OThe,type,
c_HOL_OThe: $i > $i > $i ).
thf(tp_c_HOL_Obool_Obool__size,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(tp_c_Hilbert__Choice_OEps,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(tp_c_Hilbert__Choice_Oinv__into,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__valids,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Otriple__valid,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(tp_c_If,type,
c_If: $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Ogfp,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(tp_c_Inductive_Ocomplete__lattice__class_Olfp,type,
c_Inductive_Ocomplete__lattice__class_Olfp: $i > $i > $i ).
thf(tp_c_Int_OAbs__Integ,type,
c_Int_OAbs__Integ: $i ).
thf(tp_c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
thf(tp_c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
thf(tp_c_Int_OInteg,type,
c_Int_OInteg: $i ).
thf(tp_c_Int_OMin,type,
c_Int_OMin: $i ).
thf(tp_c_Int_OPls,type,
c_Int_OPls: $i ).
thf(tp_c_Int_ORep__Integ,type,
c_Int_ORep__Integ: $i ).
thf(tp_c_Int_Oint__ge__less__than,type,
c_Int_Oint__ge__less__than: $i > $i ).
thf(tp_c_Int_Oint__ge__less__than2,type,
c_Int_Oint__ge__less__than2: $i > $i ).
thf(tp_c_Int_Ointrel,type,
c_Int_Ointrel: $i ).
thf(tp_c_Int_Oiszero,type,
c_Int_Oiszero: $i > $i > $o ).
thf(tp_c_Int_Onat,type,
c_Int_Onat: $i ).
thf(tp_c_Int_Onat__aux,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(tp_c_Int_Opred,type,
c_Int_Opred: $i > $i ).
thf(tp_c_Int_Oring__1__class_OInts,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(tp_c_Int_Oring__1__class_Oof__int,type,
c_Int_Oring__1__class_Oof__int: $i > $i ).
thf(tp_c_Int_Osucc,type,
c_Int_Osucc: $i > $i ).
thf(tp_c_Lattices_Osemilattice__inf__class_Oinf,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(tp_c_Lazy__Sequence_Oanamorph,type,
c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oappend,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Obind,type,
c_Lazy__Sequence_Obind: $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_Olazy__sequence_OEmpty,type,
c_Lazy__Sequence_Olazy__sequence_OEmpty: $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_OInsert,type,
c_Lazy__Sequence_Olazy__sequence_OInsert: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oproduct,type,
c_Lazy__Sequence_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osingle,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H,type,
c_Lazy__Sequence_Osmall__lazy_H: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H__rel,type,
c_Lazy__Sequence_Osmall__lazy_H__rel: $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy,type,
c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oyield,type,
c_Lazy__Sequence_Oyield: $i > $i ).
thf(tp_c_Lazy__Sequence_Oyieldn,type,
c_Lazy__Sequence_Oyieldn: $i > $i ).
thf(tp_c_List_Oall__interval__int,type,
c_List_Oall__interval__int: $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Oconcat,type,
c_List_Oconcat: $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(tp_c_List_Oembed__list,type,
c_List_Oembed__list: $i > $i ).
thf(tp_c_List_Ofilter,type,
c_List_Ofilter: $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i ).
thf(tp_c_List_Oinsert,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olenlex,type,
c_List_Olenlex: $i > $i > $i ).
thf(tp_c_List_Olex,type,
c_List_Olex: $i > $i > $i ).
thf(tp_c_List_Olexn,type,
c_List_Olexn: $i > $i > $i ).
thf(tp_c_List_Olexord,type,
c_List_Olexord: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__insert__key,type,
c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__key,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osort__key,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olinorder__class_Osorted__list__of__set,type,
c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_Olist__size,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(tp_c_List_Olist__all,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(tp_c_List_Olist__all2,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex1,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i ).
thf(tp_c_List_Olistrel,type,
c_List_Olistrel: $i > $i > $i ).
thf(tp_c_List_Olistrel1,type,
c_List_Olistrel1: $i > $i > $i ).
thf(tp_c_List_Olistrelp,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(tp_c_List_Olists,type,
c_List_Olists: $i > $i > $i ).
thf(tp_c_List_Olistset,type,
c_List_Olistset: $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i ).
thf(tp_c_List_Omaps,type,
c_List_Omaps: $i > $i > $i > $i > $i ).
thf(tp_c_List_Omeasures,type,
c_List_Omeasures: $i > $i > $i ).
thf(tp_c_List_Omember,type,
c_List_Omember: $i > $i ).
thf(tp_c_List_Omonoid__add__class_Olistsum,type,
c_List_Omonoid__add__class_Olistsum: $i > $i ).
thf(tp_c_List_Onat__list,type,
c_List_Onat__list: $i > $o ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i ).
thf(tp_c_List_Opartition,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(tp_c_List_Oremdups,type,
c_List_Oremdups: $i > $i > $i ).
thf(tp_c_List_Oremove1,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tp_c_List_OremoveAll,type,
c_List_OremoveAll: $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $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_Osplice,type,
c_List_Osplice: $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_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_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__DSequence_Opos__union,type,
c_New__DSequence_Opos__union: $i > $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_New__Random__Sequence_Opos__union,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_OAbs__Frac,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(tp_c_Nitpick_OFrac,type,
c_Nitpick_OFrac: $i ).
thf(tp_c_Nitpick_ORep__Frac,type,
c_Nitpick_ORep__Frac: $i > $i ).
thf(tp_c_Nitpick_Ocard_H,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(tp_c_Nitpick_Odenom,type,
c_Nitpick_Odenom: $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Ofrac,type,
c_Nitpick_Ofrac: $i > $i ).
thf(tp_c_Nitpick_Oint__gcd,type,
c_Nitpick_Oint__gcd: $i ).
thf(tp_c_Nitpick_Oint__lcm,type,
c_Nitpick_Oint__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Oinverse__frac,type,
c_Nitpick_Oinverse__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oless__eq__frac,type,
c_Nitpick_Oless__eq__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Oless__frac,type,
c_Nitpick_Oless__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd__rel,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(tp_c_Nitpick_Onat__lcm,type,
c_Nitpick_Onat__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac__rel,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(tp_c_Nitpick_Onum,type,
c_Nitpick_Onum: $i > $i ).
thf(tp_c_Nitpick_Onumber__of__frac,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oof__frac,type,
c_Nitpick_Oof__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oone__frac,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(tp_c_Nitpick_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_Ooption_Ooption__case,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord_Omax,type,
c_Orderings_Oord_Omax: $i > $i > $i ).
thf(tp_c_Orderings_Oord_Omin,type,
c_Orderings_Oord_Omin: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_OLeast,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(tp_c_Orderings_Oorder_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_Oorder__class_Omono,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).
thf(tp_c_Orderings_Oorder__class_Ostrict__mono,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $o ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Partial__Function_Oflat__lub,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(tp_c_Partial__Function_Ofun__lub,type,
c_Partial__Function_Ofun__lub: $i > $i > $i > $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_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Predicate_Oreflp,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(tp_c_Predicate_Osymp,type,
c_Predicate_Osymp: $i > $i > $o ).
thf(tp_c_Predicate_Otransp,type,
c_Predicate_Otransp: $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_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
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_Osym,type,
c_Relation_Osym: $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Otrans,type,
c_Relation_Otrans: $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_OBex,type,
c_Set_OBex: $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_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Typedef_Otype__definition,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Ofinite__psubset,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(tp_c_Wellfounded_Oless__than,type,
c_Wellfounded_Oless__than: $i ).
thf(tp_c_Wellfounded_Olex__prod,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__ext,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__extp,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(tp_c_Wellfounded_Omin__ext,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Opred__nat,type,
c_Wellfounded_Opred__nat: $i ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fFalse,type,
c_fFalse: $i ).
thf(tp_c_fNot,type,
c_fNot: $i ).
thf(tp_c_fTrue,type,
c_fTrue: $i ).
thf(tp_c_fconj,type,
c_fconj: $i ).
thf(tp_c_fdisj,type,
c_fdisj: $i ).
thf(tp_c_fequal,type,
c_fequal: $i ).
thf(tp_c_fimplies,type,
c_fimplies: $i ).
thf(tp_c_member,type,
c_member: $i > $i ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Enum_Oenum,type,
class_Enum_Oenum: $i > $o ).
thf(tp_class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
thf(tp_class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(tp_class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(tp_class_Finite__Set_Ofinite,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tp_class_Groups_Oabs__if,type,
class_Groups_Oabs__if: $i > $o ).
thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__semigroup__add,type,
class_Groups_Olinordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
thf(tp_class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tp_class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(tp_class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(tp_class_Groups_Osemigroup__add,type,
class_Groups_Osemigroup__add: $i > $o ).
thf(tp_class_Groups_Osgn__if,type,
class_Groups_Osgn__if: $i > $o ).
thf(tp_class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_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_Lazy__Sequence_Osmall__lazy,type,
class_Lazy__Sequence_Osmall__lazy: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_Nat_Osize,type,
class_Nat_Osize: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
thf(tp_class_Orderings_Owellorder,type,
class_Orderings_Owellorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Rings_Ocomm__ring,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_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK10_SY1717,type,
sK10_SY1717: $i > $i > $i > $i ).
thf(tp_sK11_SY1720,type,
sK11_SY1720: $i > $i > $i > $i ).
thf(tp_sK12_SY1808,type,
sK12_SY1808: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY1992,type,
sK13_SY1992: $i > $i > $i > $i ).
thf(tp_sK14_SY1989,type,
sK14_SY1989: $i > $i > $i > $i ).
thf(tp_sK15_SY1421,type,
sK15_SY1421: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY1491,type,
sK16_SY1491: $i > $i > $i > $i > $i ).
thf(tp_sK17_SY1986,type,
sK17_SY1986: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY1904,type,
sK18_SY1904: $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY1994,type,
sK19_SY1994: $i > $i > $i > $i > $i ).
thf(tp_sK1_B_x,type,
sK1_B_x: $i ).
thf(tp_sK20_SY940,type,
sK20_SY940: $i > $i > $i ).
thf(tp_sK21_SY1863,type,
sK21_SY1863: $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_SY1787,type,
sK22_SY1787: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK23_SY944,type,
sK23_SY944: $i > $i > $i > $i ).
thf(tp_sK24_SY1998,type,
sK24_SY1998: $i > $i > $i > $i ).
thf(tp_sK2_SY1514,type,
sK2_SY1514: $i > $i > $i ).
thf(tp_sK3_SY923,type,
sK3_SY923: $i > $i > $i ).
thf(tp_sK4_SY1556,type,
sK4_SY1556: $i > $i > $i > $i ).
thf(tp_sK5_SY1593,type,
sK5_SY1593: $i > $i > $i > $i ).
thf(tp_sK6_SY1633,type,
sK6_SY1633: $i > $i > $i > $i ).
thf(tp_sK7_SY1981,type,
sK7_SY1981: $i > $i > $i ).
thf(tp_sK8_SY1648,type,
sK8_SY1648: $i > $i > $i > $i ).
thf(tp_sK9_SY1417,type,
sK9_SY1417: $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Code__Evaluation_Oterm,type,
tc_Code__Evaluation_Oterm: $i ).
thf(tp_tc_Code__Numeral_Ocode__numeral,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lazy__Sequence_Olazy__sequence,type,
tc_Lazy__Sequence_Olazy__sequence: $i > $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_Nitpick_Opair__box,type,
tc_Nitpick_Opair__box: $i > $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_sum,type,
tc_sum: $i > $i > $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_ts,type,
v_ts: $i ).
thf(1,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(2,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(3,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(4,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(5,axiom,
! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(6,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(7,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(8,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(9,axiom,
! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(10,axiom,
! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(11,axiom,
! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(12,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(13,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(14,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(15,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(16,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19,axiom,
! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(20,axiom,
! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(64,axiom,
! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
thf(250,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(251,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(252,axiom,
! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(288,axiom,
! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sympE) ).
thf(291,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpE) ).
thf(375,axiom,
! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(376,axiom,
! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(377,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(378,axiom,
! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).
thf(543,axiom,
! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(544,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(545,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(974,axiom,
! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(975,axiom,
! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(976,axiom,
! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(977,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(978,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(979,axiom,
! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(980,axiom,
! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1225,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1226,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(1227,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1253,axiom,
! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1346,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(1417,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/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1454,axiom,
! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1561,axiom,
! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(1562,axiom,
! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1563,axiom,
! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1564,axiom,
! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1567,axiom,
! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1625,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(1628,axiom,
! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(1631,axiom,
! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(1632,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(1633,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(1634,axiom,
! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(1635,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).
thf(1658,axiom,
! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1663,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1690,axiom,
! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1691,axiom,
! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1727,axiom,
! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1738,axiom,
! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1749,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1772,axiom,
! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1775,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1776,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
thf(1839,axiom,
! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).
thf(1840,axiom,
! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectD) ).
thf(1841,axiom,
! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
<=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).
thf(1851,axiom,
! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(1855,axiom,
! [T_b: $i,V_a_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).
thf(1862,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(1961,axiom,
! [V_y_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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_Rep_2 @ ( hAPP @ V_Abs_2 @ V_y_2 ) )
= V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(1962,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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_Abs_2 @ V_x_2 )
= ( hAPP @ V_Abs_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(1963,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(1964,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(1965,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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_Rep_2 @ V_x_2 ) ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(1988,axiom,
! [V_B_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(1989,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).
thf(1990,axiom,
! [T_c: $i,V_A_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(1994,axiom,
! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(1995,axiom,
! [T_c: $i,V_B_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_a_2 )
= V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).
thf(2000,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(2001,axiom,
! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(2002,axiom,
! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(2003,axiom,
! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(2161,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
=> ! [B_xa: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_xa ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_f_2 @ B_xa ) )
=> ( B_x = B_xa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
thf(2166,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( V_x_2 = V_y_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
thf(2167,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
thf(2168,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( V_x_2 != V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_f_2 @ V_x_2 )
!= ( hAPP @ V_f_2 @ V_y_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
thf(2465,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(2547,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 )
=> ( ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(2548,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 @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2550,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 @ ( 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 @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(2551,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_x_2 )
= V_y_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(2553,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(2554,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 @ ( 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 @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2556,axiom,
! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(2645,axiom,
! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(2646,axiom,
! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(2675,axiom,
! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeast @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_k_2 ) @ V_i_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(2676,axiom,
! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatMost @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_k_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(2685,axiom,
! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_k_2 ) @ V_i_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(2686,axiom,
! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OlessThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_k_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(2745,axiom,
! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ T_b @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(2763,axiom,
! [V_u_2: $i,V_l_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ T_b @ V_less__eq_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(2773,axiom,
! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( hAPP @ c_fequal @ V_y_2 ) ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(2775,axiom,
! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(2776,axiom,
! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2777,axiom,
! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(2778,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2779,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(2780,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,V_z_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_z_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ B_x ) @ V_A_2 ) )
& ( V_z_2
= ( hAPP @ V_f_2 @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2781,axiom,
! [V_f_2: $i,T_c: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(2782,axiom,
! [T_c: $i,V_f_2: $i,V_b_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2787,axiom,
! [V_B_2: $i,V_a_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(2788,axiom,
! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
<=> ( ( V_a_2 = V_b_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(2789,axiom,
! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_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_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2790,axiom,
! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(2791,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(2812,axiom,
! [T_b: $i,V_A_2: $i,T_c: $i,V_x_2: $i,V_f_2: $i,V_b_2: $i] :
( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(2814,axiom,
! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( V_a_2 = V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(2815,axiom,
! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
=> ( ( V_a_2 != V_b_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(2820,axiom,
! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(2981,axiom,
! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(2982,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(2983,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(3386,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) @ V_B_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(3417,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(3418,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(3432,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/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(3629,axiom,
! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(3648,axiom,
! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3649,axiom,
! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(3650,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(3651,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(3690,axiom,
! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(3691,axiom,
! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(3692,axiom,
! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(5217,axiom,
! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5218,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5219,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5220,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5221,axiom,
! [V_tsa_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ T_b @ V_G_2 @ V_tsa_2 )
<=> ! [B_n: $i] :
( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) )
=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_tsa_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
thf(5222,axiom,
! [V_t: $i,V_n: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_t )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ V_n @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
thf(5223,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(5224,axiom,
! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(5225,conjecture,
! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ B_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(5226,negated_conjecture,
( ( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ B_x ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5225]) ).
thf(5227,plain,
( ( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ B_x ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5226]) ).
thf(5228,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(5229,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(5230,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5231,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(5232,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(5233,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(5234,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(5235,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(5236,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(5237,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(5238,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(5239,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(5240,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(5241,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(5242,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(5243,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5244,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5245,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5246,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(5247,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5248,plain,
( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(5249,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(5250,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(5251,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(5252,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(5253,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(5254,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(5255,plain,
( ( ! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(5256,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(5257,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(5258,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(5259,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)],[544]) ).
thf(5260,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)],[545]) ).
thf(5261,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)],[974]) ).
thf(5262,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)],[975]) ).
thf(5263,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)],[976]) ).
thf(5264,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)],[977]) ).
thf(5265,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)],[978]) ).
thf(5266,plain,
( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(5267,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)],[980]) ).
thf(5268,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)],[1225]) ).
thf(5269,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)],[1226]) ).
thf(5270,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)],[1227]) ).
thf(5271,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)],[1253]) ).
thf(5272,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)],[1346]) ).
thf(5273,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)],[1417]) ).
thf(5274,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)],[1454]) ).
thf(5275,plain,
( ( ! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1561]) ).
thf(5276,plain,
( ( ! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1562]) ).
thf(5277,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1563]) ).
thf(5278,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1564]) ).
thf(5279,plain,
( ( ! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1567]) ).
thf(5280,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)],[1625]) ).
thf(5281,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)],[1628]) ).
thf(5282,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)],[1631]) ).
thf(5283,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)],[1632]) ).
thf(5284,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)],[1633]) ).
thf(5285,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)],[1634]) ).
thf(5286,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)],[1635]) ).
thf(5287,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1658]) ).
thf(5288,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1663]) ).
thf(5289,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1690]) ).
thf(5290,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1691]) ).
thf(5291,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1727]) ).
thf(5292,plain,
( ( ! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1738]) ).
thf(5293,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)],[1749]) ).
thf(5294,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1772]) ).
thf(5295,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1775]) ).
thf(5296,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)],[1776]) ).
thf(5297,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1839]) ).
thf(5298,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1840]) ).
thf(5299,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
<=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1841]) ).
thf(5300,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1851]) ).
thf(5301,plain,
( ( ! [T_b: $i,V_a_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1855]) ).
thf(5302,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)],[1862]) ).
thf(5303,plain,
( ( ! [V_y_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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_Rep_2 @ ( hAPP @ V_Abs_2 @ V_y_2 ) )
= V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1961]) ).
thf(5304,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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_Abs_2 @ V_x_2 )
= ( hAPP @ V_Abs_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1962]) ).
thf(5305,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)],[1963]) ).
thf(5306,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)],[1964]) ).
thf(5307,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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_Rep_2 @ V_x_2 ) ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1965]) ).
thf(5308,plain,
( ( ! [V_B_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1988]) ).
thf(5309,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1989]) ).
thf(5310,plain,
( ( ! [T_c: $i,V_A_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1990]) ).
thf(5311,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1994]) ).
thf(5312,plain,
( ( ! [T_c: $i,V_B_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_a_2 )
= V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1995]) ).
thf(5313,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2000]) ).
thf(5314,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2001]) ).
thf(5315,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2002]) ).
thf(5316,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2003]) ).
thf(5317,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
=> ! [B_xa: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_xa ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_f_2 @ B_xa ) )
=> ( B_x = B_xa ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2161]) ).
thf(5318,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2166]) ).
thf(5319,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2167]) ).
thf(5320,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( V_x_2 != V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_f_2 @ V_x_2 )
!= ( hAPP @ V_f_2 @ V_y_2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2168]) ).
thf(5321,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)],[2465]) ).
thf(5322,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 )
=> ( ( 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)],[2547]) ).
thf(5323,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 @ ( 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)],[2548]) ).
thf(5324,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 @ ( 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 @ ( 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)],[2550]) ).
thf(5325,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( 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)],[2551]) ).
thf(5326,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( 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)],[2553]) ).
thf(5327,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 @ ( 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 @ ( 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)],[2554]) ).
thf(5328,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( 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)],[2556]) ).
thf(5329,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2645]) ).
thf(5330,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2646]) ).
thf(5331,plain,
( ( ! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeast @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_k_2 ) @ V_i_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2675]) ).
thf(5332,plain,
( ( ! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatMost @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_k_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2676]) ).
thf(5333,plain,
( ( ! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_k_2 ) @ V_i_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2685]) ).
thf(5334,plain,
( ( ! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OlessThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_k_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2686]) ).
thf(5335,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ T_b @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2745]) ).
thf(5336,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ T_b @ V_less__eq_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2763]) ).
thf(5337,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( hAPP @ c_fequal @ V_y_2 ) ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2773]) ).
thf(5338,plain,
( ( ! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2775]) ).
thf(5339,plain,
( ( ! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2776]) ).
thf(5340,plain,
( ( ! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2777]) ).
thf(5341,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)],[2778]) ).
thf(5342,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2779]) ).
thf(5343,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_z_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_z_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ B_x ) @ V_A_2 ) )
& ( V_z_2
= ( hAPP @ V_f_2 @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2780]) ).
thf(5344,plain,
( ( ! [V_f_2: $i,T_c: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2781]) ).
thf(5345,plain,
( ( ! [T_c: $i,V_f_2: $i,V_b_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2782]) ).
thf(5346,plain,
( ( ! [V_B_2: $i,V_a_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2787]) ).
thf(5347,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
<=> ( ( V_a_2 = V_b_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2788]) ).
thf(5348,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_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_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2789]) ).
thf(5349,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2790]) ).
thf(5350,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2791]) ).
thf(5351,plain,
( ( ! [T_b: $i,V_A_2: $i,T_c: $i,V_x_2: $i,V_f_2: $i,V_b_2: $i] :
( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2812]) ).
thf(5352,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( V_a_2 = V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2814]) ).
thf(5353,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
=> ( ( V_a_2 != V_b_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2815]) ).
thf(5354,plain,
( ( ! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2820]) ).
thf(5355,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2981]) ).
thf(5356,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)],[2982]) ).
thf(5357,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)],[2983]) ).
thf(5358,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) @ V_B_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3386]) ).
thf(5359,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)],[3417]) ).
thf(5360,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)],[3418]) ).
thf(5361,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)],[3432]) ).
thf(5362,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3629]) ).
thf(5363,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)],[3648]) ).
thf(5364,plain,
( ( ! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3649]) ).
thf(5365,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)],[3650]) ).
thf(5366,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)],[3651]) ).
thf(5367,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3690]) ).
thf(5368,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3691]) ).
thf(5369,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3692]) ).
thf(5370,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)],[5217]) ).
thf(5371,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)],[5218]) ).
thf(5372,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[5219]) ).
thf(5373,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5220]) ).
thf(5374,plain,
( ( ! [V_tsa_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ T_b @ V_G_2 @ V_tsa_2 )
<=> ! [B_n: $i] :
( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) )
=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_tsa_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5221]) ).
thf(5375,plain,
( ( ! [V_t: $i,V_n: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_t )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5222]) ).
thf(5376,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)],[5223]) ).
thf(5377,plain,
( ( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5224]) ).
thf(5378,plain,
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sK1_B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ sK1_B_x ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5227]) ).
thf(5379,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sK1_B_x ) @ v_ts ) )
= $true ),
inference(standard_cnf,[status(thm)],[5378]) ).
thf(5380,plain,
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ sK1_B_x )
= $false ),
inference(standard_cnf,[status(thm)],[5378]) ).
thf(5381,plain,
( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ sK1_B_x ) )
= $true ),
inference(polarity_switch,[status(thm)],[5380]) ).
thf(5382,plain,
( ( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ B_x ) @ v_ts ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_x ) ) )
= $true ),
inference(copy,[status(thm)],[5377]) ).
thf(5383,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)],[5376]) ).
thf(5384,plain,
( ( ! [V_t: $i,V_n: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_t )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_a @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[5375]) ).
thf(5385,plain,
( ( ! [V_tsa_2: $i,V_G_2: $i,T_b: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ T_b @ V_G_2 @ V_tsa_2 )
<=> ! [B_n: $i] :
( ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_G_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) )
=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ T_b ) ) @ B_x ) @ V_tsa_2 ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ T_b @ B_n @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5374]) ).
thf(5386,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5373]) ).
thf(5387,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5372]) ).
thf(5388,plain,
( ( ! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5371]) ).
thf(5389,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)],[5370]) ).
thf(5390,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5369]) ).
thf(5391,plain,
( ( ! [V_a_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_x ) @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5368]) ).
thf(5392,plain,
( ( ! [V_a_2: $i,V_b_2: $i,V_r_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ T_b @ V_r_2 ) @ V_a_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5367]) ).
thf(5393,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)],[5366]) ).
thf(5394,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)],[5365]) ).
thf(5395,plain,
( ( ! [T_c: $i,T_b: $i,V_P_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5364]) ).
thf(5396,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)],[5363]) ).
thf(5397,plain,
( ( ! [V_qr_H: $i,V_qr: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ V_m @ V_n ) @ V_qr_H ) )
=> ( V_qr = V_qr_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5362]) ).
thf(5398,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)],[5361]) ).
thf(5399,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)],[5360]) ).
thf(5400,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)],[5359]) ).
thf(5401,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) @ V_B_2 ) )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5358]) ).
thf(5402,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)],[5357]) ).
thf(5403,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)],[5356]) ).
thf(5404,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_y_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( ( V_y_2 = V_x_2 )
| ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5355]) ).
thf(5405,plain,
( ( ! [V_c_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5354]) ).
thf(5406,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
=> ( ( V_a_2 != V_b_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5353]) ).
thf(5407,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( V_a_2 = V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5352]) ).
thf(5408,plain,
( ( ! [T_b: $i,V_A_2: $i,T_c: $i,V_x_2: $i,V_f_2: $i,V_b_2: $i] :
( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5351]) ).
thf(5409,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5350]) ).
thf(5410,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5349]) ).
thf(5411,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_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_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5348]) ).
thf(5412,plain,
( ( ! [V_A_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_A_2 ) ) )
<=> ( ( V_a_2 = V_b_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5347]) ).
thf(5413,plain,
( ( ! [V_B_2: $i,V_a_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5346]) ).
thf(5414,plain,
( ( ! [T_c: $i,V_f_2: $i,V_b_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( V_b_2
= ( hAPP @ V_f_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_b_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5345]) ).
thf(5415,plain,
( ( ! [V_f_2: $i,T_c: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5344]) ).
thf(5416,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_z_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_z_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ B_x ) @ V_A_2 ) )
& ( V_z_2
= ( hAPP @ V_f_2 @ B_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5343]) ).
thf(5417,plain,
( ( ! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5342]) ).
thf(5418,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)],[5341]) ).
thf(5419,plain,
( ( ! [V_x_2: $i,T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5340]) ).
thf(5420,plain,
( ( ! [V_A_2: $i,T_b: $i,V_y_2: $i,V_x_2: $i] :
( ( V_x_2 = V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5339]) ).
thf(5421,plain,
( ( ! [V_A_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i] :
( ( V_a_2 = V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5338]) ).
thf(5422,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( hAPP @ c_fequal @ V_y_2 ) ) )
<=> ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5337]) ).
thf(5423,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ T_b @ V_less__eq_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5336]) ).
thf(5424,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ T_b @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5335]) ).
thf(5425,plain,
( ( ! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OlessThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_k_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5334]) ).
thf(5426,plain,
( ( ! [V_k_2: $i,V_less_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThan @ T_b @ V_less_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_k_2 ) @ V_i_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5333]) ).
thf(5427,plain,
( ( ! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatMost @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_k_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5332]) ).
thf(5428,plain,
( ( ! [V_k_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeast @ T_b @ V_less__eq_2 @ V_k_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_k_2 ) @ V_i_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5331]) ).
thf(5429,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5330]) ).
thf(5430,plain,
( ( ! [V_u_2: $i,V_l_2: $i,V_less_2: $i,V_less__eq_2: $i,V_i_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_i_2 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ T_b @ V_less__eq_2 @ V_less_2 @ V_l_2 @ V_u_2 ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_less_2 @ V_l_2 ) @ V_i_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq_2 @ V_i_2 ) @ V_u_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5329]) ).
thf(5431,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( 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)],[5328]) ).
thf(5432,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 @ ( 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 @ ( 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)],[5327]) ).
thf(5433,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( 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)],[5326]) ).
thf(5434,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( 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)],[5325]) ).
thf(5435,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 @ ( 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 @ ( 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)],[5324]) ).
thf(5436,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 @ ( 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)],[5323]) ).
thf(5437,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 )
=> ( ( 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)],[5322]) ).
thf(5438,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)],[5321]) ).
thf(5439,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( V_x_2 != V_y_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_f_2 @ V_x_2 )
!= ( hAPP @ V_f_2 @ V_y_2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5320]) ).
thf(5440,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5319]) ).
thf(5441,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
=> ( ( ( hAPP @ V_f_2 @ V_x_2 )
= ( hAPP @ V_f_2 @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_y_2 ) @ V_A_2 ) )
=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5318]) ).
thf(5442,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 )
<=> ! [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
=> ! [B_xa: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_xa ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_f_2 @ B_xa ) )
=> ( B_x = B_xa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5317]) ).
thf(5443,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
<=> ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5316]) ).
thf(5444,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5315]) ).
thf(5445,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5314]) ).
thf(5446,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Oequivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5313]) ).
thf(5447,plain,
( ( ! [T_c: $i,V_B_2: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_a_2 )
= V_b_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5312]) ).
thf(5448,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ V_A_2 @ ( hAPP @ V_f_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5311]) ).
thf(5449,plain,
( ( ! [T_c: $i,V_A_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5310]) ).
thf(5450,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5309]) ).
thf(5451,plain,
( ( ! [V_B_2: $i,V_f_2: $i,T_c: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5308]) ).
thf(5452,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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ ( hAPP @ V_Rep_2 @ V_x_2 ) ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(5453,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)],[5306]) ).
thf(5454,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)],[5305]) ).
thf(5455,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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_x_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( ( hAPP @ V_Abs_2 @ V_x_2 )
= ( hAPP @ V_Abs_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5304]) ).
thf(5456,plain,
( ( ! [V_y_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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_c ) @ V_y_2 ) @ V_A_2 ) )
=> ( ( hAPP @ V_Rep_2 @ ( hAPP @ V_Abs_2 @ V_y_2 ) )
= V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5303]) ).
thf(5457,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)],[5302]) ).
thf(5458,plain,
( ( ! [T_b: $i,V_a_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5301]) ).
thf(5459,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(copy,[status(thm)],[5300]) ).
thf(5460,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
<=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(5461,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5298]) ).
thf(5462,plain,
( ( ! [V_P_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 ) ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(5463,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)],[5296]) ).
thf(5464,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5465,plain,
( ( ! [V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Oreflp @ T_b @ V_r_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(5466,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)],[5293]) ).
thf(5467,plain,
( ( ! [T_d: $i,T_c: $i,T_b: $i,V_c_2: $i,V_s_2: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ V_b_2 ) @ V_c_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a_2 ) @ V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5292]) ).
thf(5468,plain,
( ( ! [V_a3_2: $i,V_a1_2: $i,V_s_2: $i,V_r_2: $i,T_d: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ T_b @ T_c @ T_d @ V_r_2 @ V_s_2 ) @ V_a1_2 ) @ V_a3_2 ) )
<=> ? [B_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_b ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_s_2 @ B_b ) @ V_a3_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5291]) ).
thf(5469,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5290]) ).
thf(5470,plain,
( ( ! [V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) )
<=> ? [B_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ B_a ) @ V_a2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5471,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5472,plain,
( ( ! [V_a1_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ T_b @ T_c @ V_r_2 ) @ V_a1_2 ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5473,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5474,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)],[5285]) ).
thf(5475,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)],[5284]) ).
thf(5476,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)],[5283]) ).
thf(5477,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)],[5282]) ).
thf(5478,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)],[5281]) ).
thf(5479,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)],[5280]) ).
thf(5480,plain,
( ( ! [T_b: $i,V_c_2: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(5481,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(5482,plain,
( ( ! [T_b: $i,V_P_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_P_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(5483,plain,
( ( ! [T_b: $i,B_P: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ B_P @ B_x ) )
=> ( hBOOL @ ( hAPP @ B_P @ ( c_Hilbert__Choice_OEps @ T_b @ B_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(5484,plain,
( ( ! [T_b: $i,V_x_2: $i,V_P_2: $i] :
( ( hBOOL @ ( hAPP @ V_P_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_P_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_P_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(5485,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)],[5274]) ).
thf(5486,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)],[5273]) ).
thf(5487,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)],[5272]) ).
thf(5488,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)],[5271]) ).
thf(5489,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)],[5270]) ).
thf(5490,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)],[5269]) ).
thf(5491,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)],[5268]) ).
thf(5492,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)],[5267]) ).
thf(5493,plain,
( ( ! [V_tsa_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_tsa_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_tsa_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_tsa_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(5494,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)],[5265]) ).
thf(5495,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)],[5264]) ).
thf(5496,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)],[5263]) ).
thf(5497,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)],[5262]) ).
thf(5498,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)],[5261]) ).
thf(5499,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)],[5260]) ).
thf(5500,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)],[5259]) ).
thf(5501,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[5258]) ).
thf(5502,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(5503,plain,
( ( ! [T_c: $i,T_b: $i,V_b_2: $i,V_a_2: $i,V_r_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a_2 ) @ V_b_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5256]) ).
thf(5504,plain,
( ( ! [V_a1_2: $i,V_a2_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a2_2 ) @ V_a1_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_a1_2 ) @ V_a2_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5255]) ).
thf(5505,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_r_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ T_b @ T_c @ V_r_2 ) @ V_a_2 ) @ V_b_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_b_2 ) @ V_a_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5254]) ).
thf(5506,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Otransp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(5507,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Predicate_Osymp @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_r_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5252]) ).
thf(5508,plain,
( ( ! [V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
<=> ( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ! [B_x: $i,B_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_y ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_x ) @ B_x ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ B_y ) @ B_y ) )
& ( ( hAPP @ V_R_2 @ B_x )
= ( hAPP @ V_R_2 @ B_y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(5509,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5250]) ).
thf(5510,plain,
( ( ! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( c_Equiv__Relations_Opart__equivp @ T_b @ V_R_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_y_2 ) @ V_z_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_z_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(5511,plain,
( ( ! [T_1: $i] : ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[5248]) ).
thf(5512,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5247]) ).
thf(5513,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)],[5246]) ).
thf(5514,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(5515,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(5516,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(5517,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) )
| ( V_x_2 = V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(5518,plain,
( ( ! [V_y_2: $i,V_x_2: $i] :
( ( V_x_2 != V_y_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(5519,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(5520,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(5521,plain,
( ( ! [V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) )
| ~ ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(5522,plain,
( ( ! [V_P_2: $i] :
( ~ ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_P_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(5523,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(5524,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(5525,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(5526,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5233]) ).
thf(5527,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5232]) ).
thf(5528,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_P_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5231]) ).
thf(5529,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ( hBOOL @ V_P_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5230]) ).
thf(5530,plain,
( ( ! [V_P_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5229]) ).
thf(5531,plain,
( ( ! [V_Q_2: $i,V_P_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_P_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_P_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5228]) ).
thf(5532,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ sK1_B_x ) @ v_ts ) )
= $true ),
inference(copy,[status(thm)],[5379]) ).
thf(5533,plain,
( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ sK1_B_x ) )
= $true ),
inference(copy,[status(thm)],[5381]) ).
thf(5534,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)],[5476]) ).
thf(5535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SX2 @ SX1 @ SX0 )
| ! [SX3: $i] :
( ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SX2 ) ) @ SX4 ) @ SX1 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ SX3 @ SX4 ) )
| ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SX2 ) ) @ SX4 ) @ SX0 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ SX3 @ SX4 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SX2 ) ) @ SX4 ) @ SX1 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ SX3 @ SX4 ) )
| ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SX2 ) ) @ SX4 ) @ SX0 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ SX3 @ SX4 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5385]) ).
thf(5536,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)],[5393]) ).
thf(5537,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5420]) ).
thf(5538,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)],[5454]) ).
thf(5539,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)],[5487]) ).
thf(5540,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5389]) ).
thf(5541,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ ( hAPP @ SX3 @ SX2 ) ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX0 ) @ SX2 ) @ ( hAPP @ ( c_Set_Ovimage @ SX0 @ SX4 @ SX3 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5449]) ).
thf(5542,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX7 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX7 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5468]) ).
thf(5543,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)],[5400]) ).
thf(5544,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5387]) ).
thf(5545,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5410]) ).
thf(5546,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)],[5418]) ).
thf(5547,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)],[5493]) ).
thf(5548,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ~ ( ( SX2 != SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5406]) ).
thf(5549,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX1 @ SX0 @ SX4 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5469]) ).
thf(5550,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX0 ) @ SX1 ) @ ( hAPP @ ( c_Set_OCollect @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5458]) ).
thf(5551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Typedef_Otype__definition @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX0 ) @ SX1 ) )
| ( ( hAPP @ SX3 @ ( hAPP @ SX2 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5456]) ).
thf(5552,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5404]) ).
thf(5553,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5411]) ).
thf(5554,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX2 @ SX1 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ ( hAPP @ SX1 @ SX3 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5450]) ).
thf(5555,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Predicate_Oreflp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5465]) ).
thf(5556,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5409]) ).
thf(5557,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5401]) ).
thf(5558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5392]) ).
thf(5559,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)],[5498]) ).
thf(5560,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5446]) ).
thf(5561,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5386]) ).
thf(5562,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ SX2 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5484]) ).
thf(5563,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5405]) ).
thf(5564,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ( SX1
!= ( c_Hilbert__Choice_OEps @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5480]) ).
thf(5565,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX7 @ SX6 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX5 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SX2 @ SX1 @ SX0 @ SX7 @ SX4 ) @ SX6 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5467]) ).
thf(5566,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SX4 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX3 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SX4 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5424]) ).
thf(5567,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5436]) ).
thf(5568,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( c_Fun_Oinj__on @ SX3 @ SX2 @ SX1 @ SX0 )
| ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX4 ) @ SX0 ) )
| ! [SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX5 ) @ SX0 ) )
| ( ( hAPP @ SX1 @ SX4 )
!= ( hAPP @ SX1 @ SX5 ) )
| ( SX4 = SX5 ) ) ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX4 ) @ SX0 ) )
| ! [SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX5 ) @ SX0 ) )
| ( ( hAPP @ SX1 @ SX4 )
!= ( hAPP @ SX1 @ SX5 ) )
| ( SX4 = SX5 ) ) )
| ( c_Fun_Oinj__on @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5442]) ).
thf(5569,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)],[5488]) ).
thf(5570,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ c_fequal @ SX0 ) ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ c_fequal @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5422]) ).
thf(5571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5502]) ).
thf(5572,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ c_Nat_OSuc @ SX1 )
= ( hAPP @ c_Nat_OSuc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5388]) ).
thf(5573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SX4 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX3 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX3 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SX4 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5423]) ).
thf(5574,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)],[5438]) ).
thf(5575,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( c_Set_OCollect @ SX2 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5461]) ).
thf(5576,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OlessThan @ SX3 @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OlessThan @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5425]) ).
thf(5577,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Fun_Oinj__on @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ( ( hAPP @ SX3 @ SX1 )
!= ( hAPP @ SX3 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ SX3 @ SX1 )
= ( hAPP @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5440]) ).
thf(5578,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 )
| ( c_Hoare__Mirabelle_Otriple__valid @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5384]) ).
thf(5579,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX1 @ SX0 @ SX4 ) @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5503]) ).
thf(5580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5482]) ).
thf(5581,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5490]) ).
thf(5582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5391]) ).
thf(5583,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( SX5 != SX4 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= SX0 ) )
| ~ ( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5432]) ).
thf(5584,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( hAPP @ SX2 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5448]) ).
thf(5585,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)],[5497]) ).
thf(5586,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( SX5
!= ( hAPP @ SX4 @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX3 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX0 ) @ SX5 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX0 @ SX4 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5408]) ).
thf(5587,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OgreaterThan @ SX3 @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OgreaterThan @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5426]) ).
thf(5588,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX1 ) @ SX0 ) ) )
| ( SX2 = SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( ( SX2 = SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5412]) ).
thf(5589,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SX0 ) @ v_ts ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5382]) ).
thf(5590,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX2 )
= ( hAPP @ SX0 @ SX3 ) ) )
| ~ ( ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5443]) ).
thf(5591,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) )
| ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5390]) ).
thf(5592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Predicate_Osymp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5507]) ).
thf(5593,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX4 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SX5 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX4 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX4 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX4 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SX5 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5430]) ).
thf(5594,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( c_Set_OCollect @ SX2 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( c_Set_OCollect @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5460]) ).
thf(5595,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SX1 @ SX0 )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX3 ) @ SX3 ) ) )
| ( ( hAPP @ SX0 @ SX2 )
!= ( hAPP @ SX0 @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX2 ) @ SX3 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5508]) ).
thf(5596,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 )
| ( ( hAPP @ SX2 @ SX1 )
= SX0 ) )
| ~ ( ( ( hAPP @ SX2 @ SX1 )
!= SX0 )
| ( ( c_Fun_Ofun__upd @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5433]) ).
thf(5597,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)],[5491]) ).
thf(5598,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5505]) ).
thf(5599,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)],[5494]) ).
thf(5600,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Fun_Oinj__on @ SX5 @ SX4 @ SX3 @ SX2 )
| ( ( hAPP @ SX3 @ SX1 )
!= ( hAPP @ SX3 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5441]) ).
thf(5601,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)],[5478]) ).
thf(5602,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)],[5479]) ).
thf(5603,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)],[5396]) ).
thf(5604,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SX4 @ SX3 @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5504]) ).
thf(5605,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)],[5399]) ).
thf(5606,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SX3 @ SX2 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5397]) ).
thf(5607,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX4 ) @ SX3 ) )
| ( SX2
!= ( hAPP @ SX1 @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX0 ) @ SX2 ) @ ( hAPP @ ( c_Set_Oimage @ SX5 @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5414]) ).
thf(5608,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)],[5457]) ).
thf(5609,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ ( hAPP @ SX0 @ SX3 ) ) @ ( hAPP @ ( c_Set_Oimage @ SX4 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5415]) ).
thf(5610,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)],[5394]) ).
thf(5611,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5481]) ).
thf(5612,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5472]) ).
thf(5613,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5419]) ).
thf(5614,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3 != SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5421]) ).
thf(5615,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)],[5495]) ).
thf(5616,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)],[5477]) ).
thf(5617,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX4 @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SX1 @ SX0 @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5471]) ).
thf(5618,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX4 @ SX3 )
!= SX2 )
| ( ( c_Fun_Ofun__upd @ SX1 @ SX0 @ SX4 @ SX3 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5437]) ).
thf(5619,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Typedef_Otype__definition @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ ( hAPP @ SX3 @ SX0 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5452]) ).
thf(5620,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ SX1 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ SX1 @ SX5 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5416]) ).
thf(5621,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Predicate_Otransp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5506]) ).
thf(5622,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5509]) ).
thf(5623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ SX2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5395]) ).
thf(5624,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)],[5500]) ).
thf(5625,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ ( c_Hilbert__Choice_OEps @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5483]) ).
thf(5626,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX0 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5417]) ).
thf(5627,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( c_Typedef_Otype__definition @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ( ( hAPP @ SX3 @ SX1 )
!= ( hAPP @ SX3 @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ SX3 @ SX1 )
= ( hAPP @ SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5455]) ).
thf(5628,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OatLeast @ SX3 @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OatLeast @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5428]) ).
thf(5629,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5489]) ).
thf(5630,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Fun_Oinj__on @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( ( SX1 != SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX0 ) @ SX2 ) )
| ( ( hAPP @ SX3 @ SX1 )
!= ( hAPP @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5439]) ).
thf(5631,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX2 @ SX1 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ ( hAPP @ SX1 @ SX3 ) ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ ( hAPP @ SX1 @ SX3 ) ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX4 ) @ SX3 ) @ ( hAPP @ ( c_Set_Ovimage @ SX4 @ SX2 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5451]) ).
thf(5632,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX3 @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5445]) ).
thf(5633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5518]) ).
thf(5634,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX5 @ SX4 )
!= SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX3 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX0 ) @ SX4 ) @ ( hAPP @ ( c_Set_Ovimage @ SX0 @ SX2 @ SX5 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5447]) ).
thf(5635,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OatMost @ SX3 @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( c_SetInterval_Oord_OatMost @ SX3 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5427]) ).
thf(5636,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX4 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SX3 @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5470]) ).
thf(5637,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SX4 @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5510]) ).
thf(5638,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)],[5453]) ).
thf(5639,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)],[5499]) ).
thf(5640,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( c_Set_OCollect @ SX2 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5462]) ).
thf(5641,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5444]) ).
thf(5642,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX4 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SX5 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX5 ) @ SX4 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SX5 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5429]) ).
thf(5643,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ( SX2 = SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5407]) ).
thf(5644,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( SX5 != SX4 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= SX0 ) )
| ~ ( ~ ( ( SX5 != SX4 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SX3 @ SX2 @ SX1 @ SX4 @ SX0 ) @ SX5 )
= ( hAPP @ SX1 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5435]) ).
thf(5645,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5383]) ).
thf(5646,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)],[5398]) ).
thf(5647,plain,
! [SV1: $i] :
( ( ! [SY637: $i,SY638: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY638 ) @ SY637 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY638 ) @ SY637 ) @ SV1 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY638 ) @ SY637 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5402]) ).
thf(5648,plain,
! [SV2: $i] :
( ( ! [SY639: $i,SY640: $i,SY641: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY641 ) @ SY640 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY641 ) @ SY639 ) @ SV2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY641 ) @ SY639 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY641 ) @ SY640 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5403]) ).
thf(5649,plain,
! [SV3: $i] :
( ( ! [SY642: $i,SY643: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY643 ) @ SY642 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY643 ) @ SY642 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5413]) ).
thf(5650,plain,
! [SV4: $i] :
( ( ! [SY644: $i,SY645: $i,SY646: $i] :
( ( c_Fun_Ofun__upd @ SY646 @ SY645 @ SY644 @ SV4 @ ( hAPP @ SY644 @ SV4 ) )
= SY644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(5651,plain,
! [SV5: $i] :
( ( ! [SY647: $i,SY648: $i,SY649: $i,SY650: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY650 @ SY649 @ SY648 @ SY647 @ SV5 ) @ SY647 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5434]) ).
thf(5652,plain,
! [SV6: $i] :
( ( ! [SY651: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY651 ) @ SV6 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5459]) ).
thf(5653,plain,
! [SV7: $i] :
( ( ! [SY652: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY652 ) @ SV7 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5654,plain,
! [SV8: $i] :
( ( ! [SY653: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY653 ) @ SV8 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5464]) ).
thf(5655,plain,
! [SV9: $i] :
( ( ! [SY654: $i,SY655: $i,SY656: $i,SY657: $i,SY658: $i,SY659: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY659 @ SY658 @ SY657 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY659 @ SY656 @ SY658 ) @ SY655 ) @ SY654 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY659 @ SY656 @ SY657 ) @ SY655 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY656 @ SY658 @ SY657 ) @ SY654 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5466]) ).
thf(5656,plain,
! [SV10: $i] :
( ( ! [SY660: $i,SY661: $i,SY662: $i,SY663: $i,SY664: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY664 @ SY663 @ SY662 @ SY661 ) @ SY660 ) @ SV10 )
= ( hAPP @ SY661 @ ( hAPP @ SY660 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5473]) ).
thf(5657,plain,
! [SV11: $i] :
( ( ! [SY665: $i,SY666: $i,SY667: $i,SY668: $i,SY669: $i,SY670: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY670 @ SY669 @ SY668 @ SY667 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY666 @ SY670 @ SY668 @ SY665 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY666 @ SY669 @ SY668 @ ( hAPP @ ( c_Fun_Ocomp @ SY670 @ SY669 @ SY666 @ SY667 ) @ SY665 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(5658,plain,
! [SV12: $i] :
( ( ! [SY671: $i,SY672: $i,SY673: $i,SY674: $i,SY675: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY675 @ SY674 @ SY673 @ SY672 ) @ SY671 ) @ SV12 )
= ( hAPP @ SY672 @ ( hAPP @ SY671 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5475]) ).
thf(5659,plain,
! [SV13: $i] :
( ( ! [SY676: $i,SY677: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY677 @ SY676 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY676 @ SY677 ) @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5485]) ).
thf(5660,plain,
! [SV14: $i] :
( ( ! [SY678: $i,SY679: $i,SY680: $i] :
( ( hAPP @ SY680 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY679 @ SY679 ) @ SY678 ) @ SY680 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY679 @ SY679 ) @ SY678 ) @ SY680 ) @ ( hAPP @ SY680 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(5661,plain,
! [SV15: $i] :
( ( ! [SY681: $i,SY682: $i,SY683: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SY682 ) @ SY681 ) ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SY682 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY683 ) @ SY681 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5662,plain,
! [SV16: $i] :
( ( ! [SY684: $i,SY685: $i,SY686: $i,SY687: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY687 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY687 @ SY686 ) @ SY685 ) @ SY684 ) ) @ SY685 ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY687 @ SY686 ) @ SY685 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5496]) ).
thf(5663,plain,
! [SV17: $i] :
( ( ! [SY688: $i] :
( ( hAPP @ ( c_List_Orev @ SY688 ) @ ( hAPP @ ( c_List_Orev @ SY688 ) @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(5664,plain,
! [SV18: $i] :
( ( class_Nat_Osize @ ( tc_Hoare__Mirabelle_Otriple @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5665,plain,
! [SV19: $i] :
( ( ! [SY689: $i] :
( ( hAPP @ ( c_COMBI @ SY689 ) @ SV19 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5512]) ).
thf(5666,plain,
! [SV20: $i] :
( ( ! [SY690: $i,SY691: $i,SY692: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY692 @ SY691 ) @ SY690 ) @ SV20 )
= SY690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(5667,plain,
! [SV21: $i] :
( ( ! [SY693: $i,SY694: $i,SY695: $i,SY696: $i,SY697: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY697 @ SY696 @ SY695 ) @ SY694 ) @ SY693 ) @ SV21 )
= ( hAPP @ SY694 @ ( hAPP @ SY693 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(5668,plain,
! [SV22: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i,SY701: $i,SY702: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY702 @ SY701 @ SY700 ) @ SY699 ) @ SY698 ) @ SV22 )
= ( hAPP @ ( hAPP @ SY699 @ SV22 ) @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5515]) ).
thf(5669,plain,
! [SV23: $i] :
( ( ! [SY703: $i,SY704: $i,SY705: $i,SY706: $i,SY707: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY707 @ SY706 @ SY705 ) @ SY704 ) @ SY703 ) @ SV23 )
= ( hAPP @ ( hAPP @ SY704 @ SV23 ) @ ( hAPP @ SY703 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5516]) ).
thf(5670,plain,
! [SV24: $i] :
( ( ! [SY708: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY708 ) @ SV24 ) )
| ( SY708 = SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(5671,plain,
( ( hBOOL @ c_fFalse )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5672,plain,
! [SV25: $i] :
( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV25 ) )
| ~ ( hBOOL @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(5673,plain,
! [SV26: $i] :
( ( ~ ~ ( hBOOL @ SV26 )
| ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5522]) ).
thf(5674,plain,
! [SV27: $i] :
( ( ! [SY709: $i] :
( ~ ( hBOOL @ SY709 )
| ~ ( hBOOL @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY709 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5675,plain,
! [SV28: $i] :
( ( ! [SY710: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY710 ) @ SV28 ) )
| ( hBOOL @ SY710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5676,plain,
! [SV29: $i] :
( ( ! [SY711: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY711 ) @ SV29 ) )
| ( hBOOL @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5677,plain,
! [SV30: $i] :
( ( ! [SY712: $i] :
( ~ ( hBOOL @ SY712 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY712 ) @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5526]) ).
thf(5678,plain,
! [SV31: $i] :
( ( ! [SY713: $i] :
( ~ ( hBOOL @ SY713 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV31 ) @ SY713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(5679,plain,
! [SV32: $i] :
( ( ! [SY714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY714 ) @ SV32 ) )
| ( hBOOL @ SY714 )
| ( hBOOL @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(5680,plain,
! [SV33: $i] :
( ( ! [SY715: $i] :
( ( hBOOL @ SY715 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY715 ) @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5681,plain,
! [SV34: $i] :
( ( ! [SY716: $i] :
( ~ ( hBOOL @ SY716 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV34 ) @ SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(5682,plain,
! [SV35: $i] :
( ( ! [SY717: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY717 ) @ SV35 ) )
| ~ ( hBOOL @ SY717 )
| ( hBOOL @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(5683,plain,
( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ v_n @ sK1_B_x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5684,plain,
! [SV36: $i] :
( ( ! [SY718: $i,SY719: $i,SY720: $i,SY721: $i,SY722: $i,SY723: $i,SY724: $i,SY725: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY725 @ SY724 @ SY723 @ SY722 ) @ SY721 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY720 @ SY724 @ SY723 @ SY719 ) @ SY718 ) )
| ( ( hAPP @ SY722 @ ( hAPP @ SY721 @ SV36 ) )
= ( hAPP @ SY719 @ ( hAPP @ SY718 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5534]) ).
thf(5685,plain,
! [SV37: $i] :
( ( ! [SY726: $i,SY727: $i] :
~ ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY727 @ SY726 @ SV37 )
| ! [SY728: $i] :
( ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY727 ) ) @ SX4 ) @ SY726 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY727 @ SY728 @ SX4 ) )
| ! [SY730: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY727 ) ) @ SY730 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY727 @ SY728 @ SY730 ) ) ) )
| ~ ( ~ ! [SY731: $i] :
( ~ ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY727 ) ) @ SX4 ) @ SY726 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY727 @ SY731 @ SX4 ) )
| ! [SY733: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY727 ) ) @ SY733 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY727 @ SY731 @ SY733 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SY727 @ SY726 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5686,plain,
! [SV38: $i] :
( ( ! [SY734: $i,SY735: $i,SY736: $i,SY737: $i,SY738: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY738 @ SY737 ) @ SY736 ) @ SY735 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY738 @ SY737 ) @ SY734 ) @ SV38 ) )
| ~ ( ( SY736 != SY734 )
| ( SY735 != SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5687,plain,
! [SV39: $i] :
( ( ! [SY739: $i,SY740: $i,SY741: $i] :
( ( SY741 != SY740 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY739 ) @ SY741 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY739 ) @ SY740 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY739 ) @ SY740 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY739 ) @ SY741 ) @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5688,plain,
! [SV40: $i] :
( ( ! [SY742: $i,SY743: $i,SY744: $i,SY745: $i,SY746: $i] :
( ~ ( c_Typedef_Otype__definition @ SY746 @ SY745 @ SY744 @ SY743 @ SY742 )
| ( ( hAPP @ SY743 @ ( hAPP @ SY744 @ SV40 ) )
= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5689,plain,
! [SV41: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i,SY750: $i,SY751: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY751 @ SY750 @ SY749 )
| ( ( hAPP @ ( hAPP @ SY749 @ SY748 ) @ ( hAPP @ ( hAPP @ SY749 @ SY747 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SY749 @ SY747 ) @ ( hAPP @ ( hAPP @ SY749 @ SY748 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(5690,plain,
! [SV42: $i] :
( ( ! [SY752: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY752 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SY752 = SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5691,plain,
! [SV43: $i] :
( ( ! [SY753: $i,SY754: $i,SY755: $i,SY756: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY756 ) @ ( hAPP @ SY755 @ SY754 ) ) @ SY753 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SY754 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SY756 @ SY755 ) @ SY753 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5541]) ).
thf(5692,plain,
! [SV44: $i] :
( ( ! [SY757: $i,SY758: $i,SY759: $i,SY760: $i,SY761: $i,SY762: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY762 @ SY761 @ SY760 @ SY759 @ SY758 ) @ SY757 ) @ SV44 ) )
| ~ ! [SY763: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY759 @ SY757 ) @ SY763 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY758 @ SY763 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY764: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY759 @ SY757 ) @ SY764 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY758 @ SY764 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY762 @ SY761 @ SY760 @ SY759 @ SY758 ) @ SY757 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5542]) ).
thf(5693,plain,
! [SV45: $i] :
( ( ! [SY765: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY765 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
| ( SY765 = SV45 ) )
| ~ ( ( SY765 != SV45 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY765 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(5694,plain,
! [SV46: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV46 )
!= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(5695,plain,
! [SV47: $i] :
( ( ! [SY766: $i,SY767: $i,SY768: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY768 ) @ SY767 ) @ SY766 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY768 ) @ SY767 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY768 ) @ SV47 ) @ SY766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(5696,plain,
! [SV48: $i] :
( ( ! [SY769: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY769 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
| ( SY769 = SV48 ) )
| ~ ( ( SY769 != SV48 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY769 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5697,plain,
! [SV49: $i] :
( ( ! [SY770: $i,SY771: $i,SY772: $i,SY773: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ SY771 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY770 ) @ SV49 ) )
| ~ ! [SY774: $i] :
~ ( ~ ( ( SY772
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY770 ) @ SY774 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY774 ) @ SY771 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ SY774 )
!= SY770 )
| ( SY771
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY774 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY775: $i] :
~ ( ~ ( ( SY772
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY770 ) @ SY775 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY775 ) @ SY771 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ SY775 )
!= SY770 )
| ( SY771
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY775 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY772 ) @ SY771 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY773 ) @ SY770 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(5698,plain,
! [SV50: $i] :
( ( ! [SY776: $i,SY777: $i,SY778: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY778 ) @ SY777 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY778 ) @ SY776 ) @ SV50 ) ) )
| ~ ( ( SY777 != SY776 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY778 ) @ SY777 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(5699,plain,
! [SV51: $i] :
( ( ! [SY779: $i,SY780: $i,SY781: $i,SY782: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY782 @ SY781 ) @ SY780 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY779 @ SV51 @ SY782 ) @ SY780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(5700,plain,
! [SV52: $i] :
( ( ! [SY783: $i,SY784: $i] :
( ~ ( hBOOL @ ( hAPP @ SY784 @ SY783 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV52 ) @ SY783 ) @ ( hAPP @ ( c_Set_OCollect @ SV52 ) @ SY784 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(5701,plain,
! [SV53: $i] :
( ( ! [SY785: $i,SY786: $i,SY787: $i,SY788: $i,SY789: $i] :
( ~ ( c_Typedef_Otype__definition @ SY789 @ SY788 @ SY787 @ SY786 @ SY785 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY788 ) @ SV53 ) @ SY785 ) )
| ( ( hAPP @ SY787 @ ( hAPP @ SY786 @ SV53 ) )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5551]) ).
thf(5702,plain,
! [SV54: $i] :
( ( ! [SY790: $i,SY791: $i,SY792: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY792 ) @ SY791 ) @ SY790 ) @ SV54 ) )
| ( SY791 = SV54 )
| ( hBOOL @ ( hAPP @ SY790 @ SV54 ) ) )
| ~ ( ~ ( ( SY791 = SV54 )
| ( hBOOL @ ( hAPP @ SY790 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY792 ) @ SY791 ) @ SY790 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5552]) ).
thf(5703,plain,
! [SV55: $i] :
( ( ! [SY793: $i,SY794: $i,SY795: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY795 ) @ SY794 ) @ SY793 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY795 ) @ SY794 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY795 ) @ SY794 ) @ SY793 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY795 ) @ SY794 ) @ SV55 ) )
| ( SY793 = SV55 ) )
| ~ ( ( SY793 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY795 ) @ SY794 ) @ SY793 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY795 ) @ SY794 ) @ SV55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5553]) ).
thf(5704,plain,
! [SV56: $i] :
( ( ! [SY796: $i,SY797: $i,SY798: $i,SY799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY799 ) @ SY798 ) @ ( hAPP @ ( c_Set_Ovimage @ SY799 @ SY797 @ SY796 ) @ SV56 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY797 ) @ ( hAPP @ SY796 @ SY798 ) ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5705,plain,
! [SV57: $i] :
( ( ! [SY800: $i,SY801: $i] :
( ~ ( c_Predicate_Oreflp @ SY801 @ SY800 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY800 @ SV57 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(5706,plain,
! [SV58: $i] :
( ( ! [SY802: $i,SY803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY803 ) @ SY802 ) @ SV58 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY803 ) @ SY802 ) @ SV58 )
= SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(5707,plain,
! [SV59: $i] :
( ( ! [SY804: $i,SY805: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SY805 @ SY804 ) @ SV59 ) )
| ! [SY806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY805 ) @ SY806 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SY804 @ SY806 ) ) ) )
| ~ ( ~ ! [SY807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY805 ) @ SY807 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SY804 @ SY807 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SY805 @ SY804 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(5708,plain,
! [SV60: $i] :
( ( ! [SY808: $i,SY809: $i,SY810: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY810 @ SY809 ) @ SY808 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY809 @ SV60 ) @ SY808 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY810 @ SY809 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5558]) ).
thf(5709,plain,
! [SV61: $i] :
( ( ! [SY811: $i,SY812: $i,SY813: $i,SY814: $i,SY815: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY815 ) @ SY814 ) @ SY813 )
!= SY812 )
| ( SY811
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY815 ) @ SY813 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY815 ) @ SY814 ) @ SY811 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY815 ) @ SY812 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5559]) ).
thf(5710,plain,
! [SV62: $i] :
( ( ! [SY816: $i,SY817: $i,SY818: $i,SY819: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY819 @ SY818 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY818 @ SY817 ) @ SY816 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY818 @ SY816 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY818 @ SY817 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5711,plain,
! [SV63: $i] :
( ( SV63
!= ( hAPP @ c_Nat_OSuc @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5712,plain,
! [SV64: $i] :
( ( ! [SY820: $i,SY821: $i] :
( ~ ( hBOOL @ ( hAPP @ SY821 @ SY820 ) )
| ( hBOOL @ ( hAPP @ SY821 @ ( c_Hilbert__Choice_OEps @ SV64 @ SY821 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5562]) ).
thf(5713,plain,
! [SV65: $i] :
( ( ! [SY822: $i,SY823: $i,SY824: $i] :
( ( SY824 != SY823 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY822 ) @ SV65 ) @ SY824 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY822 ) @ SV65 ) @ SY823 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY822 ) @ SV65 ) @ SY824 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY822 ) @ SV65 ) @ SY823 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5563]) ).
thf(5714,plain,
! [SV66: $i] :
( ( ! [SY825: $i,SY826: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY826 @ SX3 ) )
| ( SY825
!= ( c_Hilbert__Choice_OEps @ SV66 @ SY826 ) )
| ( hBOOL @ ( hAPP @ SY826 @ SY825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5564]) ).
thf(5715,plain,
! [SV67: $i] :
( ( ! [SY828: $i,SY829: $i,SY830: $i,SY831: $i,SY832: $i,SY833: $i,SY834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY834 @ SY833 ) @ SY832 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY831 @ SY832 ) @ SY830 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY829 @ SY828 @ SV67 @ SY834 @ SY831 ) @ SY833 ) @ SY830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5716,plain,
! [SV68: $i] :
( ( ! [SY835: $i,SY836: $i,SY837: $i,SY838: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SY837 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY838 @ SY836 @ SY835 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY836 @ SY835 ) @ SY837 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY836 @ SY837 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY836 @ SY835 ) @ SY837 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY836 @ SY837 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY838 ) @ SY837 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY838 @ SY836 @ SY835 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(5717,plain,
! [SV69: $i] :
( ( ! [SY839: $i,SY840: $i,SY841: $i,SY842: $i,SY843: $i] :
( ~ ( ( SY843 != SY842 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY841 @ SY840 @ SY839 @ SY842 @ SV69 ) @ SY843 )
= ( hAPP @ SY839 @ SY843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5718,plain,
! [SV70: $i] :
( ( ! [SY844: $i,SY845: $i,SY846: $i] :
~ ( ~ ( ~ ( c_Fun_Oinj__on @ SY846 @ SY845 @ SY844 @ SV70 )
| ! [SY847: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY846 ) @ SY847 ) @ SV70 ) )
| ! [SY848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY846 ) @ SY848 ) @ SV70 ) )
| ( ( hAPP @ SY844 @ SY847 )
!= ( hAPP @ SY844 @ SY848 ) )
| ( SY847 = SY848 ) ) ) )
| ~ ( ~ ! [SY849: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY846 ) @ SY849 ) @ SV70 ) )
| ! [SY850: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY846 ) @ SY850 ) @ SV70 ) )
| ( ( hAPP @ SY844 @ SY849 )
!= ( hAPP @ SY844 @ SY850 ) )
| ( SY849 = SY850 ) ) )
| ( c_Fun_Oinj__on @ SY846 @ SY845 @ SY844 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5568]) ).
thf(5719,plain,
! [SV71: $i] :
( ( ! [SY851: $i,SY852: $i,SY853: $i,SY854: $i,SY855: $i,SY856: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY856 @ SY855 @ SY854 @ SY853 @ SY852 @ SY851 )
| ( ( hAPP @ ( hAPP @ SY854 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5569]) ).
thf(5720,plain,
! [SV72: $i] :
( ( ! [SY857: $i,SY858: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY858 ) @ SY857 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SY857 = SV72 ) )
| ~ ( ( SY857 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY858 ) @ SY857 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(5721,plain,
! [SV73: $i] :
( ( ! [SY859: $i,SY860: $i,SY861: $i,SY862: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY862 @ SY861 @ SY860 ) @ SY859 ) @ SV73 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY860 @ SV73 ) @ SY859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5722,plain,
! [SV74: $i] :
( ( ! [SY863: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY863 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
| ( SY863 = SV74 ) )
| ~ ( ( SY863 != SV74 )
| ( ( hAPP @ c_Nat_OSuc @ SY863 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5723,plain,
! [SV75: $i] :
( ( ! [SY864: $i,SY865: $i,SY866: $i,SY867: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY867 ) @ SY866 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY867 @ SY865 @ SY864 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY865 @ SY864 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY865 @ SY866 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY865 @ SY864 ) @ SY866 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY865 @ SY866 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY867 ) @ SY866 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY867 @ SY865 @ SY864 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5573]) ).
thf(5724,plain,
! [SV76: $i] :
( ( ! [SY868: $i,SY869: $i,SY870: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY870 @ SY869 @ SY868 )
| ( ( hAPP @ ( hAPP @ SY869 @ SV76 ) @ SV76 )
= SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5725,plain,
! [SV77: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY872 ) @ SY871 ) @ ( hAPP @ ( c_Set_OCollect @ SY872 ) @ SV77 ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ SY871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5726,plain,
! [SV78: $i] :
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY875 ) @ SY874 ) @ ( c_SetInterval_Oord_OlessThan @ SY875 @ SY873 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY873 @ SY874 ) @ SV78 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY873 @ SY874 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY875 ) @ SY874 ) @ ( c_SetInterval_Oord_OlessThan @ SY875 @ SY873 @ SV78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(5727,plain,
! [SV79: $i] :
( ( ! [SY876: $i,SY877: $i,SY878: $i,SY879: $i,SY880: $i] :
( ~ ( c_Fun_Oinj__on @ SY880 @ SY879 @ SY878 @ SY877 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY880 ) @ SY876 ) @ SY877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY880 ) @ SV79 ) @ SY877 ) )
| ~ ( ~ ( ( ( hAPP @ SY878 @ SY876 )
!= ( hAPP @ SY878 @ SV79 ) )
| ( SY876 = SV79 ) )
| ~ ( ( SY876 != SV79 )
| ( ( hAPP @ SY878 @ SY876 )
= ( hAPP @ SY878 @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(5728,plain,
! [SV80: $i] :
( ( ! [SY881: $i,SY882: $i] :
( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY882 @ ( hAPP @ c_Nat_OSuc @ SY881 ) @ SV80 )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY882 @ SY881 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(5729,plain,
! [SV81: $i] :
( ( ! [SY883: $i,SY884: $i,SY885: $i,SY886: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY886 @ SY885 ) @ SY884 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY883 @ SV81 @ SY886 ) @ SY884 ) @ SY885 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5579]) ).
thf(5730,plain,
! [SV82: $i] :
( ( ! [SY887: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY887 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY887 @ ( c_Hilbert__Choice_OEps @ SV82 @ SY887 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5580]) ).
thf(5731,plain,
! [SV83: $i] :
( ( ! [SY889: $i,SY890: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY890 ) @ SY889 ) @ SV83 )
!= SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5581]) ).
thf(5732,plain,
! [SV84: $i] :
( ( ! [SY891: $i,SY892: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY892 @ SY891 ) @ SV84 ) )
| ! [SY893: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY891 @ SY893 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY892 @ SY891 ) @ SY893 ) ) ) )
| ~ ( ~ ! [SY894: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY891 @ SY894 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY892 @ SY891 ) @ SY894 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY892 @ SY891 ) @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5582]) ).
thf(5733,plain,
! [SV85: $i] :
( ( ! [SY895: $i,SY896: $i,SY897: $i,SY898: $i,SY899: $i] :
~ ( ~ ( ( SY899 != SY898 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY897 @ SY896 @ SY895 @ SY898 @ SV85 ) @ SY899 )
= SV85 ) )
| ~ ( ~ ( ( SY899 != SY898 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY897 @ SY896 @ SY895 @ SY898 @ SV85 ) @ SY899 )
= ( hAPP @ SY895 @ SY899 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5583]) ).
thf(5734,plain,
! [SV86: $i] :
( ( ! [SY900: $i,SY901: $i,SY902: $i,SY903: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY903 @ SY902 @ SY901 ) @ SY900 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SY900 @ ( hAPP @ SY901 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY900 @ ( hAPP @ SY901 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY903 @ SY902 @ SY901 ) @ SY900 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(5735,plain,
! [SV87: $i] :
( ( ! [SY904: $i,SY905: $i,SY906: $i,SY907: $i,SY908: $i] :
( ~ ( ( SY908 != SY907 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY906 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY906 @ SY905 ) @ SY908 ) @ SY904 ) ) @ SY907 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY906 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY906 @ SY905 ) @ SY907 ) @ SV87 ) ) @ SY908 ) @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(5736,plain,
! [SV88: $i] :
( ( ! [SY909: $i,SY910: $i,SY911: $i,SY912: $i,SY913: $i] :
( ( SY913
!= ( hAPP @ SY912 @ SY911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY910 ) @ SY911 ) @ SY909 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SY913 ) @ ( hAPP @ ( c_Set_Oimage @ SY910 @ SV88 @ SY912 ) @ SY909 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(5737,plain,
! [SV89: $i] :
( ( ! [SY914: $i,SY915: $i,SY916: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY916 ) @ SY915 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY916 @ SY914 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY914 @ SV89 ) @ SY915 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY914 @ SV89 ) @ SY915 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY916 ) @ SY915 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY916 @ SY914 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(5738,plain,
! [SV90: $i] :
( ( ! [SY917: $i,SY918: $i,SY919: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY919 ) @ SY918 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY919 ) @ SY917 ) @ SV90 ) ) )
| ( SY918 = SY917 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY919 ) @ SY918 ) @ SV90 ) ) )
| ~ ( ~ ( ( SY918 = SY917 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY919 ) @ SY918 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY919 ) @ SY918 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY919 ) @ SY917 ) @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(5739,plain,
! [SV91: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV91 ) @ v_ts ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(5740,plain,
! [SV92: $i] :
( ( ! [SY920: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SY920 @ SV92 )
| ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
| ~ ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SY920 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(5741,plain,
! [SV93: $i] :
( ( ! [SY925: $i,SY926: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY926 @ SY925 ) @ SV93 ) )
| ! [SY927: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY925 @ SY927 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY926 @ SY925 ) @ SY927 ) ) ) )
| ~ ( ~ ! [SY928: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY925 @ SY928 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY926 @ SY925 ) @ SY928 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY926 @ SY925 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(5742,plain,
! [SV94: $i] :
( ( ! [SY929: $i,SY930: $i,SY931: $i] :
( ~ ( c_Predicate_Osymp @ SY931 @ SY930 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY930 @ SY929 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY930 @ SV94 ) @ SY929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(5743,plain,
! [SV95: $i] :
( ( ! [SY932: $i,SY933: $i,SY934: $i,SY935: $i,SY936: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY936 ) @ SY935 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY936 @ SY934 @ SY933 @ SY932 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY933 @ SY932 ) @ SY935 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY934 @ SY935 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY933 @ SY932 ) @ SY935 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY934 @ SY935 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY936 ) @ SY935 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY936 @ SY934 @ SY933 @ SY932 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(5744,plain,
! [SV96: $i] :
( ( ! [SY937: $i,SY938: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY938 ) @ SY937 ) @ ( hAPP @ ( c_Set_OCollect @ SY938 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SY937 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV96 @ SY937 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY938 ) @ SY937 ) @ ( hAPP @ ( c_Set_OCollect @ SY938 ) @ SV96 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5594]) ).
thf(5745,plain,
! [SV97: $i] :
( ( ! [SY939: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SY939 @ SV97 )
| ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SY939 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5595]) ).
thf(5746,plain,
! [SV98: $i] :
( ( ! [SY946: $i,SY947: $i,SY948: $i,SY949: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY949 @ SY948 @ SY947 @ SY946 @ SV98 )
!= SY947 )
| ( ( hAPP @ SY947 @ SY946 )
= SV98 ) )
| ~ ( ( ( hAPP @ SY947 @ SY946 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SY949 @ SY948 @ SY947 @ SY946 @ SV98 )
= SY947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(5747,plain,
! [SV99: $i] :
( ( ! [SY950: $i,SY951: $i,SY952: $i,SY953: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY953 ) @ SY952 ) @ SY951 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY953 ) @ SY950 ) @ SV99 ) )
| ~ ( ( SY952 != SY950 )
| ( SY951 != SV99 ) ) )
| ~ ( ~ ~ ( ( SY952 != SY950 )
| ( SY951 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY953 ) @ SY952 ) @ SY951 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY953 ) @ SY950 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(5748,plain,
! [SV100: $i] :
( ( ! [SY954: $i,SY955: $i,SY956: $i,SY957: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY957 @ SY956 @ SY955 ) @ SY954 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY955 @ SV100 ) @ SY954 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY955 @ SV100 ) @ SY954 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY957 @ SY956 @ SY955 ) @ SY954 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5598]) ).
thf(5749,plain,
! [SV101: $i] :
( ( ! [SY958: $i,SY959: $i,SY960: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY960 ) @ SY959 ) @ SY958 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY960 ) @ SY959 ) @ SV101 ) )
| ( SY958 = SV101 ) )
| ~ ( ( SY958 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY960 ) @ SY959 ) @ SY958 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY960 ) @ SY959 ) @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5599]) ).
thf(5750,plain,
! [SV102: $i] :
( ( ! [SY961: $i,SY962: $i,SY963: $i,SY964: $i,SY965: $i] :
( ~ ( c_Fun_Oinj__on @ SY965 @ SY964 @ SY963 @ SY962 )
| ( ( hAPP @ SY963 @ SY961 )
!= ( hAPP @ SY963 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY965 ) @ SY961 ) @ SY962 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY965 ) @ SV102 ) @ SY962 ) )
| ( SY961 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5600]) ).
thf(5751,plain,
! [SV103: $i] :
( ( ! [SY966: $i,SY967: $i,SY968: $i,SY969: $i,SY970: $i,SY971: $i,SY972: $i,SY973: $i,SY974: $i,SY975: $i] :
( ( ( hAPP @ SY975 @ ( hAPP @ SY974 @ SY973 ) )
!= ( hAPP @ SY972 @ ( hAPP @ SY971 @ SY970 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY969 @ SY968 @ SY967 @ SY975 ) @ SY974 ) @ SY973 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY966 @ SY968 @ SV103 @ SY972 ) @ SY971 ) @ SY970 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5752,plain,
! [SV104: $i] :
( ( ! [SY976: $i,SY977: $i,SY978: $i,SY979: $i,SY980: $i,SY981: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY981 @ SY980 @ SY979 @ SY978 ) @ SY977 )
!= SY976 )
| ( ( hAPP @ SY978 @ ( hAPP @ SY977 @ SV104 ) )
= ( hAPP @ SY976 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(5753,plain,
! [SV105: $i] :
( ( ! [SY982: $i,SY983: $i,SY984: $i,SY985: $i,SY986: $i] :
( ( SY986 != SY985 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY984 @ SY983 @ SY982 ) @ SV105 ) @ SY986 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY984 @ SY983 @ SY982 ) @ SV105 ) @ SY985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(5754,plain,
! [SV106: $i] :
( ( ! [SY987: $i,SY988: $i,SY989: $i,SY990: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY990 @ SY989 @ SY988 ) @ SY987 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY988 @ SV106 ) @ SY987 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY988 @ SV106 ) @ SY987 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY990 @ SY989 @ SY988 ) @ SY987 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5604]) ).
thf(5755,plain,
! [SV107: $i] :
( ( ! [SY991: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY991 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
| ( SY991 = SV107 ) )
| ~ ( ( SY991 != SV107 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY991 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(5756,plain,
! [SV108: $i] :
( ( ! [SY992: $i,SY993: $i,SY994: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY994 @ SY993 ) @ SY992 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY994 @ SY993 ) @ SV108 ) )
| ( SY992 = SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(5757,plain,
! [SV109: $i] :
( ( ! [SY995: $i,SY996: $i,SY997: $i,SY998: $i,SY999: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY999 ) @ SY998 ) @ SY997 ) )
| ( SY996
!= ( hAPP @ SY995 @ SY998 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SY996 ) @ ( hAPP @ ( c_Set_Oimage @ SY999 @ SV109 @ SY995 ) @ SY997 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(5758,plain,
! [SV110: $i] :
( ( ! [SY1000: $i,SY1001: $i,SY1002: $i,SY1003: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1003 @ SY1002 @ SY1001 )
| ( ( hAPP @ ( hAPP @ SY1001 @ SY1000 ) @ ( hAPP @ ( hAPP @ SY1001 @ SY1000 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SY1001 @ SY1000 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5608]) ).
thf(5759,plain,
! [SV111: $i] :
( ( ! [SY1004: $i,SY1005: $i,SY1006: $i,SY1007: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1007 ) @ SY1006 ) @ SY1005 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1004 ) @ ( hAPP @ SV111 @ SY1006 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1007 @ SY1004 @ SV111 ) @ SY1005 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5609]) ).
thf(5760,plain,
! [SV112: $i] :
( ( ! [SY1008: $i,SY1009: $i,SY1010: $i,SY1011: $i,SY1012: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1012 @ SY1011 ) @ SY1010 ) @ SY1009 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1012 @ SY1011 ) @ SY1008 ) @ SV112 ) )
| ~ ( ( SY1010 != SY1008 )
| ( SY1009 != SV112 ) ) )
| ~ ( ~ ~ ( ( SY1010 != SY1008 )
| ( SY1009 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1012 @ SY1011 ) @ SY1010 ) @ SY1009 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1012 @ SY1011 ) @ SY1008 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(5761,plain,
! [SV113: $i] :
( ( ! [SY1013: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1013 @ ( c_Hilbert__Choice_OEps @ SV113 @ SY1013 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1013 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1013 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1013 @ ( c_Hilbert__Choice_OEps @ SV113 @ SY1013 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5762,plain,
! [SV114: $i] :
( ( ! [SY1016: $i,SY1017: $i,SY1018: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1018 @ SY1017 @ SY1016 ) @ SV114 ) )
| ~ ! [SY1019: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1016 @ SV114 ) @ SY1019 ) ) )
| ~ ( ~ ~ ! [SY1020: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1016 @ SV114 ) @ SY1020 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1018 @ SY1017 @ SY1016 ) @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(5763,plain,
! [SV115: $i] :
( ( ! [SY1021: $i,SY1022: $i,SY1023: $i] :
( ( SY1023 != SY1022 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1021 ) @ SV115 ) @ SY1023 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1021 ) @ SV115 ) @ SY1022 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1021 ) @ SV115 ) @ SY1022 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1021 ) @ SV115 ) @ SY1023 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5613]) ).
thf(5764,plain,
! [SV116: $i] :
( ( ! [SY1024: $i,SY1025: $i,SY1026: $i] :
( ( SY1026 != SY1025 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1024 ) @ SY1025 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1024 ) @ SY1026 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5614]) ).
thf(5765,plain,
! [SV117: $i] :
( ( ! [SY1027: $i,SY1028: $i,SY1029: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1029 ) @ SY1028 ) @ SY1027 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1029 ) @ SV117 ) @ SY1027 ) )
| ( SY1028 = SV117 ) )
| ~ ( ( SY1028 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1029 ) @ SY1028 ) @ SY1027 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1029 ) @ SV117 ) @ SY1027 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5615]) ).
thf(5766,plain,
! [SV118: $i] :
( ( ! [SY1030: $i,SY1031: $i,SY1032: $i,SY1033: $i,SY1034: $i,SY1035: $i,SY1036: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1036 @ SY1035 @ SY1034 @ SY1033 ) @ SY1032 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1031 @ SY1035 @ SY1034 @ SY1030 ) @ SV118 ) )
| ! [SY1037: $i] :
( ( hAPP @ SY1033 @ ( hAPP @ SY1032 @ SY1037 ) )
= ( hAPP @ SY1030 @ ( hAPP @ SV118 @ SY1037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5616]) ).
thf(5767,plain,
! [SV119: $i] :
( ( ! [SY1038: $i,SY1039: $i,SY1040: $i,SY1041: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1041 @ SY1040 ) @ SY1039 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1038 @ SV119 @ SY1041 ) @ SY1040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5617]) ).
thf(5768,plain,
! [SV120: $i] :
( ( ! [SY1042: $i,SY1043: $i,SY1044: $i,SY1045: $i] :
( ( ( hAPP @ SY1045 @ SY1044 )
!= SY1043 )
| ( ( c_Fun_Ofun__upd @ SY1042 @ SV120 @ SY1045 @ SY1044 @ SY1043 )
= SY1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5618]) ).
thf(5769,plain,
! [SV121: $i] :
( ( ! [SY1046: $i,SY1047: $i,SY1048: $i,SY1049: $i,SY1050: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1050 @ SY1049 @ SY1048 @ SY1047 @ SY1046 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1049 ) @ ( hAPP @ SY1048 @ SV121 ) ) @ SY1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5619]) ).
thf(5770,plain,
! [SV122: $i] :
( ( ! [SY1051: $i,SY1052: $i,SY1053: $i,SY1054: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1054 ) @ SY1053 ) @ ( hAPP @ ( c_Set_Oimage @ SY1052 @ SY1054 @ SY1051 ) @ SV122 ) ) )
| ~ ! [SY1055: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1052 ) @ SY1055 ) @ SV122 ) )
| ( SY1053
!= ( hAPP @ SY1051 @ SY1055 ) ) ) )
| ~ ( ~ ~ ! [SY1056: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1052 ) @ SY1056 ) @ SV122 ) )
| ( SY1053
!= ( hAPP @ SY1051 @ SY1056 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1054 ) @ SY1053 ) @ ( hAPP @ ( c_Set_Oimage @ SY1052 @ SY1054 @ SY1051 ) @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5620]) ).
thf(5771,plain,
! [SV123: $i] :
( ( ! [SY1057: $i,SY1058: $i,SY1059: $i,SY1060: $i] :
( ~ ( c_Predicate_Otransp @ SY1060 @ SY1059 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1059 @ SY1058 ) @ SY1057 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1059 @ SY1057 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1059 @ SY1058 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5621]) ).
thf(5772,plain,
! [SV124: $i] :
( ( ! [SY1061: $i,SY1062: $i,SY1063: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1063 @ SY1062 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1062 @ SY1061 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1062 @ SV124 ) @ SY1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5622]) ).
thf(5773,plain,
! [SV125: $i] :
( ( ! [SY1064: $i,SY1065: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1065 @ SX3 ) )
| ! [SY1067: $i,SY1068: $i] : ( hBOOL @ ( hAPP @ SY1065 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1064 @ SV125 ) @ SY1067 ) @ SY1068 ) ) ) )
| ~ ( ~ ! [SY1069: $i,SY1070: $i] : ( hBOOL @ ( hAPP @ SY1065 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1064 @ SV125 ) @ SY1069 ) @ SY1070 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1065 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(5774,plain,
! [SV126: $i] :
( ( ! [SY1072: $i,SY1073: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1073 ) @ SY1072 )
!= SV126 )
| ( SY1072
= ( hAPP @ ( c_List_Orev @ SY1073 ) @ SV126 ) ) )
| ~ ( ( SY1072
!= ( hAPP @ ( c_List_Orev @ SY1073 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1073 ) @ SY1072 )
= SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5624]) ).
thf(5775,plain,
! [SV127: $i] :
( ( ! [SY1074: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1074 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1074 @ ( c_Hilbert__Choice_OEps @ SV127 @ SY1074 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5625]) ).
thf(5776,plain,
! [SV128: $i] :
( ( ! [SY1076: $i,SY1077: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1077 ) @ SY1076 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SY1076 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV128 @ SY1076 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1077 ) @ SY1076 ) @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5626]) ).
thf(5777,plain,
! [SV129: $i] :
( ( ! [SY1078: $i,SY1079: $i,SY1080: $i,SY1081: $i,SY1082: $i,SY1083: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1083 @ SY1082 @ SY1081 @ SY1080 @ SY1079 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1082 ) @ SY1078 ) @ SY1079 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1082 ) @ SV129 ) @ SY1079 ) )
| ~ ( ~ ( ( ( hAPP @ SY1080 @ SY1078 )
!= ( hAPP @ SY1080 @ SV129 ) )
| ( SY1078 = SV129 ) )
| ~ ( ( SY1078 != SV129 )
| ( ( hAPP @ SY1080 @ SY1078 )
= ( hAPP @ SY1080 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5627]) ).
thf(5778,plain,
! [SV130: $i] :
( ( ! [SY1084: $i,SY1085: $i,SY1086: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1086 ) @ SY1085 ) @ ( c_SetInterval_Oord_OatLeast @ SY1086 @ SY1084 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1084 @ SV130 ) @ SY1085 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1084 @ SV130 ) @ SY1085 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1086 ) @ SY1085 ) @ ( c_SetInterval_Oord_OatLeast @ SY1086 @ SY1084 @ SV130 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5628]) ).
thf(5779,plain,
! [SV131: $i] :
( ( ! [SY1087: $i,SY1088: $i] :
( SY1088
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1087 ) @ SV131 ) @ SY1088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(5780,plain,
! [SV132: $i] :
( ( ! [SY1089: $i,SY1090: $i,SY1091: $i,SY1092: $i,SY1093: $i] :
( ~ ( c_Fun_Oinj__on @ SY1093 @ SY1092 @ SY1091 @ SY1090 )
| ~ ( ( SY1089 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1093 ) @ SY1089 ) @ SY1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1093 ) @ SV132 ) @ SY1090 ) )
| ( ( hAPP @ SY1091 @ SY1089 )
!= ( hAPP @ SY1091 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(5781,plain,
! [SV133: $i] :
( ( ! [SY1094: $i,SY1095: $i,SY1096: $i,SY1097: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1097 ) @ SY1096 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1097 @ SY1095 @ SY1094 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1095 ) @ ( hAPP @ SY1094 @ SY1096 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1095 ) @ ( hAPP @ SY1094 @ SY1096 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1097 ) @ SY1096 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1097 @ SY1095 @ SY1094 ) @ SV133 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(5782,plain,
! [SV134: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1100 @ SY1099 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1099 @ SY1098 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1099 @ SV134 ) @ SY1098 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(5783,plain,
! [SV135: $i] :
( ( ! [SY1101: $i] :
( ( SY1101 != SV135 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY1101 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5633]) ).
thf(5784,plain,
! [SV136: $i] :
( ( ! [SY1102: $i,SY1103: $i,SY1104: $i,SY1105: $i,SY1106: $i] :
( ( ( hAPP @ SY1106 @ SY1105 )
!= SY1104 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1103 ) @ SY1104 ) @ SY1102 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SY1105 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SY1103 @ SY1106 ) @ SY1102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(5785,plain,
! [SV137: $i] :
( ( ! [SY1107: $i,SY1108: $i,SY1109: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1109 ) @ SY1108 ) @ ( c_SetInterval_Oord_OatMost @ SY1109 @ SY1107 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1107 @ SY1108 ) @ SV137 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1107 @ SY1108 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1109 ) @ SY1108 ) @ ( c_SetInterval_Oord_OatMost @ SY1109 @ SY1107 @ SV137 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5635]) ).
thf(5786,plain,
! [SV138: $i] :
( ( ! [SY1110: $i,SY1111: $i,SY1112: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1112 @ SY1111 @ SY1110 ) @ SV138 ) )
| ~ ! [SY1113: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1110 @ SY1113 ) @ SV138 ) ) )
| ~ ( ~ ~ ! [SY1114: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1110 @ SY1114 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1112 @ SY1111 @ SY1110 ) @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(5787,plain,
! [SV139: $i] :
( ( ! [SY1115: $i,SY1116: $i,SY1117: $i,SY1118: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1118 @ SY1117 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1117 @ SY1116 ) @ SY1115 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1117 @ SY1115 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1117 @ SY1116 ) @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(5788,plain,
! [SV140: $i] :
( ( ! [SY1119: $i,SY1120: $i,SY1121: $i,SY1122: $i,SY1123: $i,SY1124: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1124 @ SY1123 @ SY1122 @ SY1121 @ SY1120 )
| ~ ( ~ ( ( ( hAPP @ SY1122 @ SY1119 )
!= ( hAPP @ SY1122 @ SV140 ) )
| ( SY1119 = SV140 ) )
| ~ ( ( SY1119 != SV140 )
| ( ( hAPP @ SY1122 @ SY1119 )
= ( hAPP @ SY1122 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(5789,plain,
! [SV141: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1126 ) @ SY1125 )
!= ( hAPP @ ( c_List_Orev @ SY1126 ) @ SV141 ) )
| ( SY1125 = SV141 ) )
| ~ ( ( SY1125 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SY1126 ) @ SY1125 )
= ( hAPP @ ( c_List_Orev @ SY1126 ) @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(5790,plain,
! [SV142: $i] :
( ( ! [SY1127: $i,SY1128: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1128 ) @ SY1127 ) @ ( hAPP @ ( c_Set_OCollect @ SY1128 ) @ SV142 ) ) )
| ( hBOOL @ ( hAPP @ SV142 @ SY1127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(5791,plain,
! [SV143: $i] :
( ( ! [SY1129: $i,SY1130: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1130 @ SY1129 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1129 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5641]) ).
thf(5792,plain,
! [SV144: $i] :
( ( ! [SY1131: $i,SY1132: $i,SY1133: $i,SY1134: $i,SY1135: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1135 ) @ SY1134 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1135 @ SY1133 @ SY1132 @ SY1131 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1133 @ SY1131 ) @ SY1134 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1132 @ SY1134 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1133 @ SY1131 ) @ SY1134 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1132 @ SY1134 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1135 ) @ SY1134 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1135 @ SY1133 @ SY1132 @ SY1131 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(5793,plain,
! [SV145: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1138 ) @ SY1137 ) @ SY1136 ) )
| ( SY1137 = SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1138 ) @ SY1137 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1138 ) @ SV145 ) @ SY1136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5643]) ).
thf(5794,plain,
! [SV146: $i] :
( ( ! [SY1139: $i,SY1140: $i,SY1141: $i,SY1142: $i,SY1143: $i] :
~ ( ~ ( ( SY1143 != SY1142 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1141 @ SY1140 @ SY1139 @ SY1142 @ SV146 ) @ SY1143 )
= SV146 ) )
| ~ ( ~ ( ( SY1143 != SY1142 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1141 @ SY1140 @ SY1139 @ SY1142 @ SV146 ) @ SY1143 )
= ( hAPP @ SY1139 @ SY1143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(5795,plain,
! [SV147: $i] :
( ( ! [SY1144: $i] :
( ~ ! [SY1145: $i] :
( ( hAPP @ SY1144 @ SY1145 )
= ( hAPP @ SV147 @ SY1145 ) )
| ( SY1144 = SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5645]) ).
thf(5796,plain,
! [SV148: $i] :
( ( ! [SY1146: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1146 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
| ( SY1146 = SV148 ) )
| ~ ( ( SY1146 != SV148 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1146 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(5797,plain,
! [SV1: $i,SV149: $i] :
( ( ! [SY1147: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1147 ) @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1147 ) @ SV149 ) @ SV1 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1147 ) @ SV149 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5647]) ).
thf(5798,plain,
! [SV2: $i,SV150: $i] :
( ( ! [SY1148: $i,SY1149: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1149 ) @ SY1148 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1149 ) @ SV150 ) @ SV2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1149 ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1149 ) @ SY1148 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(5799,plain,
! [SV3: $i,SV151: $i] :
( ( ! [SY1150: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1150 ) @ SV151 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1150 ) @ SV151 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(5800,plain,
! [SV4: $i,SV152: $i] :
( ( ! [SY1151: $i,SY1152: $i] :
( ( c_Fun_Ofun__upd @ SY1152 @ SY1151 @ SV152 @ SV4 @ ( hAPP @ SV152 @ SV4 ) )
= SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(5801,plain,
! [SV5: $i,SV153: $i] :
( ( ! [SY1153: $i,SY1154: $i,SY1155: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY1155 @ SY1154 @ SY1153 @ SV153 @ SV5 ) @ SV153 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(5802,plain,
! [SV6: $i,SV154: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV154 ) @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(5803,plain,
! [SV7: $i,SV155: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV155 ) @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5653]) ).
thf(5804,plain,
! [SV8: $i,SV156: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV156 ) @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(5805,plain,
! [SV9: $i,SV157: $i] :
( ( ! [SY1156: $i,SY1157: $i,SY1158: $i,SY1159: $i,SY1160: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1160 @ SY1159 @ SY1158 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1160 @ SY1157 @ SY1159 ) @ SY1156 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1160 @ SY1157 @ SY1158 ) @ SY1156 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1157 @ SY1159 @ SY1158 ) @ SV157 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5655]) ).
thf(5806,plain,
! [SV10: $i,SV158: $i] :
( ( ! [SY1161: $i,SY1162: $i,SY1163: $i,SY1164: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1164 @ SY1163 @ SY1162 @ SY1161 ) @ SV158 ) @ SV10 )
= ( hAPP @ SY1161 @ ( hAPP @ SV158 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5656]) ).
thf(5807,plain,
! [SV11: $i,SV159: $i] :
( ( ! [SY1165: $i,SY1166: $i,SY1167: $i,SY1168: $i,SY1169: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1169 @ SY1168 @ SY1167 @ SY1166 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1165 @ SY1169 @ SY1167 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY1165 @ SY1168 @ SY1167 @ ( hAPP @ ( c_Fun_Ocomp @ SY1169 @ SY1168 @ SY1165 @ SY1166 ) @ SV159 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(5808,plain,
! [SV12: $i,SV160: $i] :
( ( ! [SY1170: $i,SY1171: $i,SY1172: $i,SY1173: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1173 @ SY1172 @ SY1171 @ SY1170 ) @ SV160 ) @ SV12 )
= ( hAPP @ SY1170 @ ( hAPP @ SV160 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5658]) ).
thf(5809,plain,
! [SV13: $i,SV161: $i] :
( ( ! [SY1174: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1174 @ SV161 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV161 @ SY1174 ) @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5810,plain,
! [SV14: $i,SV162: $i] :
( ( ! [SY1175: $i,SY1176: $i] :
( ( hAPP @ SY1176 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1175 @ SY1175 ) @ SV162 ) @ SY1176 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1175 @ SY1175 ) @ SV162 ) @ SY1176 ) @ ( hAPP @ SY1176 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5660]) ).
thf(5811,plain,
! [SV15: $i,SV163: $i] :
( ( ! [SY1177: $i,SY1178: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1178 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1178 ) @ SY1177 ) @ SV163 ) ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1178 ) @ SY1177 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1178 ) @ SV163 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5661]) ).
thf(5812,plain,
! [SV16: $i,SV164: $i] :
( ( ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1181 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1181 @ SY1180 ) @ SY1179 ) @ SV164 ) ) @ SY1179 ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1181 @ SY1180 ) @ SY1179 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5662]) ).
thf(5813,plain,
! [SV17: $i,SV165: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV165 ) @ ( hAPP @ ( c_List_Orev @ SV165 ) @ SV17 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(5814,plain,
! [SV19: $i,SV166: $i] :
( ( ( hAPP @ ( c_COMBI @ SV166 ) @ SV19 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5665]) ).
thf(5815,plain,
! [SV20: $i,SV167: $i] :
( ( ! [SY1182: $i,SY1183: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1183 @ SY1182 ) @ SV167 ) @ SV20 )
= SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5816,plain,
! [SV21: $i,SV168: $i] :
( ( ! [SY1184: $i,SY1185: $i,SY1186: $i,SY1187: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1187 @ SY1186 @ SY1185 ) @ SY1184 ) @ SV168 ) @ SV21 )
= ( hAPP @ SY1184 @ ( hAPP @ SV168 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5817,plain,
! [SV22: $i,SV169: $i] :
( ( ! [SY1188: $i,SY1189: $i,SY1190: $i,SY1191: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1191 @ SY1190 @ SY1189 ) @ SY1188 ) @ SV169 ) @ SV22 )
= ( hAPP @ ( hAPP @ SY1188 @ SV22 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(5818,plain,
! [SV23: $i,SV170: $i] :
( ( ! [SY1192: $i,SY1193: $i,SY1194: $i,SY1195: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1195 @ SY1194 @ SY1193 ) @ SY1192 ) @ SV170 ) @ SV23 )
= ( hAPP @ ( hAPP @ SY1192 @ SV23 ) @ ( hAPP @ SV170 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5669]) ).
thf(5819,plain,
! [SV24: $i,SV171: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV171 ) @ SV24 ) )
| ( SV171 = SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5820,plain,
! [SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV25 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5672]) ).
thf(5821,plain,
! [SV26: $i] :
( ( ( ~ ~ ( hBOOL @ SV26 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5673]) ).
thf(5822,plain,
! [SV27: $i,SV172: $i] :
( ( ~ ( hBOOL @ SV172 )
| ~ ( hBOOL @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV172 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5674]) ).
thf(5823,plain,
! [SV28: $i,SV173: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV173 ) @ SV28 ) )
| ( hBOOL @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5675]) ).
thf(5824,plain,
! [SV29: $i,SV174: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV174 ) @ SV29 ) )
| ( hBOOL @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(5825,plain,
! [SV30: $i,SV175: $i] :
( ( ~ ( hBOOL @ SV175 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV175 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5677]) ).
thf(5826,plain,
! [SV31: $i,SV176: $i] :
( ( ~ ( hBOOL @ SV176 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV31 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5678]) ).
thf(5827,plain,
! [SV32: $i,SV177: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV177 ) @ SV32 ) )
| ( hBOOL @ SV177 )
| ( hBOOL @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5679]) ).
thf(5828,plain,
! [SV33: $i,SV178: $i] :
( ( ( hBOOL @ SV178 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV178 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(5829,plain,
! [SV34: $i,SV179: $i] :
( ( ~ ( hBOOL @ SV179 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV34 ) @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5830,plain,
! [SV35: $i,SV180: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV180 ) @ SV35 ) )
| ~ ( hBOOL @ SV180 )
| ( hBOOL @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(5831,plain,
! [SV36: $i,SV181: $i] :
( ( ! [SY1196: $i,SY1197: $i,SY1198: $i,SY1199: $i,SY1200: $i,SY1201: $i,SY1202: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1202 @ SY1201 @ SY1200 @ SY1199 ) @ SY1198 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1197 @ SY1201 @ SY1200 @ SY1196 ) @ SV181 ) )
| ( ( hAPP @ SY1199 @ ( hAPP @ SY1198 @ SV36 ) )
= ( hAPP @ SY1196 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(5832,plain,
! [SV37: $i,SV182: $i] :
( ( ! [SY1203: $i] :
~ ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY1203 @ SV182 @ SV37 )
| ! [SY1204: $i] :
( ~ ! [SY1205: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY1203 ) ) @ SY1205 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY1203 @ SY1204 @ SY1205 ) )
| ! [SY730: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY1203 ) ) @ SY730 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY1203 @ SY1204 @ SY730 ) ) ) )
| ~ ( ~ ! [SY1207: $i] :
( ~ ! [SY1208: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY1203 ) ) @ SY1208 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY1203 @ SY1207 @ SY1208 ) )
| ! [SY733: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SY1203 ) ) @ SY733 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY1203 @ SY1207 @ SY733 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SY1203 @ SV182 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(5833,plain,
! [SV38: $i,SV183: $i] :
( ( ! [SY1210: $i,SY1211: $i,SY1212: $i,SY1213: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1213 @ SY1212 ) @ SY1211 ) @ SY1210 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1213 @ SY1212 ) @ SV183 ) @ SV38 ) )
| ~ ( ( SY1211 != SV183 )
| ( SY1210 != SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(5834,plain,
! [SV39: $i,SV184: $i] :
( ( ! [SY1214: $i,SY1215: $i] :
( ( SY1215 != SY1214 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1215 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1214 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1214 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1215 ) @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(5835,plain,
! [SV40: $i,SV185: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i,SY1219: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1219 @ SY1218 @ SY1217 @ SY1216 @ SV185 )
| ( ( hAPP @ SY1216 @ ( hAPP @ SY1217 @ SV40 ) )
= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(5836,plain,
! [SV41: $i,SV186: $i] :
( ( ! [SY1220: $i,SY1221: $i,SY1222: $i,SY1223: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1223 @ SY1222 @ SY1221 )
| ( ( hAPP @ ( hAPP @ SY1221 @ SY1220 ) @ ( hAPP @ ( hAPP @ SY1221 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SY1221 @ SV186 ) @ ( hAPP @ ( hAPP @ SY1221 @ SY1220 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(5837,plain,
! [SV42: $i,SV187: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV187 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SV187 = SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(5838,plain,
! [SV43: $i,SV188: $i] :
( ( ! [SY1224: $i,SY1225: $i,SY1226: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1226 ) @ ( hAPP @ SY1225 @ SY1224 ) ) @ SV188 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SY1224 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SY1226 @ SY1225 ) @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5691]) ).
thf(5839,plain,
! [SV44: $i,SV189: $i] :
( ( ! [SY1227: $i,SY1228: $i,SY1229: $i,SY1230: $i,SY1231: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1231 @ SY1230 @ SY1229 @ SY1228 @ SY1227 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1232: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1228 @ SV189 ) @ SY1232 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1227 @ SY1232 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1233: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1228 @ SV189 ) @ SY1233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1227 @ SY1233 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1231 @ SY1230 @ SY1229 @ SY1228 @ SY1227 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5692]) ).
thf(5840,plain,
! [SV45: $i,SV190: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
| ( SV190 = SV45 ) )
| ~ ( ( SV190 != SV45 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(5841,plain,
! [SV46: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV46 )
= SV46 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5842,plain,
! [SV47: $i,SV191: $i] :
( ( ! [SY1234: $i,SY1235: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1235 ) @ SY1234 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1235 ) @ SY1234 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1235 ) @ SV47 ) @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5695]) ).
thf(5843,plain,
! [SV48: $i,SV192: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
| ( SV192 = SV48 ) )
| ~ ( ( SV192 != SV48 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5696]) ).
thf(5844,plain,
! [SV49: $i,SV193: $i] :
( ( ! [SY1236: $i,SY1237: $i,SY1238: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1237 ) @ SY1236 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1239: $i] :
~ ( ~ ( ( SY1237
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SV193 ) @ SY1239 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1239 ) @ SY1236 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1237 ) @ SY1239 )
!= SV193 )
| ( SY1236
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1239 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY1240: $i] :
~ ( ~ ( ( SY1237
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SV193 ) @ SY1240 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1240 ) @ SY1236 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1237 ) @ SY1240 )
!= SV193 )
| ( SY1236
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1240 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SY1237 ) @ SY1236 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1238 ) @ SV193 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(5845,plain,
! [SV50: $i,SV194: $i] :
( ( ! [SY1241: $i,SY1242: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1242 ) @ SY1241 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1242 ) @ SV194 ) @ SV50 ) ) )
| ~ ( ( SY1241 != SV194 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1242 ) @ SY1241 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(5846,plain,
! [SV51: $i,SV195: $i] :
( ( ! [SY1243: $i,SY1244: $i,SY1245: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1245 @ SY1244 ) @ SY1243 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SY1245 ) @ SY1243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(5847,plain,
! [SV52: $i,SV196: $i] :
( ( ! [SY1246: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1246 @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV52 ) @ SV196 ) @ ( hAPP @ ( c_Set_OCollect @ SV52 ) @ SY1246 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(5848,plain,
! [SV53: $i,SV197: $i] :
( ( ! [SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1250 @ SY1249 @ SY1248 @ SY1247 @ SV197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1249 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SY1248 @ ( hAPP @ SY1247 @ SV53 ) )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5701]) ).
thf(5849,plain,
! [SV54: $i,SV198: $i] :
( ( ! [SY1251: $i,SY1252: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1252 ) @ SY1251 ) @ SV198 ) @ SV54 ) )
| ( SY1251 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ~ ( ~ ( ( SY1251 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1252 ) @ SY1251 ) @ SV198 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(5850,plain,
! [SV55: $i,SV199: $i] :
( ( ! [SY1253: $i,SY1254: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1254 ) @ SY1253 ) @ SV199 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1254 ) @ SY1253 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1254 ) @ SY1253 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1254 ) @ SY1253 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1254 ) @ SY1253 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1254 ) @ SY1253 ) @ SV55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(5851,plain,
! [SV56: $i,SV200: $i] :
( ( ! [SY1255: $i,SY1256: $i,SY1257: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1257 ) @ SY1256 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1257 @ SY1255 @ SV200 ) @ SV56 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1255 ) @ ( hAPP @ SV200 @ SY1256 ) ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5704]) ).
thf(5852,plain,
! [SV57: $i,SV201: $i] :
( ( ! [SY1258: $i] :
( ~ ( c_Predicate_Oreflp @ SY1258 @ SV201 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV201 @ SV57 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(5853,plain,
! [SV58: $i,SV202: $i] :
( ( ! [SY1259: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1259 ) @ SV202 ) @ SV58 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1259 ) @ SV202 ) @ SV58 )
= SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(5854,plain,
! [SV59: $i,SV203: $i] :
( ( ! [SY1260: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SY1260 @ SV203 ) @ SV59 ) )
| ! [SY1261: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1260 ) @ SY1261 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1261 ) ) ) )
| ~ ( ~ ! [SY1262: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1260 ) @ SY1262 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1262 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SY1260 @ SV203 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5707]) ).
thf(5855,plain,
! [SV60: $i,SV204: $i] :
( ( ! [SY1263: $i,SY1264: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1264 @ SY1263 ) @ SV204 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1263 @ SV60 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1264 @ SY1263 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(5856,plain,
! [SV61: $i,SV205: $i] :
( ( ! [SY1265: $i,SY1266: $i,SY1267: $i,SY1268: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1268 ) @ SY1267 ) @ SY1266 )
!= SY1265 )
| ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1268 ) @ SY1266 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1268 ) @ SY1267 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1268 ) @ SY1265 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5857,plain,
! [SV62: $i,SV206: $i] :
( ( ! [SY1269: $i,SY1270: $i,SY1271: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1271 @ SY1270 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1270 @ SY1269 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1270 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1270 @ SY1269 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5710]) ).
thf(5858,plain,
! [SV63: $i] :
( ( SV63
= ( hAPP @ c_Nat_OSuc @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(5859,plain,
! [SV64: $i,SV207: $i] :
( ( ! [SY1272: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1272 @ SV207 ) )
| ( hBOOL @ ( hAPP @ SY1272 @ ( c_Hilbert__Choice_OEps @ SV64 @ SY1272 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5712]) ).
thf(5860,plain,
! [SV65: $i,SV208: $i] :
( ( ! [SY1273: $i,SY1274: $i] :
( ( SY1274 != SY1273 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1273 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1274 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(5861,plain,
! [SV66: $i,SV209: $i] :
( ( ! [SY1275: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY1275 @ SX3 ) )
| ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SY1275 ) )
| ( hBOOL @ ( hAPP @ SY1275 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5714]) ).
thf(5862,plain,
! [SV67: $i,SV210: $i] :
( ( ! [SY1277: $i,SY1278: $i,SY1279: $i,SY1280: $i,SY1281: $i,SY1282: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1282 @ SY1281 ) @ SY1280 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1279 @ SY1280 ) @ SY1278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1277 @ SV210 @ SV67 @ SY1282 @ SY1279 ) @ SY1281 ) @ SY1278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5715]) ).
thf(5863,plain,
! [SV68: $i,SV211: $i] :
( ( ! [SY1283: $i,SY1284: $i,SY1285: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1285 ) @ SY1284 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1285 @ SY1283 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1283 @ SV211 ) @ SY1284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1283 @ SY1284 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1283 @ SV211 ) @ SY1284 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1283 @ SY1284 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1285 ) @ SY1284 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1285 @ SY1283 @ SV211 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(5864,plain,
! [SV69: $i,SV212: $i] :
( ( ! [SY1286: $i,SY1287: $i,SY1288: $i,SY1289: $i] :
( ~ ( ( SY1289 != SY1288 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1287 @ SY1286 @ SV212 @ SY1288 @ SV69 ) @ SY1289 )
= ( hAPP @ SV212 @ SY1289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5717]) ).
thf(5865,plain,
! [SV70: $i,SV213: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
~ ( ~ ( ~ ( c_Fun_Oinj__on @ SY1291 @ SY1290 @ SV213 @ SV70 )
| ! [SY1292: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1291 ) @ SY1292 ) @ SV70 ) )
| ! [SY1293: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1291 ) @ SY1293 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1292 )
!= ( hAPP @ SV213 @ SY1293 ) )
| ( SY1292 = SY1293 ) ) ) )
| ~ ( ~ ! [SY1294: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1291 ) @ SY1294 ) @ SV70 ) )
| ! [SY1295: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1291 ) @ SY1295 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1294 )
!= ( hAPP @ SV213 @ SY1295 ) )
| ( SY1294 = SY1295 ) ) )
| ( c_Fun_Oinj__on @ SY1291 @ SY1290 @ SV213 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5718]) ).
thf(5866,plain,
! [SV71: $i,SV214: $i] :
( ( ! [SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i,SY1300: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1300 @ SY1299 @ SY1298 @ SY1297 @ SY1296 @ SV214 )
| ( ( hAPP @ ( hAPP @ SY1298 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5719]) ).
thf(5867,plain,
! [SV72: $i,SV215: $i] :
( ( ! [SY1301: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1301 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SV215 = SV72 ) )
| ~ ( ( SV215 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1301 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5720]) ).
thf(5868,plain,
! [SV73: $i,SV216: $i] :
( ( ! [SY1302: $i,SY1303: $i,SY1304: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1304 @ SY1303 @ SY1302 ) @ SV216 ) @ SV73 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1302 @ SV73 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5721]) ).
thf(5869,plain,
! [SV74: $i,SV217: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
| ( SV217 = SV74 ) )
| ~ ( ( SV217 != SV74 )
| ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5722]) ).
thf(5870,plain,
! [SV75: $i,SV218: $i] :
( ( ! [SY1305: $i,SY1306: $i,SY1307: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1307 ) @ SY1306 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1307 @ SY1305 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1305 @ SV218 ) @ SY1306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1305 @ SY1306 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1305 @ SV218 ) @ SY1306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1305 @ SY1306 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1307 ) @ SY1306 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1307 @ SY1305 @ SV218 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5723]) ).
thf(5871,plain,
! [SV76: $i,SV219: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1309 @ SY1308 @ SV219 )
| ( ( hAPP @ ( hAPP @ SY1308 @ SV76 ) @ SV76 )
= SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5724]) ).
thf(5872,plain,
! [SV77: $i,SV220: $i] :
( ( ! [SY1310: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1310 ) @ SV220 ) @ ( hAPP @ ( c_Set_OCollect @ SY1310 ) @ SV77 ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(5873,plain,
! [SV78: $i,SV221: $i] :
( ( ! [SY1311: $i,SY1312: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1312 ) @ SY1311 ) @ ( c_SetInterval_Oord_OlessThan @ SY1312 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SY1311 ) @ SV78 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SY1311 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1312 ) @ SY1311 ) @ ( c_SetInterval_Oord_OlessThan @ SY1312 @ SV221 @ SV78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5726]) ).
thf(5874,plain,
! [SV79: $i,SV222: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i,SY1316: $i] :
( ~ ( c_Fun_Oinj__on @ SY1316 @ SY1315 @ SY1314 @ SY1313 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1316 ) @ SV222 ) @ SY1313 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1316 ) @ SV79 ) @ SY1313 ) )
| ~ ( ~ ( ( ( hAPP @ SY1314 @ SV222 )
!= ( hAPP @ SY1314 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SY1314 @ SV222 )
= ( hAPP @ SY1314 @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5727]) ).
thf(5875,plain,
! [SV80: $i,SV223: $i] :
( ( ! [SY1317: $i] :
( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY1317 @ ( hAPP @ c_Nat_OSuc @ SV223 ) @ SV80 )
| ( c_Hoare__Mirabelle_Otriple__valid @ SY1317 @ SV223 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5728]) ).
thf(5876,plain,
! [SV81: $i,SV224: $i] :
( ( ! [SY1318: $i,SY1319: $i,SY1320: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1320 @ SY1319 ) @ SY1318 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SY1320 ) @ SY1318 ) @ SY1319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5729]) ).
thf(5877,plain,
! [SV82: $i,SV225: $i] :
( ( ~ ~ ! [SY1321: $i] :
~ ( hBOOL @ ( hAPP @ SV225 @ SY1321 ) )
| ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5730]) ).
thf(5878,plain,
! [SV83: $i,SV226: $i] :
( ( ! [SY1322: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1322 ) @ SV226 ) @ SV83 )
!= SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5731]) ).
thf(5879,plain,
! [SV84: $i,SV227: $i] :
( ( ! [SY1323: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1323 @ SV227 ) @ SV84 ) )
| ! [SY1324: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1324 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1323 @ SV227 ) @ SY1324 ) ) ) )
| ~ ( ~ ! [SY1325: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1325 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1323 @ SV227 ) @ SY1325 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1323 @ SV227 ) @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5732]) ).
thf(5880,plain,
! [SV85: $i,SV228: $i] :
( ( ! [SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
~ ( ~ ( ( SY1329 != SY1328 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1327 @ SY1326 @ SV228 @ SY1328 @ SV85 ) @ SY1329 )
= SV85 ) )
| ~ ( ~ ( ( SY1329 != SY1328 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1327 @ SY1326 @ SV228 @ SY1328 @ SV85 ) @ SY1329 )
= ( hAPP @ SV228 @ SY1329 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5733]) ).
thf(5881,plain,
! [SV86: $i,SV229: $i] :
( ( ! [SY1330: $i,SY1331: $i,SY1332: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1332 @ SY1331 @ SY1330 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SY1330 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SY1330 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1332 @ SY1331 @ SY1330 ) @ SV229 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5734]) ).
thf(5882,plain,
! [SV87: $i,SV230: $i] :
( ( ! [SY1333: $i,SY1334: $i,SY1335: $i,SY1336: $i] :
( ~ ( ( SY1336 != SY1335 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1334 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1334 @ SY1333 ) @ SY1336 ) @ SV230 ) ) @ SY1335 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1334 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1334 @ SY1333 ) @ SY1335 ) @ SV87 ) ) @ SY1336 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5735]) ).
thf(5883,plain,
! [SV88: $i,SV231: $i] :
( ( ! [SY1337: $i,SY1338: $i,SY1339: $i,SY1340: $i] :
( ( SY1340
!= ( hAPP @ SY1339 @ SY1338 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1337 ) @ SY1338 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SY1340 ) @ ( hAPP @ ( c_Set_Oimage @ SY1337 @ SV88 @ SY1339 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5736]) ).
thf(5884,plain,
! [SV89: $i,SV232: $i] :
( ( ! [SY1341: $i,SY1342: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1342 ) @ SY1341 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY1342 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SY1341 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SY1341 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1342 ) @ SY1341 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY1342 @ SV232 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5737]) ).
thf(5885,plain,
! [SV90: $i,SV233: $i] :
( ( ! [SY1343: $i,SY1344: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1344 ) @ SY1343 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1344 ) @ SV233 ) @ SV90 ) ) )
| ( SY1343 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1344 ) @ SY1343 ) @ SV90 ) ) )
| ~ ( ~ ( ( SY1343 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1344 ) @ SY1343 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1344 ) @ SY1343 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1344 ) @ SV233 ) @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5738]) ).
thf(5886,plain,
! [SV91: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV91 ) @ v_ts ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(5887,plain,
! [SV92: $i,SV234: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
| ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
| ~ ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5740]) ).
thf(5888,plain,
! [SV93: $i,SV235: $i] :
( ( ! [SY1349: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV235 ) @ SV93 ) )
| ! [SY1350: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1350 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV235 ) @ SY1350 ) ) ) )
| ~ ( ~ ! [SY1351: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1351 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV235 ) @ SY1351 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1349 @ SV235 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5741]) ).
thf(5889,plain,
! [SV94: $i,SV236: $i] :
( ( ! [SY1352: $i,SY1353: $i] :
( ~ ( c_Predicate_Osymp @ SY1353 @ SY1352 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1352 @ SV236 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1352 @ SV94 ) @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(5890,plain,
! [SV95: $i,SV237: $i] :
( ( ! [SY1354: $i,SY1355: $i,SY1356: $i,SY1357: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1357 ) @ SY1356 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1357 @ SY1355 @ SY1354 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1354 @ SV237 ) @ SY1356 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1355 @ SY1356 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1354 @ SV237 ) @ SY1356 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1355 @ SY1356 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1357 ) @ SY1356 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1357 @ SY1355 @ SY1354 @ SV237 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(5891,plain,
! [SV96: $i,SV238: $i] :
( ( ! [SY1358: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1358 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SY1358 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1358 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SY1358 ) @ SV96 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5744]) ).
thf(5892,plain,
! [SV97: $i,SV239: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
| ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5745]) ).
thf(5893,plain,
! [SV98: $i,SV240: $i] :
( ( ! [SY1365: $i,SY1366: $i,SY1367: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1367 @ SY1366 @ SY1365 @ SV240 @ SV98 )
!= SY1365 )
| ( ( hAPP @ SY1365 @ SV240 )
= SV98 ) )
| ~ ( ( ( hAPP @ SY1365 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SY1367 @ SY1366 @ SY1365 @ SV240 @ SV98 )
= SY1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5746]) ).
thf(5894,plain,
! [SV99: $i,SV241: $i] :
( ( ! [SY1368: $i,SY1369: $i,SY1370: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1370 ) @ SY1369 ) @ SY1368 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1370 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SY1369 != SV241 )
| ( SY1368 != SV99 ) ) )
| ~ ( ~ ~ ( ( SY1369 != SV241 )
| ( SY1368 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1370 ) @ SY1369 ) @ SY1368 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1370 ) @ SV241 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(5895,plain,
! [SV100: $i,SV242: $i] :
( ( ! [SY1371: $i,SY1372: $i,SY1373: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1373 @ SY1372 @ SY1371 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1371 @ SV100 ) @ SV242 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1371 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1373 @ SY1372 @ SY1371 ) @ SV242 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(5896,plain,
! [SV101: $i,SV243: $i] :
( ( ! [SY1374: $i,SY1375: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1375 ) @ SY1374 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1375 ) @ SY1374 ) @ SV101 ) )
| ( SV243 = SV101 ) )
| ~ ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1375 ) @ SY1374 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1375 ) @ SY1374 ) @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5749]) ).
thf(5897,plain,
! [SV102: $i,SV244: $i] :
( ( ! [SY1376: $i,SY1377: $i,SY1378: $i,SY1379: $i] :
( ~ ( c_Fun_Oinj__on @ SY1379 @ SY1378 @ SY1377 @ SY1376 )
| ( ( hAPP @ SY1377 @ SV244 )
!= ( hAPP @ SY1377 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1379 ) @ SV244 ) @ SY1376 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1379 ) @ SV102 ) @ SY1376 ) )
| ( SV244 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5750]) ).
thf(5898,plain,
! [SV103: $i,SV245: $i] :
( ( ! [SY1380: $i,SY1381: $i,SY1382: $i,SY1383: $i,SY1384: $i,SY1385: $i,SY1386: $i,SY1387: $i,SY1388: $i] :
( ( ( hAPP @ SY1388 @ ( hAPP @ SY1387 @ SY1386 ) )
!= ( hAPP @ SY1385 @ ( hAPP @ SY1384 @ SY1383 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1382 @ SY1381 @ SY1380 @ SY1388 ) @ SY1387 ) @ SY1386 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SY1381 @ SV103 @ SY1385 ) @ SY1384 ) @ SY1383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(5899,plain,
! [SV104: $i,SV246: $i] :
( ( ! [SY1389: $i,SY1390: $i,SY1391: $i,SY1392: $i,SY1393: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1393 @ SY1392 @ SY1391 @ SY1390 ) @ SY1389 )
!= SV246 )
| ( ( hAPP @ SY1390 @ ( hAPP @ SY1389 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5752]) ).
thf(5900,plain,
! [SV105: $i,SV247: $i] :
( ( ! [SY1394: $i,SY1395: $i,SY1396: $i,SY1397: $i] :
( ( SY1397 != SY1396 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1395 @ SY1394 @ SV247 ) @ SV105 ) @ SY1397 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1395 @ SY1394 @ SV247 ) @ SV105 ) @ SY1396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5753]) ).
thf(5901,plain,
! [SV106: $i,SV248: $i] :
( ( ! [SY1398: $i,SY1399: $i,SY1400: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1400 @ SY1399 @ SY1398 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1398 @ SV106 ) @ SV248 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1398 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1400 @ SY1399 @ SY1398 ) @ SV248 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(5902,plain,
! [SV107: $i,SV249: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
| ( SV249 = SV107 ) )
| ~ ( ( SV249 != SV107 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5755]) ).
thf(5903,plain,
! [SV108: $i,SV250: $i] :
( ( ! [SY1401: $i,SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1402 @ SY1401 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1402 @ SY1401 ) @ SV108 ) )
| ( SV250 = SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(5904,plain,
! [SV109: $i,SV251: $i] :
( ( ! [SY1403: $i,SY1404: $i,SY1405: $i,SY1406: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1406 ) @ SY1405 ) @ SY1404 ) )
| ( SY1403
!= ( hAPP @ SV251 @ SY1405 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SY1403 ) @ ( hAPP @ ( c_Set_Oimage @ SY1406 @ SV109 @ SV251 ) @ SY1404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(5905,plain,
! [SV110: $i,SV252: $i] :
( ( ! [SY1407: $i,SY1408: $i,SY1409: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1409 @ SY1408 @ SY1407 )
| ( ( hAPP @ ( hAPP @ SY1407 @ SV252 ) @ ( hAPP @ ( hAPP @ SY1407 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SY1407 @ SV252 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5758]) ).
thf(5906,plain,
! [SV111: $i,SV253: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1412 ) @ SY1411 ) @ SY1410 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SY1411 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1412 @ SV253 @ SV111 ) @ SY1410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5759]) ).
thf(5907,plain,
! [SV112: $i,SV254: $i] :
( ( ! [SY1413: $i,SY1414: $i,SY1415: $i,SY1416: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1416 @ SY1415 ) @ SY1414 ) @ SY1413 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1416 @ SY1415 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SY1414 != SV254 )
| ( SY1413 != SV112 ) ) )
| ~ ( ~ ~ ( ( SY1414 != SV254 )
| ( SY1413 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1416 @ SY1415 ) @ SY1414 ) @ SY1413 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1416 @ SY1415 ) @ SV254 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5760]) ).
thf(5908,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
| ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
| ~ ( ~ ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) )
| ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(5909,plain,
! [SV114: $i,SV256: $i] :
( ( ! [SY1419: $i,SY1420: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1420 @ SY1419 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
| ~ ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1420 @ SY1419 @ SV256 ) @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5762]) ).
thf(5910,plain,
! [SV115: $i,SV257: $i] :
( ( ! [SY1423: $i,SY1424: $i] :
( ( SY1424 != SY1423 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1424 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1423 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1423 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1424 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5763]) ).
thf(5911,plain,
! [SV116: $i,SV258: $i] :
( ( ! [SY1425: $i,SY1426: $i] :
( ( SY1426 != SY1425 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SY1425 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SY1426 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(5912,plain,
! [SV117: $i,SV259: $i] :
( ( ! [SY1427: $i,SY1428: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1428 ) @ SY1427 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1428 ) @ SV117 ) @ SV259 ) )
| ( SY1427 = SV117 ) )
| ~ ( ( SY1427 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1428 ) @ SY1427 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1428 ) @ SV117 ) @ SV259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5765]) ).
thf(5913,plain,
! [SV118: $i,SV260: $i] :
( ( ! [SY1429: $i,SY1430: $i,SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1434 @ SY1433 @ SY1432 @ SY1431 ) @ SY1430 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1429 @ SY1433 @ SY1432 @ SV260 ) @ SV118 ) )
| ! [SY1435: $i] :
( ( hAPP @ SY1431 @ ( hAPP @ SY1430 @ SY1435 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5766]) ).
thf(5914,plain,
! [SV119: $i,SV261: $i] :
( ( ! [SY1436: $i,SY1437: $i,SY1438: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1438 @ SY1437 ) @ SY1436 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SY1438 ) @ SY1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5767]) ).
thf(5915,plain,
! [SV120: $i,SV262: $i] :
( ( ! [SY1439: $i,SY1440: $i,SY1441: $i] :
( ( ( hAPP @ SY1441 @ SY1440 )
!= SY1439 )
| ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SY1441 @ SY1440 @ SY1439 )
= SY1441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5768]) ).
thf(5916,plain,
! [SV121: $i,SV263: $i] :
( ( ! [SY1442: $i,SY1443: $i,SY1444: $i,SY1445: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1445 @ SY1444 @ SY1443 @ SY1442 @ SV263 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1444 ) @ ( hAPP @ SY1443 @ SV121 ) ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(5917,plain,
! [SV122: $i,SV264: $i] :
( ( ! [SY1446: $i,SY1447: $i,SY1448: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1448 ) @ SY1447 ) @ ( hAPP @ ( c_Set_Oimage @ SY1446 @ SY1448 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1449: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1446 ) @ SY1449 ) @ SV122 ) )
| ( SY1447
!= ( hAPP @ SV264 @ SY1449 ) ) ) )
| ~ ( ~ ~ ! [SY1450: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1446 ) @ SY1450 ) @ SV122 ) )
| ( SY1447
!= ( hAPP @ SV264 @ SY1450 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1448 ) @ SY1447 ) @ ( hAPP @ ( c_Set_Oimage @ SY1446 @ SY1448 @ SV264 ) @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5770]) ).
thf(5918,plain,
! [SV123: $i,SV265: $i] :
( ( ! [SY1451: $i,SY1452: $i,SY1453: $i] :
( ~ ( c_Predicate_Otransp @ SY1453 @ SY1452 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1452 @ SY1451 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1452 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1452 @ SY1451 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(5919,plain,
! [SV124: $i,SV266: $i] :
( ( ! [SY1454: $i,SY1455: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1455 @ SY1454 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1454 @ SV266 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1454 @ SV124 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5772]) ).
thf(5920,plain,
! [SV125: $i,SV267: $i] :
( ( ! [SY1456: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1456 @ SX3 ) )
| ! [SY1458: $i,SY1459: $i] : ( hBOOL @ ( hAPP @ SY1456 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1458 ) @ SY1459 ) ) ) )
| ~ ( ~ ! [SY1460: $i,SY1461: $i] : ( hBOOL @ ( hAPP @ SY1456 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1460 ) @ SY1461 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1456 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(5921,plain,
! [SV126: $i,SV268: $i] :
( ( ! [SY1463: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1463 ) @ SV268 )
!= SV126 )
| ( SV268
= ( hAPP @ ( c_List_Orev @ SY1463 ) @ SV126 ) ) )
| ~ ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SY1463 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1463 ) @ SV268 )
= SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5774]) ).
thf(5922,plain,
! [SV127: $i,SV269: $i] :
( ( ~ ~ ! [SY1464: $i] :
~ ( hBOOL @ ( hAPP @ SV269 @ SY1464 ) )
| ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(5923,plain,
! [SV128: $i,SV270: $i] :
( ( ! [SY1465: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1465 ) @ SV270 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1465 ) @ SV270 ) @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5776]) ).
thf(5924,plain,
! [SV129: $i,SV271: $i] :
( ( ! [SY1466: $i,SY1467: $i,SY1468: $i,SY1469: $i,SY1470: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1470 @ SY1469 @ SY1468 @ SY1467 @ SY1466 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1469 ) @ SV271 ) @ SY1466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1469 ) @ SV129 ) @ SY1466 ) )
| ~ ( ~ ( ( ( hAPP @ SY1467 @ SV271 )
!= ( hAPP @ SY1467 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SY1467 @ SV271 )
= ( hAPP @ SY1467 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5777]) ).
thf(5925,plain,
! [SV130: $i,SV272: $i] :
( ( ! [SY1471: $i,SY1472: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1472 ) @ SY1471 ) @ ( c_SetInterval_Oord_OatLeast @ SY1472 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SY1471 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SY1471 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1472 ) @ SY1471 ) @ ( c_SetInterval_Oord_OatLeast @ SY1472 @ SV272 @ SV130 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5778]) ).
thf(5926,plain,
! [SV131: $i,SV273: $i] :
( ( ! [SY1473: $i] :
( SY1473
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV273 ) @ SV131 ) @ SY1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(5927,plain,
! [SV132: $i,SV274: $i] :
( ( ! [SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ~ ( c_Fun_Oinj__on @ SY1477 @ SY1476 @ SY1475 @ SY1474 )
| ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1477 ) @ SV274 ) @ SY1474 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1477 ) @ SV132 ) @ SY1474 ) )
| ( ( hAPP @ SY1475 @ SV274 )
!= ( hAPP @ SY1475 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(5928,plain,
! [SV133: $i,SV275: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1480 ) @ SY1479 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1480 @ SY1478 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1478 ) @ ( hAPP @ SV275 @ SY1479 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1478 ) @ ( hAPP @ SV275 @ SY1479 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1480 ) @ SY1479 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1480 @ SY1478 @ SV275 ) @ SV133 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5781]) ).
thf(5929,plain,
! [SV134: $i,SV276: $i] :
( ( ! [SY1481: $i,SY1482: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1482 @ SY1481 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1481 @ SV276 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1481 @ SV134 ) @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5782]) ).
thf(5930,plain,
! [SV135: $i,SV277: $i] :
( ( ( SV277 != SV135 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV277 ) @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5783]) ).
thf(5931,plain,
! [SV136: $i,SV278: $i] :
( ( ! [SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i] :
( ( ( hAPP @ SY1486 @ SY1485 )
!= SY1484 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1483 ) @ SY1484 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SY1485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SY1483 @ SY1486 ) @ SV278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5784]) ).
thf(5932,plain,
! [SV137: $i,SV279: $i] :
( ( ! [SY1487: $i,SY1488: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1488 ) @ SY1487 ) @ ( c_SetInterval_Oord_OatMost @ SY1488 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SY1487 ) @ SV137 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SY1487 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1488 ) @ SY1487 ) @ ( c_SetInterval_Oord_OatMost @ SY1488 @ SV279 @ SV137 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5785]) ).
thf(5933,plain,
! [SV138: $i,SV280: $i] :
( ( ! [SY1489: $i,SY1490: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1490 @ SY1489 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
| ~ ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1490 @ SY1489 @ SV280 ) @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5786]) ).
thf(5934,plain,
! [SV139: $i,SV281: $i] :
( ( ! [SY1493: $i,SY1494: $i,SY1495: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1495 @ SY1494 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1494 @ SY1493 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1494 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1494 @ SY1493 ) @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5787]) ).
thf(5935,plain,
! [SV140: $i,SV282: $i] :
( ( ! [SY1496: $i,SY1497: $i,SY1498: $i,SY1499: $i,SY1500: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1500 @ SY1499 @ SY1498 @ SY1497 @ SY1496 )
| ~ ( ~ ( ( ( hAPP @ SY1498 @ SV282 )
!= ( hAPP @ SY1498 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SY1498 @ SV282 )
= ( hAPP @ SY1498 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5788]) ).
thf(5936,plain,
! [SV141: $i,SV283: $i] :
( ( ! [SY1501: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1501 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SY1501 ) @ SV141 ) )
| ( SV283 = SV141 ) )
| ~ ( ( SV283 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SY1501 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SY1501 ) @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5789]) ).
thf(5937,plain,
! [SV142: $i,SV284: $i] :
( ( ! [SY1502: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1502 ) @ SV284 ) @ ( hAPP @ ( c_Set_OCollect @ SY1502 ) @ SV142 ) ) )
| ( hBOOL @ ( hAPP @ SV142 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5790]) ).
thf(5938,plain,
! [SV143: $i,SV285: $i] :
( ( ! [SY1503: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1503 @ SV285 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV285 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5791]) ).
thf(5939,plain,
! [SV144: $i,SV286: $i] :
( ( ! [SY1504: $i,SY1505: $i,SY1506: $i,SY1507: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1507 ) @ SY1506 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1507 @ SY1505 @ SY1504 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1505 @ SV286 ) @ SY1506 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1504 @ SY1506 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1505 @ SV286 ) @ SY1506 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1504 @ SY1506 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1507 ) @ SY1506 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1507 @ SY1505 @ SY1504 @ SV286 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5792]) ).
thf(5940,plain,
! [SV145: $i,SV287: $i] :
( ( ! [SY1508: $i,SY1509: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1509 ) @ SY1508 ) @ SV287 ) )
| ( SY1508 = SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1509 ) @ SY1508 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1509 ) @ SV145 ) @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(5941,plain,
! [SV146: $i,SV288: $i] :
( ( ! [SY1510: $i,SY1511: $i,SY1512: $i,SY1513: $i] :
~ ( ~ ( ( SY1513 != SY1512 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1511 @ SY1510 @ SV288 @ SY1512 @ SV146 ) @ SY1513 )
= SV146 ) )
| ~ ( ~ ( ( SY1513 != SY1512 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1511 @ SY1510 @ SV288 @ SY1512 @ SV146 ) @ SY1513 )
= ( hAPP @ SV288 @ SY1513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5794]) ).
thf(5942,plain,
! [SV147: $i,SV289: $i] :
( ( ~ ! [SY1514: $i] :
( ( hAPP @ SV289 @ SY1514 )
= ( hAPP @ SV147 @ SY1514 ) )
| ( SV289 = SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5795]) ).
thf(5943,plain,
! [SV148: $i,SV290: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
| ( SV290 = SV148 ) )
| ~ ( ( SV290 != SV148 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5796]) ).
thf(5944,plain,
! [SV1: $i,SV149: $i,SV291: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV291 ) @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV291 ) @ SV149 ) @ SV1 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV291 ) @ SV149 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(5945,plain,
! [SV2: $i,SV150: $i,SV292: $i] :
( ( ! [SY1515: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1515 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1515 ) @ SV150 ) @ SV2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1515 ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1515 ) @ SV292 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(5946,plain,
! [SV3: $i,SV151: $i,SV293: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV293 ) @ SV151 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV293 ) @ SV151 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(5947,plain,
! [SV4: $i,SV152: $i,SV294: $i] :
( ( ! [SY1516: $i] :
( ( c_Fun_Ofun__upd @ SY1516 @ SV294 @ SV152 @ SV4 @ ( hAPP @ SV152 @ SV4 ) )
= SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(5948,plain,
! [SV5: $i,SV153: $i,SV295: $i] :
( ( ! [SY1517: $i,SY1518: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY1518 @ SY1517 @ SV295 @ SV153 @ SV5 ) @ SV153 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5801]) ).
thf(5949,plain,
! [SV9: $i,SV157: $i,SV296: $i] :
( ( ! [SY1519: $i,SY1520: $i,SY1521: $i,SY1522: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1522 @ SY1521 @ SY1520 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1522 @ SY1519 @ SY1521 ) @ SV296 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1522 @ SY1519 @ SY1520 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1519 @ SY1521 @ SY1520 ) @ SV157 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5805]) ).
thf(5950,plain,
! [SV10: $i,SV158: $i,SV297: $i] :
( ( ! [SY1523: $i,SY1524: $i,SY1525: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1525 @ SY1524 @ SY1523 @ SV297 ) @ SV158 ) @ SV10 )
= ( hAPP @ SV297 @ ( hAPP @ SV158 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5806]) ).
thf(5951,plain,
! [SV11: $i,SV159: $i,SV298: $i] :
( ( ! [SY1526: $i,SY1527: $i,SY1528: $i,SY1529: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1529 @ SY1528 @ SY1527 @ SY1526 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1529 @ SY1527 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1528 @ SY1527 @ ( hAPP @ ( c_Fun_Ocomp @ SY1529 @ SY1528 @ SV298 @ SY1526 ) @ SV159 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5807]) ).
thf(5952,plain,
! [SV12: $i,SV160: $i,SV299: $i] :
( ( ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1532 @ SY1531 @ SY1530 @ SV299 ) @ SV160 ) @ SV12 )
= ( hAPP @ SV299 @ ( hAPP @ SV160 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(5953,plain,
! [SV13: $i,SV161: $i,SV300: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV300 @ SV161 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV161 @ SV300 ) @ SV13 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(5954,plain,
! [SV14: $i,SV162: $i,SV301: $i] :
( ( ! [SY1533: $i] :
( ( hAPP @ SY1533 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV301 @ SV301 ) @ SV162 ) @ SY1533 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV301 @ SV301 ) @ SV162 ) @ SY1533 ) @ ( hAPP @ SY1533 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(5955,plain,
! [SV15: $i,SV163: $i,SV302: $i] :
( ( ! [SY1534: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1534 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1534 ) @ SV302 ) @ SV163 ) ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1534 ) @ SV302 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1534 ) @ SV163 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5811]) ).
thf(5956,plain,
! [SV16: $i,SV164: $i,SV303: $i] :
( ( ! [SY1535: $i,SY1536: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1536 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1536 @ SY1535 ) @ SV303 ) @ SV164 ) ) @ SV303 ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1536 @ SY1535 ) @ SV303 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(5957,plain,
! [SV20: $i,SV167: $i,SV304: $i] :
( ( ! [SY1537: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1537 @ SV304 ) @ SV167 ) @ SV20 )
= SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(5958,plain,
! [SV21: $i,SV168: $i,SV305: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1540 @ SY1539 @ SY1538 ) @ SV305 ) @ SV168 ) @ SV21 )
= ( hAPP @ SV305 @ ( hAPP @ SV168 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5816]) ).
thf(5959,plain,
! [SV22: $i,SV169: $i,SV306: $i] :
( ( ! [SY1541: $i,SY1542: $i,SY1543: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1543 @ SY1542 @ SY1541 ) @ SV306 ) @ SV169 ) @ SV22 )
= ( hAPP @ ( hAPP @ SV306 @ SV22 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5817]) ).
thf(5960,plain,
! [SV23: $i,SV170: $i,SV307: $i] :
( ( ! [SY1544: $i,SY1545: $i,SY1546: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1546 @ SY1545 @ SY1544 ) @ SV307 ) @ SV170 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV307 @ SV23 ) @ ( hAPP @ SV170 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(5961,plain,
! [SV24: $i,SV171: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV171 ) @ SV24 ) ) )
= $true )
| ( ( SV171 = SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5819]) ).
thf(5962,plain,
! [SV25: $i] :
( ( ( hBOOL @ ( hAPP @ c_fNot @ SV25 ) )
= $false )
| ( ( ~ ( hBOOL @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5963,plain,
! [SV26: $i] :
( ( ( ~ ( hBOOL @ SV26 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5964,plain,
! [SV27: $i,SV172: $i] :
( ( ( ~ ( hBOOL @ SV172 )
| ~ ( hBOOL @ SV27 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV172 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5822]) ).
thf(5965,plain,
! [SV28: $i,SV173: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV173 ) @ SV28 ) ) )
= $true )
| ( ( hBOOL @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5823]) ).
thf(5966,plain,
! [SV29: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV174 ) @ SV29 ) ) )
= $true )
| ( ( hBOOL @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5824]) ).
thf(5967,plain,
! [SV30: $i,SV175: $i] :
( ( ( ~ ( hBOOL @ SV175 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV175 ) @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5825]) ).
thf(5968,plain,
! [SV31: $i,SV176: $i] :
( ( ( ~ ( hBOOL @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV31 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5826]) ).
thf(5969,plain,
! [SV32: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV177 ) @ SV32 ) )
| ( hBOOL @ SV177 ) )
= $true )
| ( ( hBOOL @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5827]) ).
thf(5970,plain,
! [SV33: $i,SV178: $i] :
( ( ( hBOOL @ SV178 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV178 ) @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(5971,plain,
! [SV34: $i,SV179: $i] :
( ( ( ~ ( hBOOL @ SV179 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV34 ) @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5829]) ).
thf(5972,plain,
! [SV35: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV180 ) @ SV35 ) )
| ~ ( hBOOL @ SV180 ) )
= $true )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5830]) ).
thf(5973,plain,
! [SV36: $i,SV181: $i,SV308: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i,SY1550: $i,SY1551: $i,SY1552: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1552 @ SY1551 @ SY1550 @ SY1549 ) @ SY1548 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1547 @ SY1551 @ SY1550 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SY1549 @ ( hAPP @ SY1548 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5831]) ).
thf(5974,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
| ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) )
| ~ ( ~ ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5832]) ).
thf(5975,plain,
! [SV38: $i,SV183: $i,SV310: $i] :
( ( ! [SY1559: $i,SY1560: $i,SY1561: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1561 @ SY1560 ) @ SY1559 ) @ SV310 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1561 @ SY1560 ) @ SV183 ) @ SV38 ) )
| ~ ( ( SY1559 != SV183 )
| ( SV310 != SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5833]) ).
thf(5976,plain,
! [SV39: $i,SV184: $i,SV311: $i] :
( ( ! [SY1562: $i] :
( ( SY1562 != SV311 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1562 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SY1562 ) @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(5977,plain,
! [SV40: $i,SV185: $i,SV312: $i] :
( ( ! [SY1563: $i,SY1564: $i,SY1565: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1565 @ SY1564 @ SY1563 @ SV312 @ SV185 )
| ( ( hAPP @ SV312 @ ( hAPP @ SY1563 @ SV40 ) )
= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5835]) ).
thf(5978,plain,
! [SV41: $i,SV186: $i,SV313: $i] :
( ( ! [SY1566: $i,SY1567: $i,SY1568: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1568 @ SY1567 @ SY1566 )
| ( ( hAPP @ ( hAPP @ SY1566 @ SV313 ) @ ( hAPP @ ( hAPP @ SY1566 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SY1566 @ SV186 ) @ ( hAPP @ ( hAPP @ SY1566 @ SV313 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5836]) ).
thf(5979,plain,
! [SV42: $i,SV187: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV187 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $true )
| ( ( SV187 = SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5837]) ).
thf(5980,plain,
! [SV43: $i,SV188: $i,SV314: $i] :
( ( ! [SY1569: $i,SY1570: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1570 ) @ ( hAPP @ SY1569 @ SV314 ) ) @ SV188 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SV314 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SY1570 @ SY1569 ) @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5838]) ).
thf(5981,plain,
! [SV44: $i,SV189: $i,SV315: $i] :
( ( ! [SY1571: $i,SY1572: $i,SY1573: $i,SY1574: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1574 @ SY1573 @ SY1572 @ SY1571 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1575: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1571 @ SV189 ) @ SY1575 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1575 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1576: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1571 @ SV189 ) @ SY1576 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1576 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1574 @ SY1573 @ SY1572 @ SY1571 @ SV315 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5839]) ).
thf(5982,plain,
! [SV45: $i,SV190: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
| ( SV190 = SV45 ) )
| ~ ( ( SV190 != SV45 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(5983,plain,
! [SV47: $i,SV191: $i,SV316: $i] :
( ( ! [SY1577: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1577 ) @ SV316 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1577 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1577 ) @ SV47 ) @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5842]) ).
thf(5984,plain,
! [SV48: $i,SV192: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
| ( SV192 = SV48 ) )
| ~ ( ( SV192 != SV48 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(5985,plain,
! [SV49: $i,SV193: $i,SV317: $i] :
( ( ! [SY1578: $i,SY1579: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1578 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1580: $i] :
~ ( ~ ( ( SY1578
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SV193 ) @ SY1580 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1580 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1578 ) @ SY1580 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1580 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY1581: $i] :
~ ( ~ ( ( SY1578
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SV193 ) @ SY1581 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1581 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1578 ) @ SY1581 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1581 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SY1578 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1579 ) @ SV193 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(5986,plain,
! [SV50: $i,SV194: $i,SV318: $i] :
( ( ! [SY1582: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1582 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1582 ) @ SV194 ) @ SV50 ) ) )
| ~ ( ( SV318 != SV194 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1582 ) @ SV318 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5845]) ).
thf(5987,plain,
! [SV51: $i,SV195: $i,SV319: $i] :
( ( ! [SY1583: $i,SY1584: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1584 @ SY1583 ) @ SV319 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SY1584 ) @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5846]) ).
thf(5988,plain,
! [SV52: $i,SV196: $i,SV320: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV320 @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV52 ) @ SV196 ) @ ( hAPP @ ( c_Set_OCollect @ SV52 ) @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5847]) ).
thf(5989,plain,
! [SV53: $i,SV197: $i,SV321: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1587 @ SY1586 @ SY1585 @ SV321 @ SV197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1586 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SY1585 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5848]) ).
thf(5990,plain,
! [SV54: $i,SV198: $i,SV322: $i] :
( ( ! [SY1588: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1588 ) @ SV322 ) @ SV198 ) @ SV54 ) )
| ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ~ ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1588 ) @ SV322 ) @ SV198 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5849]) ).
thf(5991,plain,
! [SV55: $i,SV199: $i,SV323: $i] :
( ( ! [SY1589: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1589 ) @ SV323 ) @ SV199 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1589 ) @ SV323 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1589 ) @ SV323 ) @ SV55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5850]) ).
thf(5992,plain,
! [SV56: $i,SV200: $i,SV324: $i] :
( ( ! [SY1590: $i,SY1591: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1591 ) @ SY1590 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1591 @ SV324 @ SV200 ) @ SV56 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ ( hAPP @ SV200 @ SY1590 ) ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5851]) ).
thf(5993,plain,
! [SV57: $i,SV201: $i,SV325: $i] :
( ( ~ ( c_Predicate_Oreflp @ SV325 @ SV201 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV201 @ SV57 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5852]) ).
thf(5994,plain,
! [SV58: $i,SV202: $i,SV326: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV326 ) @ SV202 ) @ SV58 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV326 ) @ SV202 ) @ SV58 )
= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5853]) ).
thf(5995,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
| ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) )
| ~ ( ~ ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5854]) ).
thf(5996,plain,
! [SV60: $i,SV204: $i,SV328: $i] :
( ( ! [SY1594: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1594 @ SV328 ) @ SV204 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1594 @ SV328 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5855]) ).
thf(5997,plain,
! [SV61: $i,SV205: $i,SV329: $i] :
( ( ! [SY1595: $i,SY1596: $i,SY1597: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1597 ) @ SY1596 ) @ SY1595 )
!= SV329 )
| ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1597 ) @ SY1595 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1597 ) @ SY1596 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1597 ) @ SV329 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5856]) ).
thf(5998,plain,
! [SV62: $i,SV206: $i,SV330: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1599 @ SY1598 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1598 @ SV330 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1598 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1598 @ SV330 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5857]) ).
thf(5999,plain,
! [SV64: $i,SV207: $i,SV331: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV207 ) )
| ( hBOOL @ ( hAPP @ SV331 @ ( c_Hilbert__Choice_OEps @ SV64 @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5859]) ).
thf(6000,plain,
! [SV65: $i,SV208: $i,SV332: $i] :
( ( ! [SY1600: $i] :
( ( SY1600 != SV332 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1600 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SY1600 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5860]) ).
thf(6001,plain,
! [SV66: $i,SV209: $i,SV333: $i] :
( ( ~ ~ ! [SY1601: $i] :
~ ( hBOOL @ ( hAPP @ SV333 @ SY1601 ) )
| ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5861]) ).
thf(6002,plain,
! [SV67: $i,SV210: $i,SV334: $i] :
( ( ! [SY1602: $i,SY1603: $i,SY1604: $i,SY1605: $i,SY1606: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1606 @ SY1605 ) @ SY1604 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1603 @ SY1604 ) @ SY1602 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SY1606 @ SY1603 ) @ SY1605 ) @ SY1602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5862]) ).
thf(6003,plain,
! [SV68: $i,SV211: $i,SV335: $i] :
( ( ! [SY1607: $i,SY1608: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1608 ) @ SY1607 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1608 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SY1607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SY1607 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SY1607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SY1607 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1608 ) @ SY1607 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1608 @ SV335 @ SV211 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5863]) ).
thf(6004,plain,
! [SV69: $i,SV212: $i,SV336: $i] :
( ( ! [SY1609: $i,SY1610: $i,SY1611: $i] :
( ~ ( ( SY1611 != SY1610 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1609 @ SV336 @ SV212 @ SY1610 @ SV69 ) @ SY1611 )
= ( hAPP @ SV212 @ SY1611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5864]) ).
thf(6005,plain,
! [SV70: $i,SV213: $i,SV337: $i] :
( ( ! [SY1612: $i] :
~ ( ~ ( ~ ( c_Fun_Oinj__on @ SY1612 @ SV337 @ SV213 @ SV70 )
| ! [SY1292: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1612 ) @ SY1292 ) @ SV70 ) )
| ! [SY1293: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1612 ) @ SY1293 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1292 )
!= ( hAPP @ SV213 @ SY1293 ) )
| ( SY1292 = SY1293 ) ) ) )
| ~ ( ~ ! [SY1294: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1612 ) @ SY1294 ) @ SV70 ) )
| ! [SY1295: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1612 ) @ SY1295 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1294 )
!= ( hAPP @ SV213 @ SY1295 ) )
| ( SY1294 = SY1295 ) ) )
| ( c_Fun_Oinj__on @ SY1612 @ SV337 @ SV213 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5865]) ).
thf(6006,plain,
! [SV71: $i,SV214: $i,SV338: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i,SY1620: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1620 @ SY1619 @ SY1618 @ SY1617 @ SV338 @ SV214 )
| ( ( hAPP @ ( hAPP @ SY1618 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5866]) ).
thf(6007,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SV215 = SV72 ) )
| ~ ( ( SV215 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5867]) ).
thf(6008,plain,
! [SV73: $i,SV216: $i,SV340: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1622 @ SY1621 @ SV340 ) @ SV216 ) @ SV73 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV340 @ SV73 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5868]) ).
thf(6009,plain,
! [SV74: $i,SV217: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
| ( SV217 = SV74 ) )
| ~ ( ( SV217 != SV74 )
| ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(6010,plain,
! [SV75: $i,SV218: $i,SV341: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1624 ) @ SY1623 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1624 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SY1623 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY1623 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SY1623 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY1623 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1624 ) @ SY1623 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1624 @ SV341 @ SV218 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5870]) ).
thf(6011,plain,
! [SV76: $i,SV219: $i,SV342: $i] :
( ( ! [SY1625: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1625 @ SV342 @ SV219 )
| ( ( hAPP @ ( hAPP @ SV342 @ SV76 ) @ SV76 )
= SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5871]) ).
thf(6012,plain,
! [SV77: $i,SV220: $i,SV343: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV343 ) @ SV220 ) @ ( hAPP @ ( c_Set_OCollect @ SV343 ) @ SV77 ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5872]) ).
thf(6013,plain,
! [SV78: $i,SV221: $i,SV344: $i] :
( ( ! [SY1626: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1626 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SY1626 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1626 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SY1626 @ SV221 @ SV78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5873]) ).
thf(6014,plain,
! [SV79: $i,SV222: $i,SV345: $i] :
( ( ! [SY1627: $i,SY1628: $i,SY1629: $i] :
( ~ ( c_Fun_Oinj__on @ SY1629 @ SY1628 @ SY1627 @ SV345 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1629 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1629 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SY1627 @ SV222 )
!= ( hAPP @ SY1627 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SY1627 @ SV222 )
= ( hAPP @ SY1627 @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5874]) ).
thf(6015,plain,
! [SV80: $i,SV223: $i,SV346: $i] :
( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ ( hAPP @ c_Nat_OSuc @ SV223 ) @ SV80 )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ SV223 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5875]) ).
thf(6016,plain,
! [SV81: $i,SV224: $i,SV347: $i] :
( ( ! [SY1630: $i,SY1631: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1631 @ SY1630 ) @ SV347 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SY1631 ) @ SV347 ) @ SY1630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5876]) ).
thf(6017,plain,
! [SV82: $i,SV225: $i] :
( ( ( ~ ~ ! [SY1321: $i] :
~ ( hBOOL @ ( hAPP @ SV225 @ SY1321 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5877]) ).
thf(6018,plain,
! [SV83: $i,SV226: $i,SV348: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV348 ) @ SV226 ) @ SV83 )
!= SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5878]) ).
thf(6019,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
| ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) )
| ~ ( ~ ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5879]) ).
thf(6020,plain,
! [SV85: $i,SV228: $i,SV350: $i] :
( ( ! [SY1634: $i,SY1635: $i,SY1636: $i] :
~ ( ~ ( ( SY1636 != SY1635 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1634 @ SV350 @ SV228 @ SY1635 @ SV85 ) @ SY1636 )
= SV85 ) )
| ~ ( ~ ( ( SY1636 != SY1635 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1634 @ SV350 @ SV228 @ SY1635 @ SV85 ) @ SY1636 )
= ( hAPP @ SV228 @ SY1636 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5880]) ).
thf(6021,plain,
! [SV86: $i,SV229: $i,SV351: $i] :
( ( ! [SY1637: $i,SY1638: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1638 @ SY1637 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1638 @ SY1637 @ SV351 ) @ SV229 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5881]) ).
thf(6022,plain,
! [SV87: $i,SV230: $i,SV352: $i] :
( ( ! [SY1639: $i,SY1640: $i,SY1641: $i] :
( ~ ( ( SY1641 != SY1640 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1639 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1639 @ SV352 ) @ SY1641 ) @ SV230 ) ) @ SY1640 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1639 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1639 @ SV352 ) @ SY1640 ) @ SV87 ) ) @ SY1641 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5882]) ).
thf(6023,plain,
! [SV88: $i,SV231: $i,SV353: $i] :
( ( ! [SY1642: $i,SY1643: $i,SY1644: $i] :
( ( SY1644
!= ( hAPP @ SY1643 @ SY1642 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SY1642 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SY1644 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SY1643 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5883]) ).
thf(6024,plain,
! [SV89: $i,SV232: $i,SV354: $i] :
( ( ! [SY1645: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1645 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY1645 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1645 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY1645 @ SV232 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5884]) ).
thf(6025,plain,
! [SV90: $i,SV233: $i,SV355: $i] :
( ( ! [SY1646: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1646 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1646 ) @ SV233 ) @ SV90 ) ) )
| ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1646 ) @ SV355 ) @ SV90 ) ) )
| ~ ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1646 ) @ SV355 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1646 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1646 ) @ SV233 ) @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5885]) ).
thf(6026,plain,
! [SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV91 ) @ v_ts ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ t_a @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(6027,plain,
! [SV92: $i,SV234: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
| ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
| ~ ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(6028,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
| ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) )
| ~ ( ~ ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5888]) ).
thf(6029,plain,
! [SV94: $i,SV236: $i,SV357: $i] :
( ( ! [SY1649: $i] :
( ~ ( c_Predicate_Osymp @ SY1649 @ SV357 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5889]) ).
thf(6030,plain,
! [SV95: $i,SV237: $i,SV358: $i] :
( ( ! [SY1650: $i,SY1651: $i,SY1652: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1652 ) @ SY1651 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1652 @ SY1650 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SY1651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1650 @ SY1651 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SY1651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1650 @ SY1651 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1652 ) @ SY1651 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1652 @ SY1650 @ SV358 @ SV237 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5890]) ).
thf(6031,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5891]) ).
thf(6032,plain,
! [SV97: $i,SV239: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
| ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(6033,plain,
! [SV98: $i,SV240: $i,SV360: $i] :
( ( ! [SY1653: $i,SY1654: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1654 @ SY1653 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) )
| ~ ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SY1654 @ SY1653 @ SV360 @ SV240 @ SV98 )
= SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5893]) ).
thf(6034,plain,
! [SV99: $i,SV241: $i,SV361: $i] :
( ( ! [SY1655: $i,SY1656: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1656 ) @ SY1655 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1656 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SY1655 != SV241 )
| ( SV361 != SV99 ) ) )
| ~ ( ~ ~ ( ( SY1655 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1656 ) @ SY1655 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1656 ) @ SV241 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5894]) ).
thf(6035,plain,
! [SV100: $i,SV242: $i,SV362: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1658 @ SY1657 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1658 @ SY1657 @ SV362 ) @ SV242 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5895]) ).
thf(6036,plain,
! [SV101: $i,SV243: $i,SV363: $i] :
( ( ! [SY1659: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1659 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1659 ) @ SV363 ) @ SV101 ) )
| ( SV243 = SV101 ) )
| ~ ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1659 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1659 ) @ SV363 ) @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5896]) ).
thf(6037,plain,
! [SV102: $i,SV244: $i,SV364: $i] :
( ( ! [SY1660: $i,SY1661: $i,SY1662: $i] :
( ~ ( c_Fun_Oinj__on @ SY1662 @ SY1661 @ SY1660 @ SV364 )
| ( ( hAPP @ SY1660 @ SV244 )
!= ( hAPP @ SY1660 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1662 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1662 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5897]) ).
thf(6038,plain,
! [SV103: $i,SV245: $i,SV365: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i,SY1666: $i,SY1667: $i,SY1668: $i,SY1669: $i,SY1670: $i] :
( ( ( hAPP @ SY1670 @ ( hAPP @ SY1669 @ SY1668 ) )
!= ( hAPP @ SY1667 @ ( hAPP @ SY1666 @ SY1665 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1664 @ SY1663 @ SV365 @ SY1670 ) @ SY1669 ) @ SY1668 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SY1663 @ SV103 @ SY1667 ) @ SY1666 ) @ SY1665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5898]) ).
thf(6039,plain,
! [SV104: $i,SV246: $i,SV366: $i] :
( ( ! [SY1671: $i,SY1672: $i,SY1673: $i,SY1674: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1674 @ SY1673 @ SY1672 @ SY1671 ) @ SV366 )
!= SV246 )
| ( ( hAPP @ SY1671 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5899]) ).
thf(6040,plain,
! [SV105: $i,SV247: $i,SV367: $i] :
( ( ! [SY1675: $i,SY1676: $i,SY1677: $i] :
( ( SY1677 != SY1676 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1675 @ SV367 @ SV247 ) @ SV105 ) @ SY1677 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1675 @ SV367 @ SV247 ) @ SV105 ) @ SY1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5900]) ).
thf(6041,plain,
! [SV106: $i,SV248: $i,SV368: $i] :
( ( ! [SY1678: $i,SY1679: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1679 @ SY1678 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1679 @ SY1678 @ SV368 ) @ SV248 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5901]) ).
thf(6042,plain,
! [SV107: $i,SV249: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
| ( SV249 = SV107 ) )
| ~ ( ( SV249 != SV107 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(6043,plain,
! [SV108: $i,SV250: $i,SV369: $i] :
( ( ! [SY1680: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1680 @ SV369 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1680 @ SV369 ) @ SV108 ) )
| ( SV250 = SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5903]) ).
thf(6044,plain,
! [SV109: $i,SV251: $i,SV370: $i] :
( ( ! [SY1681: $i,SY1682: $i,SY1683: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1683 ) @ SY1682 ) @ SY1681 ) )
| ( SV370
!= ( hAPP @ SV251 @ SY1682 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SY1683 @ SV109 @ SV251 ) @ SY1681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(6045,plain,
! [SV110: $i,SV252: $i,SV371: $i] :
( ( ! [SY1684: $i,SY1685: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1685 @ SY1684 @ SV371 )
| ( ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(6046,plain,
! [SV111: $i,SV253: $i,SV372: $i] :
( ( ! [SY1686: $i,SY1687: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1687 ) @ SY1686 ) @ SV372 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SY1686 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1687 @ SV253 @ SV111 ) @ SV372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5906]) ).
thf(6047,plain,
! [SV112: $i,SV254: $i,SV373: $i] :
( ( ! [SY1688: $i,SY1689: $i,SY1690: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1690 @ SY1689 ) @ SY1688 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1690 @ SY1689 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SY1688 != SV254 )
| ( SV373 != SV112 ) ) )
| ~ ( ~ ~ ( ( SY1688 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1690 @ SY1689 ) @ SY1688 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1690 @ SY1689 ) @ SV254 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5907]) ).
thf(6048,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
| ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
| ~ ( ~ ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) )
| ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(6049,plain,
! [SV114: $i,SV256: $i,SV374: $i] :
( ( ! [SY1691: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1691 @ SV374 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
| ~ ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1691 @ SV374 @ SV256 ) @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5909]) ).
thf(6050,plain,
! [SV115: $i,SV257: $i,SV375: $i] :
( ( ! [SY1694: $i] :
( ( SY1694 != SV375 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1694 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SY1694 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5910]) ).
thf(6051,plain,
! [SV116: $i,SV258: $i,SV376: $i] :
( ( ! [SY1695: $i] :
( ( SY1695 != SV376 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SY1695 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5911]) ).
thf(6052,plain,
! [SV117: $i,SV259: $i,SV377: $i] :
( ( ! [SY1696: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1696 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1696 ) @ SV117 ) @ SV259 ) )
| ( SV377 = SV117 ) )
| ~ ( ( SV377 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1696 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1696 ) @ SV117 ) @ SV259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5912]) ).
thf(6053,plain,
! [SV118: $i,SV260: $i,SV378: $i] :
( ( ! [SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i,SY1701: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1701 @ SY1700 @ SY1699 @ SY1698 ) @ SY1697 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SY1700 @ SY1699 @ SV260 ) @ SV118 ) )
| ! [SY1435: $i] :
( ( hAPP @ SY1698 @ ( hAPP @ SY1697 @ SY1435 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5913]) ).
thf(6054,plain,
! [SV119: $i,SV261: $i,SV379: $i] :
( ( ! [SY1703: $i,SY1704: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1704 @ SY1703 ) @ SV379 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SY1704 ) @ SY1703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5914]) ).
thf(6055,plain,
! [SV120: $i,SV262: $i,SV380: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
( ( ( hAPP @ SY1706 @ SY1705 )
!= SV380 )
| ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SY1706 @ SY1705 @ SV380 )
= SY1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5915]) ).
thf(6056,plain,
! [SV121: $i,SV263: $i,SV381: $i] :
( ( ! [SY1707: $i,SY1708: $i,SY1709: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1709 @ SY1708 @ SY1707 @ SV381 @ SV263 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1708 ) @ ( hAPP @ SY1707 @ SV121 ) ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5916]) ).
thf(6057,plain,
! [SV122: $i,SV264: $i,SV382: $i] :
( ( ! [SY1710: $i,SY1711: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1711 ) @ SY1710 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SY1711 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1712: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1712 ) @ SV122 ) )
| ( SY1710
!= ( hAPP @ SV264 @ SY1712 ) ) ) )
| ~ ( ~ ~ ! [SY1713: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1713 ) @ SV122 ) )
| ( SY1710
!= ( hAPP @ SV264 @ SY1713 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1711 ) @ SY1710 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SY1711 @ SV264 ) @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5917]) ).
thf(6058,plain,
! [SV123: $i,SV265: $i,SV383: $i] :
( ( ! [SY1714: $i,SY1715: $i] :
( ~ ( c_Predicate_Otransp @ SY1715 @ SY1714 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1714 @ SV383 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1714 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1714 @ SV383 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5918]) ).
thf(6059,plain,
! [SV124: $i,SV266: $i,SV384: $i] :
( ( ! [SY1716: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1716 @ SV384 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5919]) ).
thf(6060,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ( ~ ( ~ ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) )
| ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
| ~ ( ~ ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) )
| ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5920]) ).
thf(6061,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
!= SV126 )
| ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) ) )
| ~ ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5921]) ).
thf(6062,plain,
! [SV127: $i,SV269: $i] :
( ( ( ~ ~ ! [SY1464: $i] :
~ ( hBOOL @ ( hAPP @ SV269 @ SY1464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5922]) ).
thf(6063,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5923]) ).
thf(6064,plain,
! [SV129: $i,SV271: $i,SV388: $i] :
( ( ! [SY1723: $i,SY1724: $i,SY1725: $i,SY1726: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1726 @ SY1725 @ SY1724 @ SY1723 @ SV388 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1725 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1725 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SY1723 @ SV271 )
!= ( hAPP @ SY1723 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SY1723 @ SV271 )
= ( hAPP @ SY1723 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5924]) ).
thf(6065,plain,
! [SV130: $i,SV272: $i,SV389: $i] :
( ( ! [SY1727: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1727 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SY1727 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1727 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SY1727 @ SV272 @ SV130 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5925]) ).
thf(6066,plain,
! [SV131: $i,SV273: $i,SV390: $i] :
( ( SV390
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV273 ) @ SV131 ) @ SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(6067,plain,
! [SV132: $i,SV274: $i,SV391: $i] :
( ( ! [SY1728: $i,SY1729: $i,SY1730: $i] :
( ~ ( c_Fun_Oinj__on @ SY1730 @ SY1729 @ SY1728 @ SV391 )
| ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1730 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1730 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SY1728 @ SV274 )
!= ( hAPP @ SY1728 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5927]) ).
thf(6068,plain,
! [SV133: $i,SV275: $i,SV392: $i] :
( ( ! [SY1731: $i,SY1732: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1732 ) @ SY1731 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1732 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SY1731 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SY1731 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1732 ) @ SY1731 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1732 @ SV392 @ SV275 ) @ SV133 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5928]) ).
thf(6069,plain,
! [SV134: $i,SV276: $i,SV393: $i] :
( ( ! [SY1733: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1733 @ SV393 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5929]) ).
thf(6070,plain,
! [SV135: $i,SV277: $i] :
( ( ( SV277 != SV135 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV277 ) @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5930]) ).
thf(6071,plain,
! [SV136: $i,SV278: $i,SV394: $i] :
( ( ! [SY1734: $i,SY1735: $i,SY1736: $i] :
( ( ( hAPP @ SY1736 @ SY1735 )
!= SY1734 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SY1734 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SY1735 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SY1736 ) @ SV278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5931]) ).
thf(6072,plain,
! [SV137: $i,SV279: $i,SV395: $i] :
( ( ! [SY1737: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1737 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SY1737 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1737 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SY1737 @ SV279 @ SV137 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(6073,plain,
! [SV138: $i,SV280: $i,SV396: $i] :
( ( ! [SY1738: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1738 @ SV396 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
| ~ ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1738 @ SV396 @ SV280 ) @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5933]) ).
thf(6074,plain,
! [SV139: $i,SV281: $i,SV397: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1742 @ SY1741 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1741 @ SV397 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1741 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1741 @ SV397 ) @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5934]) ).
thf(6075,plain,
! [SV140: $i,SV282: $i,SV398: $i] :
( ( ! [SY1743: $i,SY1744: $i,SY1745: $i,SY1746: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1746 @ SY1745 @ SY1744 @ SY1743 @ SV398 )
| ~ ( ~ ( ( ( hAPP @ SY1744 @ SV282 )
!= ( hAPP @ SY1744 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SY1744 @ SV282 )
= ( hAPP @ SY1744 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5935]) ).
thf(6076,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
| ( SV283 = SV141 ) )
| ~ ( ( SV283 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5936]) ).
thf(6077,plain,
! [SV142: $i,SV284: $i,SV400: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV400 ) @ SV284 ) @ ( hAPP @ ( c_Set_OCollect @ SV400 ) @ SV142 ) ) )
| ( hBOOL @ ( hAPP @ SV142 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5937]) ).
thf(6078,plain,
! [SV143: $i,SV285: $i,SV401: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV401 @ SV285 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV285 @ SV143 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5938]) ).
thf(6079,plain,
! [SV144: $i,SV286: $i,SV402: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1749 ) @ SY1748 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1749 @ SY1747 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1747 @ SV286 ) @ SY1748 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SY1748 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1747 @ SV286 ) @ SY1748 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SY1748 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1749 ) @ SY1748 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1749 @ SY1747 @ SV402 @ SV286 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5939]) ).
thf(6080,plain,
! [SV145: $i,SV287: $i,SV403: $i] :
( ( ! [SY1750: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1750 ) @ SV403 ) @ SV287 ) )
| ( SV403 = SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1750 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1750 ) @ SV145 ) @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5940]) ).
thf(6081,plain,
! [SV146: $i,SV288: $i,SV404: $i] :
( ( ! [SY1751: $i,SY1752: $i,SY1753: $i] :
~ ( ~ ( ( SY1753 != SY1752 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1751 @ SV404 @ SV288 @ SY1752 @ SV146 ) @ SY1753 )
= SV146 ) )
| ~ ( ~ ( ( SY1753 != SY1752 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1751 @ SV404 @ SV288 @ SY1752 @ SV146 ) @ SY1753 )
= ( hAPP @ SV288 @ SY1753 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5941]) ).
thf(6082,plain,
! [SV147: $i,SV289: $i] :
( ( ( ~ ! [SY1514: $i] :
( ( hAPP @ SV289 @ SY1514 )
= ( hAPP @ SV147 @ SY1514 ) ) )
= $true )
| ( ( SV289 = SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(6083,plain,
! [SV148: $i,SV290: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
| ( SV290 = SV148 ) )
| ~ ( ( SV290 != SV148 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5943]) ).
thf(6084,plain,
! [SV2: $i,SV150: $i,SV292: $i,SV405: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV405 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV405 ) @ SV150 ) @ SV2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV405 ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV405 ) @ SV292 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5945]) ).
thf(6085,plain,
! [SV4: $i,SV152: $i,SV294: $i,SV406: $i] :
( ( ( c_Fun_Ofun__upd @ SV406 @ SV294 @ SV152 @ SV4 @ ( hAPP @ SV152 @ SV4 ) )
= SV152 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5947]) ).
thf(6086,plain,
! [SV5: $i,SV153: $i,SV295: $i,SV407: $i] :
( ( ! [SY1754: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY1754 @ SV407 @ SV295 @ SV153 @ SV5 ) @ SV153 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6087,plain,
! [SV9: $i,SV157: $i,SV296: $i,SV408: $i] :
( ( ! [SY1755: $i,SY1756: $i,SY1757: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1757 @ SY1756 @ SY1755 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1757 @ SV408 @ SY1756 ) @ SV296 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1757 @ SV408 @ SY1755 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV408 @ SY1756 @ SY1755 ) @ SV157 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5949]) ).
thf(6088,plain,
! [SV10: $i,SV158: $i,SV297: $i,SV409: $i] :
( ( ! [SY1758: $i,SY1759: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1759 @ SY1758 @ SV409 @ SV297 ) @ SV158 ) @ SV10 )
= ( hAPP @ SV297 @ ( hAPP @ SV158 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5950]) ).
thf(6089,plain,
! [SV11: $i,SV159: $i,SV298: $i,SV410: $i] :
( ( ! [SY1760: $i,SY1761: $i,SY1762: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1762 @ SY1761 @ SY1760 @ SV410 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1762 @ SY1760 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1761 @ SY1760 @ ( hAPP @ ( c_Fun_Ocomp @ SY1762 @ SY1761 @ SV298 @ SV410 ) @ SV159 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5951]) ).
thf(6090,plain,
! [SV12: $i,SV160: $i,SV299: $i,SV411: $i] :
( ( ! [SY1763: $i,SY1764: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1764 @ SY1763 @ SV411 @ SV299 ) @ SV160 ) @ SV12 )
= ( hAPP @ SV299 @ ( hAPP @ SV160 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5952]) ).
thf(6091,plain,
! [SV14: $i,SV162: $i,SV301: $i,SV412: $i] :
( ( ( hAPP @ SV412 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV301 @ SV301 ) @ SV162 ) @ SV412 ) @ SV14 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV301 @ SV301 ) @ SV162 ) @ SV412 ) @ ( hAPP @ SV412 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5954]) ).
thf(6092,plain,
! [SV15: $i,SV163: $i,SV302: $i,SV413: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV413 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV413 ) @ SV302 ) @ SV163 ) ) @ SV15 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV413 ) @ SV302 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV413 ) @ SV163 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5955]) ).
thf(6093,plain,
! [SV16: $i,SV164: $i,SV303: $i,SV414: $i] :
( ( ! [SY1765: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1765 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1765 @ SV414 ) @ SV303 ) @ SV164 ) ) @ SV303 ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1765 @ SV414 ) @ SV303 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(6094,plain,
! [SV20: $i,SV167: $i,SV304: $i,SV415: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV415 @ SV304 ) @ SV167 ) @ SV20 )
= SV167 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5957]) ).
thf(6095,plain,
! [SV21: $i,SV168: $i,SV305: $i,SV416: $i] :
( ( ! [SY1766: $i,SY1767: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1767 @ SY1766 @ SV416 ) @ SV305 ) @ SV168 ) @ SV21 )
= ( hAPP @ SV305 @ ( hAPP @ SV168 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5958]) ).
thf(6096,plain,
! [SV22: $i,SV169: $i,SV306: $i,SV417: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1769 @ SY1768 @ SV417 ) @ SV306 ) @ SV169 ) @ SV22 )
= ( hAPP @ ( hAPP @ SV306 @ SV22 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5959]) ).
thf(6097,plain,
! [SV23: $i,SV170: $i,SV307: $i,SV418: $i] :
( ( ! [SY1770: $i,SY1771: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1771 @ SY1770 @ SV418 ) @ SV307 ) @ SV170 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV307 @ SV23 ) @ ( hAPP @ SV170 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(6098,plain,
! [SV24: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV171 ) @ SV24 ) )
= $false )
| ( ( SV171 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5961]) ).
thf(6099,plain,
! [SV25: $i] :
( ( ( hBOOL @ SV25 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5962]) ).
thf(6100,plain,
! [SV26: $i] :
( ( ( hBOOL @ SV26 )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5963]) ).
thf(6101,plain,
! [SV27: $i,SV172: $i] :
( ( ( ~ ( hBOOL @ SV172 ) )
= $true )
| ( ( ~ ( hBOOL @ SV27 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV172 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5964]) ).
thf(6102,plain,
! [SV28: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV173 ) @ SV28 ) )
= $false )
| ( ( hBOOL @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(6103,plain,
! [SV29: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV174 ) @ SV29 ) )
= $false )
| ( ( hBOOL @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5966]) ).
thf(6104,plain,
! [SV30: $i,SV175: $i] :
( ( ( hBOOL @ SV175 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV175 ) @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5967]) ).
thf(6105,plain,
! [SV31: $i,SV176: $i] :
( ( ( hBOOL @ SV176 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV31 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5968]) ).
thf(6106,plain,
! [SV32: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV177 ) @ SV32 ) ) )
= $true )
| ( ( hBOOL @ SV177 )
= $true )
| ( ( hBOOL @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5969]) ).
thf(6107,plain,
! [SV34: $i,SV179: $i] :
( ( ( hBOOL @ SV179 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV34 ) @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(6108,plain,
! [SV35: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV180 ) @ SV35 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV180 ) )
= $true )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5972]) ).
thf(6109,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i,SY1775: $i,SY1776: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1776 @ SY1775 @ SY1774 @ SY1773 ) @ SY1772 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SY1775 @ SY1774 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SY1773 @ ( hAPP @ SY1772 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5973]) ).
thf(6110,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
| ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) )
| ~ ( ~ ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5974]) ).
thf(6111,plain,
! [SV38: $i,SV183: $i,SV310: $i,SV420: $i] :
( ( ! [SY1777: $i,SY1778: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1778 @ SY1777 ) @ SV420 ) @ SV310 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1778 @ SY1777 ) @ SV183 ) @ SV38 ) )
| ~ ( ( SV420 != SV183 )
| ( SV310 != SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5975]) ).
thf(6112,plain,
! [SV39: $i,SV184: $i,SV311: $i,SV421: $i] :
( ( ( SV421 != SV311 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5976]) ).
thf(6113,plain,
! [SV40: $i,SV185: $i,SV312: $i,SV422: $i] :
( ( ! [SY1779: $i,SY1780: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1780 @ SY1779 @ SV422 @ SV312 @ SV185 )
| ( ( hAPP @ SV312 @ ( hAPP @ SV422 @ SV40 ) )
= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5977]) ).
thf(6114,plain,
! [SV41: $i,SV186: $i,SV313: $i,SV423: $i] :
( ( ! [SY1781: $i,SY1782: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1782 @ SY1781 @ SV423 )
| ( ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5978]) ).
thf(6115,plain,
! [SV42: $i,SV187: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV187 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $false )
| ( ( SV187 = SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5979]) ).
thf(6116,plain,
! [SV43: $i,SV188: $i,SV314: $i,SV424: $i] :
( ( ! [SY1783: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1783 ) @ ( hAPP @ SV424 @ SV314 ) ) @ SV188 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SV314 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SY1783 @ SV424 ) @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5980]) ).
thf(6117,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1786 @ SY1785 @ SY1784 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1786 @ SY1785 @ SY1784 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5981]) ).
thf(6118,plain,
! [SV45: $i,SV190: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
| ( SV190 = SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5982]) ).
thf(6119,plain,
! [SV45: $i,SV190: $i] :
( ( ~ ( ( SV190 != SV45 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5982]) ).
thf(6120,plain,
! [SV47: $i,SV191: $i,SV316: $i,SV426: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV426 ) @ SV47 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6121,plain,
! [SV48: $i,SV192: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
| ( SV192 = SV48 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5984]) ).
thf(6122,plain,
! [SV48: $i,SV192: $i] :
( ( ~ ( ( SV192 != SV48 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5984]) ).
thf(6123,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i] :
( ( ! [SY1789: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1790: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV193 ) @ SY1790 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SY1790 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV427 ) @ SY1790 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SY1790 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY1791: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV193 ) @ SY1791 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SY1791 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV427 ) @ SY1791 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SY1791 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1789 ) @ SV193 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5985]) ).
thf(6124,plain,
! [SV50: $i,SV194: $i,SV318: $i,SV428: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) )
| ~ ( ( SV318 != SV194 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5986]) ).
thf(6125,plain,
! [SV51: $i,SV195: $i,SV319: $i,SV429: $i] :
( ( ! [SY1792: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1792 @ SV429 ) @ SV319 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SY1792 ) @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5987]) ).
thf(6126,plain,
! [SV52: $i,SV196: $i,SV320: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV320 @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV52 ) @ SV196 ) @ ( hAPP @ ( c_Set_OCollect @ SV52 ) @ SV320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5988]) ).
thf(6127,plain,
! [SV53: $i,SV197: $i,SV321: $i,SV430: $i] :
( ( ! [SY1793: $i,SY1794: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1794 @ SY1793 @ SV430 @ SV321 @ SV197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1793 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5989]) ).
thf(6128,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
| ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ~ ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5990]) ).
thf(6129,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5991]) ).
thf(6130,plain,
! [SV56: $i,SV200: $i,SV324: $i,SV433: $i] :
( ( ! [SY1795: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1795 ) @ SV433 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1795 @ SV324 @ SV200 ) @ SV56 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ ( hAPP @ SV200 @ SV433 ) ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6131,plain,
! [SV57: $i,SV201: $i,SV325: $i] :
( ( ( ~ ( c_Predicate_Oreflp @ SV325 @ SV201 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV201 @ SV57 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5993]) ).
thf(6132,plain,
! [SV58: $i,SV202: $i,SV326: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV326 ) @ SV202 ) @ SV58 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV326 ) @ SV202 ) @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5994]) ).
thf(6133,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
| ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) )
| ~ ( ~ ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5995]) ).
thf(6134,plain,
! [SV60: $i,SV204: $i,SV328: $i,SV434: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV204 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5996]) ).
thf(6135,plain,
! [SV61: $i,SV205: $i,SV329: $i,SV435: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1797 ) @ SY1796 ) @ SV435 )
!= SV329 )
| ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1797 ) @ SV435 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1797 ) @ SY1796 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1797 ) @ SV329 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5997]) ).
thf(6136,plain,
! [SV62: $i,SV206: $i,SV330: $i,SV436: $i] :
( ( ! [SY1798: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1798 @ SV436 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5998]) ).
thf(6137,plain,
! [SV64: $i,SV207: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV207 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV331 @ ( c_Hilbert__Choice_OEps @ SV64 @ SV331 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5999]) ).
thf(6138,plain,
! [SV65: $i,SV208: $i,SV332: $i,SV437: $i] :
( ( ( SV437 != SV332 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6139,plain,
! [SV66: $i,SV209: $i,SV333: $i] :
( ( ( ~ ~ ! [SY1601: $i] :
~ ( hBOOL @ ( hAPP @ SV333 @ SY1601 ) ) )
= $true )
| ( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6001]) ).
thf(6140,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i] :
( ( ! [SY1799: $i,SY1800: $i,SY1801: $i,SY1802: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1802 @ SY1801 ) @ SY1800 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1799 @ SY1800 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SY1802 @ SY1799 ) @ SY1801 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6002]) ).
thf(6141,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i] :
( ( ! [SY1803: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1803 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1803 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1803 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY1803 @ SV335 @ SV211 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6003]) ).
thf(6142,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i] :
( ( ! [SY1804: $i,SY1805: $i] :
( ~ ( ( SY1805 != SY1804 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SY1804 @ SV69 ) @ SY1805 )
= ( hAPP @ SV212 @ SY1805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6004]) ).
thf(6143,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ~ ( ~ ( ~ ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
| ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) )
| ~ ( ~ ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) )
| ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6144,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i] :
( ( ! [SY1810: $i,SY1811: $i,SY1812: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1812 @ SY1811 @ SY1810 @ SV442 @ SV338 @ SV214 )
| ( ( hAPP @ ( hAPP @ SY1810 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6145,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SV215 = SV72 ) )
| ~ ( ( SV215 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6007]) ).
thf(6146,plain,
! [SV73: $i,SV216: $i,SV340: $i,SV443: $i] :
( ( ! [SY1813: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1813 @ SV443 @ SV340 ) @ SV216 ) @ SV73 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV340 @ SV73 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6147,plain,
! [SV74: $i,SV217: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
| ( SV217 = SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6009]) ).
thf(6148,plain,
! [SV74: $i,SV217: $i] :
( ( ~ ( ( SV217 != SV74 )
| ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6009]) ).
thf(6149,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i] :
( ( ! [SY1814: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1814 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1814 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1814 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY1814 @ SV341 @ SV218 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6010]) ).
thf(6150,plain,
! [SV76: $i,SV219: $i,SV342: $i,SV445: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV445 @ SV342 @ SV219 )
| ( ( hAPP @ ( hAPP @ SV342 @ SV76 ) @ SV76 )
= SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6011]) ).
thf(6151,plain,
! [SV77: $i,SV220: $i,SV343: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV343 ) @ SV220 ) @ ( hAPP @ ( c_Set_OCollect @ SV343 ) @ SV77 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV77 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6012]) ).
thf(6152,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6153,plain,
! [SV79: $i,SV222: $i,SV345: $i,SV447: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ~ ( c_Fun_Oinj__on @ SY1816 @ SY1815 @ SV447 @ SV345 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1816 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1816 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6154,plain,
! [SV80: $i,SV223: $i,SV346: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ ( hAPP @ c_Nat_OSuc @ SV223 ) @ SV80 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ SV223 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6015]) ).
thf(6155,plain,
! [SV81: $i,SV224: $i,SV347: $i,SV448: $i] :
( ( ! [SY1817: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1817 @ SV448 ) @ SV347 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SY1817 ) @ SV347 ) @ SV448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6156,plain,
! [SV82: $i,SV225: $i] :
( ( ( ~ ! [SY1321: $i] :
~ ( hBOOL @ ( hAPP @ SV225 @ SY1321 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6157,plain,
! [SV83: $i,SV226: $i,SV348: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV348 ) @ SV226 ) @ SV83 )
= SV83 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6158,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
| ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) )
| ~ ( ~ ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(6159,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i] :
( ( ! [SY1818: $i,SY1819: $i] :
~ ( ~ ( ( SY1819 != SY1818 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SY1818 @ SV85 ) @ SY1819 )
= SV85 ) )
| ~ ( ~ ( ( SY1819 != SY1818 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SY1818 @ SV85 ) @ SY1819 )
= ( hAPP @ SV228 @ SY1819 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6020]) ).
thf(6160,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i] :
( ( ! [SY1820: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1820 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1820 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6021]) ).
thf(6161,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i] :
( ( ! [SY1821: $i,SY1822: $i] :
( ~ ( ( SY1822 != SY1821 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SY1822 ) @ SV230 ) ) @ SY1821 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SY1821 ) @ SV87 ) ) @ SY1822 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6022]) ).
thf(6162,plain,
! [SV88: $i,SV231: $i,SV353: $i,SV452: $i] :
( ( ! [SY1823: $i,SY1824: $i] :
( ( SY1824
!= ( hAPP @ SY1823 @ SV452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SY1824 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SY1823 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6163,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6024]) ).
thf(6164,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
| ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ~ ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6025]) ).
thf(6165,plain,
! [SV92: $i,SV234: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
| ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6027]) ).
thf(6166,plain,
! [SV234: $i,SV92: $i] :
( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6027]) ).
thf(6167,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
| ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) )
| ~ ( ~ ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6028]) ).
thf(6168,plain,
! [SV94: $i,SV236: $i,SV357: $i,SV455: $i] :
( ( ~ ( c_Predicate_Osymp @ SV455 @ SV357 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6029]) ).
thf(6169,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i] :
( ( ! [SY1825: $i,SY1826: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1826 ) @ SY1825 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1826 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SY1825 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SY1825 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SY1825 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SY1825 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1826 ) @ SY1825 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1826 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6030]) ).
thf(6170,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6031]) ).
thf(6171,plain,
! [SV97: $i,SV239: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
| ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6032]) ).
thf(6172,plain,
! [SV239: $i,SV97: $i] :
( ( ~ ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6032]) ).
thf(6173,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i] :
( ( ! [SY1827: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1827 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) )
| ~ ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SY1827 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6033]) ).
thf(6174,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i] :
( ( ! [SY1828: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1828 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1828 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
| ~ ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1828 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1828 ) @ SV241 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6034]) ).
thf(6175,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i] :
( ( ! [SY1829: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1829 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1829 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6035]) ).
thf(6176,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
| ( SV243 = SV101 ) )
| ~ ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6036]) ).
thf(6177,plain,
! [SV102: $i,SV244: $i,SV364: $i,SV461: $i] :
( ( ! [SY1830: $i,SY1831: $i] :
( ~ ( c_Fun_Oinj__on @ SY1831 @ SY1830 @ SV461 @ SV364 )
| ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1831 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1831 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6037]) ).
thf(6178,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i] :
( ( ! [SY1832: $i,SY1833: $i,SY1834: $i,SY1835: $i,SY1836: $i,SY1837: $i,SY1838: $i] :
( ( ( hAPP @ SY1838 @ ( hAPP @ SY1837 @ SY1836 ) )
!= ( hAPP @ SY1835 @ ( hAPP @ SY1834 @ SY1833 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1832 @ SV462 @ SV365 @ SY1838 ) @ SY1837 ) @ SY1836 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SY1835 ) @ SY1834 ) @ SY1833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6038]) ).
thf(6179,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i] :
( ( ! [SY1839: $i,SY1840: $i,SY1841: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1841 @ SY1840 @ SY1839 @ SV463 ) @ SV366 )
!= SV246 )
| ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6039]) ).
thf(6180,plain,
! [SV105: $i,SV247: $i,SV367: $i,SV464: $i] :
( ( ! [SY1842: $i,SY1843: $i] :
( ( SY1843 != SY1842 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SY1843 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SY1842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6181,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i] :
( ( ! [SY1844: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1844 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1844 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6041]) ).
thf(6182,plain,
! [SV107: $i,SV249: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
| ( SV249 = SV107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6042]) ).
thf(6183,plain,
! [SV107: $i,SV249: $i] :
( ( ~ ( ( SV249 != SV107 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6042]) ).
thf(6184,plain,
! [SV108: $i,SV250: $i,SV369: $i,SV466: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV108 ) )
| ( SV250 = SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6043]) ).
thf(6185,plain,
! [SV109: $i,SV251: $i,SV370: $i,SV467: $i] :
( ( ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1846 ) @ SY1845 ) @ SV467 ) )
| ( SV370
!= ( hAPP @ SV251 @ SY1845 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SY1846 @ SV109 @ SV251 ) @ SV467 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6044]) ).
thf(6186,plain,
! [SV110: $i,SV252: $i,SV371: $i,SV468: $i] :
( ( ! [SY1847: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1847 @ SV468 @ SV371 )
| ( ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6045]) ).
thf(6187,plain,
! [SV111: $i,SV253: $i,SV372: $i,SV469: $i] :
( ( ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1848 ) @ SV469 ) @ SV372 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SV469 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1848 @ SV253 @ SV111 ) @ SV372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6046]) ).
thf(6188,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1850 @ SY1849 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1850 @ SY1849 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
| ~ ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1850 @ SY1849 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1850 @ SY1849 ) @ SV254 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6047]) ).
thf(6189,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
| ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6048]) ).
thf(6190,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ( ~ ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) )
| ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6048]) ).
thf(6191,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
| ~ ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6049]) ).
thf(6192,plain,
! [SV115: $i,SV257: $i,SV375: $i,SV472: $i] :
( ( ( SV472 != SV375 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6050]) ).
thf(6193,plain,
! [SV116: $i,SV258: $i,SV376: $i,SV473: $i] :
( ( ( SV473 != SV376 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV473 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6051]) ).
thf(6194,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
| ( SV377 = SV117 ) )
| ~ ( ( SV377 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6052]) ).
thf(6195,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i] :
( ( ! [SY1853: $i,SY1854: $i,SY1855: $i,SY1856: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1856 @ SY1855 @ SY1854 @ SY1853 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SY1855 @ SY1854 @ SV260 ) @ SV118 ) )
| ! [SY1857: $i] :
( ( hAPP @ SY1853 @ ( hAPP @ SV475 @ SY1857 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1857 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6053]) ).
thf(6196,plain,
! [SV119: $i,SV261: $i,SV379: $i,SV476: $i] :
( ( ! [SY1858: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1858 @ SV476 ) @ SV379 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SY1858 ) @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6054]) ).
thf(6197,plain,
! [SV120: $i,SV262: $i,SV380: $i,SV477: $i] :
( ( ! [SY1859: $i] :
( ( ( hAPP @ SY1859 @ SV477 )
!= SV380 )
| ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SY1859 @ SV477 @ SV380 )
= SY1859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6055]) ).
thf(6198,plain,
! [SV121: $i,SV263: $i,SV381: $i,SV478: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1861 @ SY1860 @ SV478 @ SV381 @ SV263 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1860 ) @ ( hAPP @ SV478 @ SV121 ) ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6056]) ).
thf(6199,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i] :
( ( ! [SY1862: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1862 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SY1862 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
| ~ ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1862 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SY1862 @ SV264 ) @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6057]) ).
thf(6200,plain,
! [SV123: $i,SV265: $i,SV383: $i,SV480: $i] :
( ( ! [SY1865: $i] :
( ~ ( c_Predicate_Otransp @ SY1865 @ SV480 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6058]) ).
thf(6201,plain,
! [SV124: $i,SV266: $i,SV384: $i,SV481: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV481 @ SV384 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6059]) ).
thf(6202,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ( ~ ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) )
| ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
| ~ ( ~ ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) )
| ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6060]) ).
thf(6203,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
!= SV126 )
| ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) ) )
| ~ ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6061]) ).
thf(6204,plain,
! [SV127: $i,SV269: $i] :
( ( ( ~ ! [SY1464: $i] :
~ ( hBOOL @ ( hAPP @ SV269 @ SY1464 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6062]) ).
thf(6205,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(6206,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1868 @ SY1867 @ SY1866 @ SV482 @ SV388 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6064]) ).
thf(6207,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6065]) ).
thf(6208,plain,
! [SV131: $i,SV273: $i,SV390: $i] :
( ( SV390
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV273 ) @ SV131 ) @ SV390 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(6209,plain,
! [SV132: $i,SV274: $i,SV391: $i,SV484: $i] :
( ( ! [SY1869: $i,SY1870: $i] :
( ~ ( c_Fun_Oinj__on @ SY1870 @ SY1869 @ SV484 @ SV391 )
| ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1870 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1870 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6210,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i] :
( ( ! [SY1871: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1871 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1871 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1871 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SY1871 @ SV392 @ SV275 ) @ SV133 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6068]) ).
thf(6211,plain,
! [SV134: $i,SV276: $i,SV393: $i,SV486: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV486 @ SV393 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6069]) ).
thf(6212,plain,
! [SV135: $i,SV277: $i] :
( ( ( SV277 = SV135 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV277 ) @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6213,plain,
! [SV136: $i,SV278: $i,SV394: $i,SV487: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ( ( hAPP @ SY1873 @ SY1872 )
!= SV487 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SY1872 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SY1873 ) @ SV278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6071]) ).
thf(6214,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6072]) ).
thf(6215,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
| ~ ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6073]) ).
thf(6216,plain,
! [SV139: $i,SV281: $i,SV397: $i,SV490: $i] :
( ( ! [SY1876: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1876 @ SV490 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6074]) ).
thf(6217,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i] :
( ( ! [SY1877: $i,SY1878: $i,SY1879: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1879 @ SY1878 @ SY1877 @ SV491 @ SV398 )
| ~ ( ~ ( ( ( hAPP @ SY1877 @ SV282 )
!= ( hAPP @ SY1877 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SY1877 @ SV282 )
= ( hAPP @ SY1877 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6075]) ).
thf(6218,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
| ( SV283 = SV141 ) )
| ~ ( ( SV283 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6076]) ).
thf(6219,plain,
! [SV142: $i,SV284: $i,SV400: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV400 ) @ SV284 ) @ ( hAPP @ ( c_Set_OCollect @ SV400 ) @ SV142 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV142 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6077]) ).
thf(6220,plain,
! [SV143: $i,SV285: $i,SV401: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV401 @ SV285 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV285 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6078]) ).
thf(6221,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1881 ) @ SY1880 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1881 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SY1880 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SY1880 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SY1880 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SY1880 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1881 ) @ SY1880 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1881 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6079]) ).
thf(6222,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) )
| ( SV403 = SV145 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6080]) ).
thf(6223,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i] :
( ( ! [SY1882: $i,SY1883: $i] :
~ ( ~ ( ( SY1883 != SY1882 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SY1882 @ SV146 ) @ SY1883 )
= SV146 ) )
| ~ ( ~ ( ( SY1883 != SY1882 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SY1882 @ SV146 ) @ SY1883 )
= ( hAPP @ SV288 @ SY1883 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6081]) ).
thf(6224,plain,
! [SV147: $i,SV289: $i] :
( ( ( ! [SY1514: $i] :
( ( hAPP @ SV289 @ SY1514 )
= ( hAPP @ SV147 @ SY1514 ) ) )
= $false )
| ( ( SV289 = SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6082]) ).
thf(6225,plain,
! [SV148: $i,SV290: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
| ( SV290 = SV148 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6083]) ).
thf(6226,plain,
! [SV148: $i,SV290: $i] :
( ( ~ ( ( SV290 != SV148 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6083]) ).
thf(6227,plain,
! [SV5: $i,SV153: $i,SV295: $i,SV407: $i,SV495: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV495 @ SV407 @ SV295 @ SV153 @ SV5 ) @ SV153 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6086]) ).
thf(6228,plain,
! [SV9: $i,SV157: $i,SV296: $i,SV408: $i,SV496: $i] :
( ( ! [SY1884: $i,SY1885: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1885 @ SY1884 @ SV496 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1885 @ SV408 @ SY1884 ) @ SV296 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1885 @ SV408 @ SV496 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV408 @ SY1884 @ SV496 ) @ SV157 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6087]) ).
thf(6229,plain,
! [SV10: $i,SV158: $i,SV297: $i,SV409: $i,SV497: $i] :
( ( ! [SY1886: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1886 @ SV497 @ SV409 @ SV297 ) @ SV158 ) @ SV10 )
= ( hAPP @ SV297 @ ( hAPP @ SV158 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6088]) ).
thf(6230,plain,
! [SV11: $i,SV159: $i,SV298: $i,SV410: $i,SV498: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1888 @ SY1887 @ SV498 @ SV410 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1888 @ SV498 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1887 @ SV498 @ ( hAPP @ ( c_Fun_Ocomp @ SY1888 @ SY1887 @ SV298 @ SV410 ) @ SV159 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6089]) ).
thf(6231,plain,
! [SV12: $i,SV160: $i,SV299: $i,SV411: $i,SV499: $i] :
( ( ! [SY1889: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1889 @ SV499 @ SV411 @ SV299 ) @ SV160 ) @ SV12 )
= ( hAPP @ SV299 @ ( hAPP @ SV160 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6090]) ).
thf(6232,plain,
! [SV16: $i,SV164: $i,SV303: $i,SV414: $i,SV500: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV500 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV500 @ SV414 ) @ SV303 ) @ SV164 ) ) @ SV303 ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV500 @ SV414 ) @ SV303 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6093]) ).
thf(6233,plain,
! [SV21: $i,SV168: $i,SV305: $i,SV416: $i,SV501: $i] :
( ( ! [SY1890: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1890 @ SV501 @ SV416 ) @ SV305 ) @ SV168 ) @ SV21 )
= ( hAPP @ SV305 @ ( hAPP @ SV168 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6095]) ).
thf(6234,plain,
! [SV22: $i,SV169: $i,SV306: $i,SV417: $i,SV502: $i] :
( ( ! [SY1891: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1891 @ SV502 @ SV417 ) @ SV306 ) @ SV169 ) @ SV22 )
= ( hAPP @ ( hAPP @ SV306 @ SV22 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6096]) ).
thf(6235,plain,
! [SV23: $i,SV170: $i,SV307: $i,SV418: $i,SV503: $i] :
( ( ! [SY1892: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1892 @ SV503 @ SV418 ) @ SV307 ) @ SV170 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV307 @ SV23 ) @ ( hAPP @ SV170 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6097]) ).
thf(6236,plain,
! [SV27: $i,SV172: $i] :
( ( ( hBOOL @ SV172 )
= $false )
| ( ( ~ ( hBOOL @ SV27 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV172 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6101]) ).
thf(6237,plain,
! [SV32: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV177 ) @ SV32 ) )
= $false )
| ( ( hBOOL @ SV177 )
= $true )
| ( ( hBOOL @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6106]) ).
thf(6238,plain,
! [SV35: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV180 ) @ SV35 ) )
= $false )
| ( ( ~ ( hBOOL @ SV180 ) )
= $true )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6108]) ).
thf(6239,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i] :
( ( ! [SY1893: $i,SY1894: $i,SY1895: $i,SY1896: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1896 @ SY1895 @ SY1894 @ SY1893 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SY1895 @ SY1894 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SY1893 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6109]) ).
thf(6240,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
| ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6110]) ).
thf(6241,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ( ~ ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6110]) ).
thf(6242,plain,
! [SV38: $i,SV183: $i,SV310: $i,SV420: $i,SV505: $i] :
( ( ! [SY1897: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1897 @ SV505 ) @ SV420 ) @ SV310 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1897 @ SV505 ) @ SV183 ) @ SV38 ) )
| ~ ( ( SV420 != SV183 )
| ( SV310 != SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6111]) ).
thf(6243,plain,
! [SV39: $i,SV184: $i,SV311: $i,SV421: $i] :
( ( ( SV421 != SV311 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6112]) ).
thf(6244,plain,
! [SV40: $i,SV185: $i,SV312: $i,SV422: $i,SV506: $i] :
( ( ! [SY1898: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1898 @ SV506 @ SV422 @ SV312 @ SV185 )
| ( ( hAPP @ SV312 @ ( hAPP @ SV422 @ SV40 ) )
= SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6113]) ).
thf(6245,plain,
! [SV41: $i,SV186: $i,SV313: $i,SV423: $i,SV507: $i] :
( ( ! [SY1899: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1899 @ SV507 @ SV423 )
| ( ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6114]) ).
thf(6246,plain,
! [SV43: $i,SV188: $i,SV314: $i,SV424: $i,SV508: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV508 ) @ ( hAPP @ SV424 @ SV314 ) ) @ SV188 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SV314 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SV508 @ SV424 ) @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6116]) ).
thf(6247,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i] :
( ( ! [SY1900: $i,SY1901: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1901 @ SY1900 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1901 @ SY1900 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6117]) ).
thf(6248,plain,
! [SV45: $i,SV190: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
| ( SV190 = SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6118]) ).
thf(6249,plain,
! [SV45: $i,SV190: $i] :
( ( ( SV190 != SV45 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6119]) ).
thf(6250,plain,
! [SV47: $i,SV191: $i,SV316: $i,SV426: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ SV191 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV426 ) @ SV47 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6120]) ).
thf(6251,plain,
! [SV48: $i,SV192: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
| ( SV192 = SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6121]) ).
thf(6252,plain,
! [SV48: $i,SV192: $i] :
( ( ( SV192 != SV48 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6122]) ).
thf(6253,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6123]) ).
thf(6254,plain,
! [SV50: $i,SV194: $i,SV318: $i,SV428: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ( SV318 != SV194 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6124]) ).
thf(6255,plain,
! [SV51: $i,SV195: $i,SV319: $i,SV429: $i,SV511: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV511 @ SV429 ) @ SV319 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SV511 ) @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6125]) ).
thf(6256,plain,
! [SV52: $i,SV196: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ SV320 @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV52 ) @ SV196 ) @ ( hAPP @ ( c_Set_OCollect @ SV52 ) @ SV320 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6126]) ).
thf(6257,plain,
! [SV53: $i,SV197: $i,SV321: $i,SV430: $i,SV512: $i] :
( ( ! [SY1906: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1906 @ SV512 @ SV430 @ SV321 @ SV197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6127]) ).
thf(6258,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
| ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ~ ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6128]) ).
thf(6259,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6129]) ).
thf(6260,plain,
! [SV56: $i,SV200: $i,SV324: $i,SV433: $i,SV513: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV513 ) @ SV433 ) @ ( hAPP @ ( c_Set_Ovimage @ SV513 @ SV324 @ SV200 ) @ SV56 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ ( hAPP @ SV200 @ SV433 ) ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6130]) ).
thf(6261,plain,
! [SV57: $i,SV201: $i,SV325: $i] :
( ( ( c_Predicate_Oreflp @ SV325 @ SV201 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV201 @ SV57 ) @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6131]) ).
thf(6262,plain,
! [SV58: $i,SV202: $i,SV326: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV326 ) @ SV202 ) @ SV58 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV326 ) @ SV202 ) @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6132]) ).
thf(6263,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
| ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6133]) ).
thf(6264,plain,
! [SV203: $i,SV59: $i,SV327: $i] :
( ( ~ ( ~ ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6133]) ).
thf(6265,plain,
! [SV60: $i,SV204: $i,SV328: $i,SV434: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV204 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6266,plain,
! [SV61: $i,SV205: $i,SV329: $i,SV435: $i,SV514: $i] :
( ( ! [SY1907: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1907 ) @ SV514 ) @ SV435 )
!= SV329 )
| ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1907 ) @ SV435 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1907 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1907 ) @ SV329 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6135]) ).
thf(6267,plain,
! [SV62: $i,SV206: $i,SV330: $i,SV436: $i,SV515: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6136]) ).
thf(6268,plain,
! [SV64: $i,SV207: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ SV331 @ SV207 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV331 @ ( c_Hilbert__Choice_OEps @ SV64 @ SV331 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6137]) ).
thf(6269,plain,
! [SV65: $i,SV208: $i,SV332: $i,SV437: $i] :
( ( ( SV437 != SV332 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6138]) ).
thf(6270,plain,
! [SV66: $i,SV209: $i,SV333: $i] :
( ( ( ~ ! [SY1601: $i] :
~ ( hBOOL @ ( hAPP @ SV333 @ SY1601 ) ) )
= $false )
| ( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6139]) ).
thf(6271,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i] :
( ( ! [SY1908: $i,SY1909: $i,SY1910: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1910 @ SY1909 ) @ SY1908 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SY1908 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SY1910 @ SV516 ) @ SY1909 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6140]) ).
thf(6272,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6141]) ).
thf(6273,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i,SV518: $i] :
( ( ! [SY1911: $i] :
( ~ ( ( SY1911 != SV518 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SV518 @ SV69 ) @ SY1911 )
= ( hAPP @ SV212 @ SY1911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6142]) ).
thf(6274,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ~ ( ~ ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
| ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) )
| ~ ( ~ ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) )
| ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6143]) ).
thf(6275,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i,SV519: $i] :
( ( ! [SY1912: $i,SY1913: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1913 @ SY1912 @ SV519 @ SV442 @ SV338 @ SV214 )
| ( ( hAPP @ ( hAPP @ SV519 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6144]) ).
thf(6276,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SV215 = SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6145]) ).
thf(6277,plain,
! [SV339: $i,SV72: $i,SV215: $i] :
( ( ~ ( ( SV215 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6145]) ).
thf(6278,plain,
! [SV73: $i,SV216: $i,SV340: $i,SV443: $i,SV520: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV520 @ SV443 @ SV340 ) @ SV216 ) @ SV73 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV340 @ SV73 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6146]) ).
thf(6279,plain,
! [SV74: $i,SV217: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
| ( SV217 = SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6147]) ).
thf(6280,plain,
! [SV74: $i,SV217: $i] :
( ( ( SV217 != SV74 )
| ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6148]) ).
thf(6281,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6149]) ).
thf(6282,plain,
! [SV76: $i,SV219: $i,SV342: $i,SV445: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV445 @ SV342 @ SV219 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV342 @ SV76 ) @ SV76 )
= SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6150]) ).
thf(6283,plain,
! [SV77: $i,SV220: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV343 ) @ SV220 ) @ ( hAPP @ ( c_Set_OCollect @ SV343 ) @ SV77 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV77 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(6284,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6152]) ).
thf(6285,plain,
! [SV79: $i,SV222: $i,SV345: $i,SV447: $i,SV522: $i] :
( ( ! [SY1914: $i] :
( ~ ( c_Fun_Oinj__on @ SY1914 @ SV522 @ SV447 @ SV345 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1914 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1914 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6153]) ).
thf(6286,plain,
! [SV80: $i,SV223: $i,SV346: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ ( hAPP @ c_Nat_OSuc @ SV223 ) @ SV80 )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV346 @ SV223 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6154]) ).
thf(6287,plain,
! [SV81: $i,SV224: $i,SV347: $i,SV448: $i,SV523: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV448 ) @ SV347 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SV523 ) @ SV347 ) @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6155]) ).
thf(6288,plain,
! [SV82: $i,SV225: $i] :
( ( ( ! [SY1321: $i] :
~ ( hBOOL @ ( hAPP @ SV225 @ SY1321 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6156]) ).
thf(6289,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
| ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6158]) ).
thf(6290,plain,
! [SV349: $i,SV84: $i,SV227: $i] :
( ( ~ ( ~ ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6158]) ).
thf(6291,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i] :
( ( ! [SY1915: $i] :
~ ( ~ ( ( SY1915 != SV524 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SY1915 )
= SV85 ) )
| ~ ( ~ ( ( SY1915 != SV524 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SY1915 )
= ( hAPP @ SV228 @ SY1915 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6159]) ).
thf(6292,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6160]) ).
thf(6293,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i,SV526: $i] :
( ( ! [SY1916: $i] :
( ~ ( ( SY1916 != SV526 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SY1916 ) @ SV230 ) ) @ SV526 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV526 ) @ SV87 ) ) @ SY1916 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6161]) ).
thf(6294,plain,
! [SV88: $i,SV231: $i,SV353: $i,SV452: $i,SV527: $i] :
( ( ! [SY1917: $i] :
( ( SY1917
!= ( hAPP @ SV527 @ SV452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SY1917 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6162]) ).
thf(6295,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6163]) ).
thf(6296,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
| ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ~ ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6164]) ).
thf(6297,plain,
! [SV92: $i,SV234: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
| ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6165]) ).
thf(6298,plain,
! [SV234: $i,SV92: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6166]) ).
thf(6299,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
| ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6167]) ).
thf(6300,plain,
! [SV356: $i,SV93: $i,SV235: $i] :
( ( ~ ( ~ ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6167]) ).
thf(6301,plain,
! [SV94: $i,SV236: $i,SV357: $i,SV455: $i] :
( ( ( ~ ( c_Predicate_Osymp @ SV455 @ SV357 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6168]) ).
thf(6302,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i] :
( ( ! [SY1918: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1918 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1918 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1918 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY1918 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6169]) ).
thf(6303,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6170]) ).
thf(6304,plain,
! [SV359: $i,SV238: $i,SV96: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6170]) ).
thf(6305,plain,
! [SV97: $i,SV239: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
| ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6171]) ).
thf(6306,plain,
! [SV239: $i,SV97: $i] :
( ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6172]) ).
thf(6307,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ~ ( ~ ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) )
| ~ ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6173]) ).
thf(6308,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
| ~ ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6174]) ).
thf(6309,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6175]) ).
thf(6310,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
| ( SV243 = SV101 ) )
| ~ ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(6311,plain,
! [SV102: $i,SV244: $i,SV364: $i,SV461: $i,SV532: $i] :
( ( ! [SY1919: $i] :
( ~ ( c_Fun_Oinj__on @ SY1919 @ SV532 @ SV461 @ SV364 )
| ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1919 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1919 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6177]) ).
thf(6312,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i] :
( ( ! [SY1920: $i,SY1921: $i,SY1922: $i,SY1923: $i,SY1924: $i,SY1925: $i] :
( ( ( hAPP @ SY1925 @ ( hAPP @ SY1924 @ SY1923 ) )
!= ( hAPP @ SY1922 @ ( hAPP @ SY1921 @ SY1920 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1925 ) @ SY1924 ) @ SY1923 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SY1922 ) @ SY1921 ) @ SY1920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6178]) ).
thf(6313,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i,SV534: $i] :
( ( ! [SY1926: $i,SY1927: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1927 @ SY1926 @ SV534 @ SV463 ) @ SV366 )
!= SV246 )
| ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6179]) ).
thf(6314,plain,
! [SV105: $i,SV247: $i,SV367: $i,SV464: $i,SV535: $i] :
( ( ! [SY1928: $i] :
( ( SY1928 != SV535 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SY1928 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6180]) ).
thf(6315,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6181]) ).
thf(6316,plain,
! [SV107: $i,SV249: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
| ( SV249 = SV107 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6182]) ).
thf(6317,plain,
! [SV107: $i,SV249: $i] :
( ( ( SV249 != SV107 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6183]) ).
thf(6318,plain,
! [SV108: $i,SV250: $i,SV369: $i,SV466: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV250 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV108 ) )
| ( SV250 = SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6184]) ).
thf(6319,plain,
! [SV109: $i,SV251: $i,SV370: $i,SV467: $i,SV537: $i] :
( ( ! [SY1929: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1929 ) @ SV537 ) @ SV467 ) )
| ( SV370
!= ( hAPP @ SV251 @ SV537 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SY1929 @ SV109 @ SV251 ) @ SV467 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6185]) ).
thf(6320,plain,
! [SV110: $i,SV252: $i,SV371: $i,SV468: $i,SV538: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV538 @ SV468 @ SV371 )
| ( ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6186]) ).
thf(6321,plain,
! [SV111: $i,SV253: $i,SV372: $i,SV469: $i,SV539: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV539 ) @ SV469 ) @ SV372 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SV469 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV539 @ SV253 @ SV111 ) @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6187]) ).
thf(6322,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i] :
( ( ! [SY1930: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1930 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1930 @ SV540 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
| ~ ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1930 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1930 @ SV540 ) @ SV254 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6188]) ).
thf(6323,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
| ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6189]) ).
thf(6324,plain,
! [SV113: $i,SV255: $i] :
( ( ~ ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) )
| ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6190]) ).
thf(6325,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
| ~ ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6191]) ).
thf(6326,plain,
! [SV115: $i,SV257: $i,SV375: $i,SV472: $i] :
( ( ( SV472 != SV375 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6192]) ).
thf(6327,plain,
! [SV116: $i,SV258: $i,SV376: $i,SV473: $i] :
( ( ( SV473 != SV376 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV473 ) @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6193]) ).
thf(6328,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
| ( SV377 = SV117 ) )
| ~ ( ( SV377 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6194]) ).
thf(6329,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1933 @ SY1932 @ SY1931 @ SV541 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SY1932 @ SY1931 @ SV260 ) @ SV118 ) )
| ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6195]) ).
thf(6330,plain,
! [SV119: $i,SV261: $i,SV379: $i,SV476: $i,SV542: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV542 @ SV476 ) @ SV379 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SV542 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6196]) ).
thf(6331,plain,
! [SV120: $i,SV262: $i,SV380: $i,SV477: $i,SV543: $i] :
( ( ( ( hAPP @ SV543 @ SV477 )
!= SV380 )
| ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SV543 @ SV477 @ SV380 )
= SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6197]) ).
thf(6332,plain,
! [SV121: $i,SV263: $i,SV381: $i,SV478: $i,SV544: $i] :
( ( ! [SY1935: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1935 @ SV544 @ SV478 @ SV381 @ SV263 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV544 ) @ ( hAPP @ SV478 @ SV121 ) ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6198]) ).
thf(6333,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
| ~ ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6199]) ).
thf(6334,plain,
! [SV123: $i,SV265: $i,SV383: $i,SV480: $i,SV546: $i] :
( ( ~ ( c_Predicate_Otransp @ SV546 @ SV480 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6200]) ).
thf(6335,plain,
! [SV124: $i,SV266: $i,SV384: $i,SV481: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV481 @ SV384 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6201]) ).
thf(6336,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ( ~ ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) )
| ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6202]) ).
thf(6337,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ( ~ ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) )
| ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6202]) ).
thf(6338,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
!= SV126 )
| ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6203]) ).
thf(6339,plain,
! [SV126: $i,SV386: $i,SV268: $i] :
( ( ~ ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6203]) ).
thf(6340,plain,
! [SV127: $i,SV269: $i] :
( ( ( ! [SY1464: $i] :
~ ( hBOOL @ ( hAPP @ SV269 @ SY1464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6204]) ).
thf(6341,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6205]) ).
thf(6342,plain,
! [SV387: $i,SV270: $i,SV128: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6205]) ).
thf(6343,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i,SV547: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1939 @ SY1938 @ SV547 @ SV482 @ SV388 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1938 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1938 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6206]) ).
thf(6344,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(6345,plain,
! [SV132: $i,SV274: $i,SV391: $i,SV484: $i,SV548: $i] :
( ( ! [SY1940: $i] :
( ~ ( c_Fun_Oinj__on @ SY1940 @ SV548 @ SV484 @ SV391 )
| ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1940 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1940 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6209]) ).
thf(6346,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6210]) ).
thf(6347,plain,
! [SV134: $i,SV276: $i,SV393: $i,SV486: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV486 @ SV393 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6211]) ).
thf(6348,plain,
! [SV136: $i,SV278: $i,SV394: $i,SV487: $i,SV550: $i] :
( ( ! [SY1941: $i] :
( ( ( hAPP @ SY1941 @ SV550 )
!= SV487 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SY1941 ) @ SV278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6213]) ).
thf(6349,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6214]) ).
thf(6350,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
| ~ ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6215]) ).
thf(6351,plain,
! [SV139: $i,SV281: $i,SV397: $i,SV490: $i,SV551: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6216]) ).
thf(6352,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i,SV552: $i] :
( ( ! [SY1942: $i,SY1943: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1943 @ SY1942 @ SV552 @ SV491 @ SV398 )
| ~ ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6217]) ).
thf(6353,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
| ( SV283 = SV141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6218]) ).
thf(6354,plain,
! [SV399: $i,SV141: $i,SV283: $i] :
( ( ~ ( ( SV283 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6218]) ).
thf(6355,plain,
! [SV142: $i,SV284: $i,SV400: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV400 ) @ SV284 ) @ ( hAPP @ ( c_Set_OCollect @ SV400 ) @ SV142 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV142 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6219]) ).
thf(6356,plain,
! [SV143: $i,SV285: $i,SV401: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV401 @ SV285 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV285 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6220]) ).
thf(6357,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i] :
( ( ! [SY1944: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1944 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1944 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1944 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY1944 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6221]) ).
thf(6358,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) )
| ( SV403 = SV145 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6222]) ).
thf(6359,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i] :
( ( ! [SY1945: $i] :
~ ( ~ ( ( SY1945 != SV554 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SY1945 )
= SV146 ) )
| ~ ( ~ ( ( SY1945 != SV554 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SY1945 )
= ( hAPP @ SV288 @ SY1945 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6223]) ).
thf(6360,plain,
! [SV147: $i,SV289: $i] :
( ( ( ( hAPP @ SV289 @ ( sK2_SY1514 @ SV147 @ SV289 ) )
= ( hAPP @ SV147 @ ( sK2_SY1514 @ SV147 @ SV289 ) ) )
= $false )
| ( ( SV289 = SV147 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6224]) ).
thf(6361,plain,
! [SV148: $i,SV290: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
| ( SV290 = SV148 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6225]) ).
thf(6362,plain,
! [SV148: $i,SV290: $i] :
( ( ( SV290 != SV148 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6226]) ).
thf(6363,plain,
! [SV9: $i,SV157: $i,SV296: $i,SV408: $i,SV496: $i,SV555: $i] :
( ( ! [SY1946: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1946 @ SV555 @ SV496 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1946 @ SV408 @ SV555 ) @ SV296 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1946 @ SV408 @ SV496 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV408 @ SV555 @ SV496 ) @ SV157 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6228]) ).
thf(6364,plain,
! [SV10: $i,SV158: $i,SV297: $i,SV409: $i,SV497: $i,SV556: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV556 @ SV497 @ SV409 @ SV297 ) @ SV158 ) @ SV10 )
= ( hAPP @ SV297 @ ( hAPP @ SV158 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6229]) ).
thf(6365,plain,
! [SV11: $i,SV159: $i,SV298: $i,SV410: $i,SV498: $i,SV557: $i] :
( ( ! [SY1947: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1947 @ SV557 @ SV498 @ SV410 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SY1947 @ SV498 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SV557 @ SV498 @ ( hAPP @ ( c_Fun_Ocomp @ SY1947 @ SV557 @ SV298 @ SV410 ) @ SV159 ) ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6230]) ).
thf(6366,plain,
! [SV12: $i,SV160: $i,SV299: $i,SV411: $i,SV499: $i,SV558: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV558 @ SV499 @ SV411 @ SV299 ) @ SV160 ) @ SV12 )
= ( hAPP @ SV299 @ ( hAPP @ SV160 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6231]) ).
thf(6367,plain,
! [SV21: $i,SV168: $i,SV305: $i,SV416: $i,SV501: $i,SV559: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV559 @ SV501 @ SV416 ) @ SV305 ) @ SV168 ) @ SV21 )
= ( hAPP @ SV305 @ ( hAPP @ SV168 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6233]) ).
thf(6368,plain,
! [SV22: $i,SV169: $i,SV306: $i,SV417: $i,SV502: $i,SV560: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV560 @ SV502 @ SV417 ) @ SV306 ) @ SV169 ) @ SV22 )
= ( hAPP @ ( hAPP @ SV306 @ SV22 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6234]) ).
thf(6369,plain,
! [SV23: $i,SV170: $i,SV307: $i,SV418: $i,SV503: $i,SV561: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV561 @ SV503 @ SV418 ) @ SV307 ) @ SV170 ) @ SV23 )
= ( hAPP @ ( hAPP @ SV307 @ SV23 ) @ ( hAPP @ SV170 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6235]) ).
thf(6370,plain,
! [SV172: $i,SV27: $i] :
( ( ( hBOOL @ SV27 )
= $false )
| ( ( hBOOL @ SV172 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV172 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6236]) ).
thf(6371,plain,
! [SV35: $i,SV180: $i] :
( ( ( hBOOL @ SV180 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV180 ) @ SV35 ) )
= $false )
| ( ( hBOOL @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6238]) ).
thf(6372,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i] :
( ( ! [SY1948: $i,SY1949: $i,SY1950: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1950 @ SY1949 @ SY1948 @ SV562 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SY1949 @ SY1948 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6239]) ).
thf(6373,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
| ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6240]) ).
thf(6374,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ~ ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) )
| ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6241]) ).
thf(6375,plain,
! [SV38: $i,SV183: $i,SV310: $i,SV420: $i,SV505: $i,SV563: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
| ~ ( ( SV420 != SV183 )
| ( SV310 != SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6242]) ).
thf(6376,plain,
! [SV39: $i,SV184: $i,SV311: $i,SV421: $i] :
( ( ( SV421 = SV311 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6243]) ).
thf(6377,plain,
! [SV40: $i,SV185: $i,SV312: $i,SV422: $i,SV506: $i,SV564: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV564 @ SV506 @ SV422 @ SV312 @ SV185 )
| ( ( hAPP @ SV312 @ ( hAPP @ SV422 @ SV40 ) )
= SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6244]) ).
thf(6378,plain,
! [SV41: $i,SV186: $i,SV313: $i,SV423: $i,SV507: $i,SV565: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV565 @ SV507 @ SV423 )
| ( ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6245]) ).
thf(6379,plain,
! [SV43: $i,SV188: $i,SV314: $i,SV424: $i,SV508: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV508 ) @ ( hAPP @ SV424 @ SV314 ) ) @ SV188 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SV314 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SV508 @ SV424 ) @ SV188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6246]) ).
thf(6380,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i] :
( ( ! [SY1951: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1951 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1951 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6247]) ).
thf(6381,plain,
! [SV45: $i,SV190: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
= $true )
| ( ( SV190 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6248]) ).
thf(6382,plain,
! [SV45: $i,SV190: $i] :
( ( ( SV190 != SV45 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6249]) ).
thf(6383,plain,
! [SV47: $i,SV191: $i,SV316: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ SV191 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV426 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV426 ) @ SV47 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6250]) ).
thf(6384,plain,
! [SV48: $i,SV192: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
!= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
= $true )
| ( ( SV192 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6251]) ).
thf(6385,plain,
! [SV48: $i,SV192: $i] :
( ( ( SV192 != SV48 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6252]) ).
thf(6386,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
| ~ ( ~ ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6253]) ).
thf(6387,plain,
! [SV50: $i,SV194: $i,SV318: $i,SV428: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( ( SV318 != SV194 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6254]) ).
thf(6388,plain,
! [SV51: $i,SV195: $i,SV319: $i,SV429: $i,SV511: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV511 @ SV429 ) @ SV319 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SV511 ) @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6255]) ).
thf(6389,plain,
! [SV53: $i,SV197: $i,SV321: $i,SV430: $i,SV512: $i,SV567: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV567 @ SV512 @ SV430 @ SV321 @ SV197 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6257]) ).
thf(6390,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
| ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6258]) ).
thf(6391,plain,
! [SV431: $i,SV198: $i,SV54: $i,SV322: $i] :
( ( ~ ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6258]) ).
thf(6392,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6259]) ).
thf(6393,plain,
! [SV56: $i,SV200: $i,SV324: $i,SV433: $i,SV513: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV513 ) @ SV433 ) @ ( hAPP @ ( c_Set_Ovimage @ SV513 @ SV324 @ SV200 ) @ SV56 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ ( hAPP @ SV200 @ SV433 ) ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6260]) ).
thf(6394,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
| ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6263]) ).
thf(6395,plain,
! [SV203: $i,SV59: $i,SV327: $i] :
( ( ~ ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6264]) ).
thf(6396,plain,
! [SV60: $i,SV204: $i,SV328: $i,SV434: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV204 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(6397,plain,
! [SV61: $i,SV205: $i,SV329: $i,SV435: $i,SV514: $i,SV568: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV435 )
!= SV329 )
| ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV435 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV329 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6266]) ).
thf(6398,plain,
! [SV62: $i,SV206: $i,SV330: $i,SV436: $i,SV515: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6267]) ).
thf(6399,plain,
! [SV65: $i,SV208: $i,SV332: $i,SV437: $i] :
( ( ( SV437 = SV332 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6269]) ).
thf(6400,plain,
! [SV66: $i,SV209: $i,SV333: $i] :
( ( ( ! [SY1601: $i] :
~ ( hBOOL @ ( hAPP @ SV333 @ SY1601 ) ) )
= $true )
| ( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6270]) ).
thf(6401,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i,SV569: $i] :
( ( ! [SY1954: $i,SY1955: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1955 @ SY1954 ) @ SV569 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SY1955 @ SV516 ) @ SY1954 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6271]) ).
thf(6402,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6272]) ).
thf(6403,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i,SV518: $i,SV570: $i] :
( ( ~ ( ( SV570 != SV518 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SV518 @ SV69 ) @ SV570 )
= ( hAPP @ SV212 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6273]) ).
thf(6404,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ~ ( ~ ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
| ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6274]) ).
thf(6405,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV441: $i] :
( ( ~ ( ~ ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) )
| ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6274]) ).
thf(6406,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i,SV519: $i,SV571: $i] :
( ( ! [SY1956: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1956 @ SV571 @ SV519 @ SV442 @ SV338 @ SV214 )
| ( ( hAPP @ ( hAPP @ SV519 @ SV71 ) @ SV71 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6275]) ).
thf(6407,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
| ( SV215 = SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6276]) ).
thf(6408,plain,
! [SV339: $i,SV72: $i,SV215: $i] :
( ( ( SV215 != SV72 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6277]) ).
thf(6409,plain,
! [SV73: $i,SV216: $i,SV340: $i,SV443: $i,SV520: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV520 @ SV443 @ SV340 ) @ SV216 ) @ SV73 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV340 @ SV73 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6278]) ).
thf(6410,plain,
! [SV74: $i,SV217: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
!= ( hAPP @ c_Nat_OSuc @ SV74 ) )
= $true )
| ( ( SV217 = SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6279]) ).
thf(6411,plain,
! [SV74: $i,SV217: $i] :
( ( ( SV217 != SV74 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6280]) ).
thf(6412,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6413,plain,
! [SV76: $i,SV219: $i,SV342: $i,SV445: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV445 @ SV342 @ SV219 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV342 @ SV76 ) @ SV76 )
= SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6414,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6284]) ).
thf(6415,plain,
! [SV446: $i,SV78: $i,SV344: $i,SV221: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6284]) ).
thf(6416,plain,
! [SV79: $i,SV222: $i,SV345: $i,SV447: $i,SV522: $i,SV572: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6285]) ).
thf(6417,plain,
! [SV81: $i,SV224: $i,SV347: $i,SV448: $i,SV523: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV448 ) @ SV347 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SV523 ) @ SV347 ) @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6287]) ).
thf(6418,plain,
! [SV82: $i,SV573: $i,SV225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV225 @ SV573 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6288]) ).
thf(6419,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
| ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6289]) ).
thf(6420,plain,
! [SV349: $i,SV84: $i,SV227: $i] :
( ( ~ ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6290]) ).
thf(6421,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ~ ( ~ ( ( SV574 != SV524 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 ) )
| ~ ( ~ ( ( SV574 != SV524 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6291]) ).
thf(6422,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(6423,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i,SV526: $i,SV575: $i] :
( ( ~ ( ( SV575 != SV526 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV575 ) @ SV230 ) ) @ SV526 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV526 ) @ SV87 ) ) @ SV575 ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6293]) ).
thf(6424,plain,
! [SV88: $i,SV231: $i,SV353: $i,SV452: $i,SV527: $i,SV576: $i] :
( ( ( SV576
!= ( hAPP @ SV527 @ SV452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SV576 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6294]) ).
thf(6425,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6295]) ).
thf(6426,plain,
! [SV453: $i,SV354: $i,SV89: $i,SV232: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6295]) ).
thf(6427,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
| ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6296]) ).
thf(6428,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ~ ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6296]) ).
thf(6429,plain,
! [SV92: $i,SV234: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 ) )
= $true )
| ( ( ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6297]) ).
thf(6430,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6298]) ).
thf(6431,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
| ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6299]) ).
thf(6432,plain,
! [SV356: $i,SV93: $i,SV235: $i] :
( ( ~ ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6300]) ).
thf(6433,plain,
! [SV94: $i,SV236: $i,SV357: $i,SV455: $i] :
( ( ( c_Predicate_Osymp @ SV455 @ SV357 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6301]) ).
thf(6434,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6302]) ).
thf(6435,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
| ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6303]) ).
thf(6436,plain,
! [SV359: $i,SV238: $i,SV96: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6304]) ).
thf(6437,plain,
! [SV97: $i,SV239: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6305]) ).
thf(6438,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6306]) ).
thf(6439,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) )
| ~ ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6307]) ).
thf(6440,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
| ~ ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6308]) ).
thf(6441,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(6442,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
| ( SV243 = SV101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6310]) ).
thf(6443,plain,
! [SV363: $i,SV460: $i,SV101: $i,SV243: $i] :
( ( ~ ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6310]) ).
thf(6444,plain,
! [SV102: $i,SV244: $i,SV364: $i,SV461: $i,SV532: $i,SV578: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
| ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6311]) ).
thf(6445,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i] :
( ( ! [SY1957: $i,SY1958: $i,SY1959: $i,SY1960: $i,SY1961: $i] :
( ( ( hAPP @ SY1961 @ ( hAPP @ SY1960 @ SY1959 ) )
!= ( hAPP @ SY1958 @ ( hAPP @ SY1957 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1961 ) @ SY1960 ) @ SY1959 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SY1958 ) @ SY1957 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6312]) ).
thf(6446,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i,SV534: $i,SV580: $i] :
( ( ! [SY1962: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1962 @ SV580 @ SV534 @ SV463 ) @ SV366 )
!= SV246 )
| ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6313]) ).
thf(6447,plain,
! [SV105: $i,SV247: $i,SV367: $i,SV464: $i,SV535: $i,SV581: $i] :
( ( ( SV581 != SV535 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV581 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6314]) ).
thf(6448,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(6449,plain,
! [SV107: $i,SV249: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
= $true )
| ( ( SV249 = SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6316]) ).
thf(6450,plain,
! [SV107: $i,SV249: $i] :
( ( ( SV249 != SV107 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6317]) ).
thf(6451,plain,
! [SV108: $i,SV250: $i,SV369: $i,SV466: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV250 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV108 ) )
| ( SV250 = SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6318]) ).
thf(6452,plain,
! [SV109: $i,SV251: $i,SV370: $i,SV467: $i,SV537: $i,SV582: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV582 ) @ SV537 ) @ SV467 ) )
| ( SV370
!= ( hAPP @ SV251 @ SV537 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SV582 @ SV109 @ SV251 ) @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6319]) ).
thf(6453,plain,
! [SV110: $i,SV252: $i,SV371: $i,SV468: $i,SV538: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV538 @ SV468 @ SV371 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6320]) ).
thf(6454,plain,
! [SV111: $i,SV253: $i,SV372: $i,SV469: $i,SV539: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV539 ) @ SV469 ) @ SV372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SV469 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV539 @ SV253 @ SV111 ) @ SV372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6321]) ).
thf(6455,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
| ~ ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6322]) ).
thf(6456,plain,
! [SV113: $i,SV255: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) ) )
= $true )
| ( ( ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6323]) ).
thf(6457,plain,
! [SV113: $i,SV255: $i] :
( ( ( ~ ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6324]) ).
thf(6458,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6325]) ).
thf(6459,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ~ ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6325]) ).
thf(6460,plain,
! [SV115: $i,SV257: $i,SV375: $i,SV472: $i] :
( ( ( SV472 = SV375 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6326]) ).
thf(6461,plain,
! [SV116: $i,SV258: $i,SV376: $i,SV473: $i] :
( ( ( SV473 = SV376 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV473 ) @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6327]) ).
thf(6462,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
| ( SV377 = SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6328]) ).
thf(6463,plain,
! [SV259: $i,SV474: $i,SV117: $i,SV377: $i] :
( ( ~ ( ( SV377 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6328]) ).
thf(6464,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i,SV584: $i] :
( ( ! [SY1963: $i,SY1964: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1964 @ SY1963 @ SV584 @ SV541 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SY1963 @ SV584 @ SV260 ) @ SV118 ) )
| ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6329]) ).
thf(6465,plain,
! [SV119: $i,SV261: $i,SV379: $i,SV476: $i,SV542: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV542 @ SV476 ) @ SV379 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SV542 ) @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6330]) ).
thf(6466,plain,
! [SV120: $i,SV262: $i,SV380: $i,SV477: $i,SV543: $i] :
( ( ( ( hAPP @ SV543 @ SV477 )
!= SV380 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SV543 @ SV477 @ SV380 )
= SV543 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6331]) ).
thf(6467,plain,
! [SV121: $i,SV263: $i,SV381: $i,SV478: $i,SV544: $i,SV585: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV585 @ SV544 @ SV478 @ SV381 @ SV263 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV544 ) @ ( hAPP @ SV478 @ SV121 ) ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6332]) ).
thf(6468,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
| ~ ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6333]) ).
thf(6469,plain,
! [SV123: $i,SV265: $i,SV383: $i,SV480: $i,SV546: $i] :
( ( ( ~ ( c_Predicate_Otransp @ SV546 @ SV480 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6334]) ).
thf(6470,plain,
! [SV124: $i,SV266: $i,SV384: $i,SV481: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV481 @ SV384 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6335]) ).
thf(6471,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) )
| ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6336]) ).
thf(6472,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ~ ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) )
| ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6337]) ).
thf(6473,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
!= SV126 )
| ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6338]) ).
thf(6474,plain,
! [SV126: $i,SV386: $i,SV268: $i] :
( ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
| ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6339]) ).
thf(6475,plain,
! [SV127: $i,SV586: $i,SV269: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV269 @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6340]) ).
thf(6476,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
| ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6341]) ).
thf(6477,plain,
! [SV387: $i,SV270: $i,SV128: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6342]) ).
thf(6478,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i,SV547: $i,SV587: $i] :
( ( ! [SY1966: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1966 @ SV587 @ SV547 @ SV482 @ SV388 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6343]) ).
thf(6479,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6344]) ).
thf(6480,plain,
! [SV483: $i,SV389: $i,SV130: $i,SV272: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6344]) ).
thf(6481,plain,
! [SV132: $i,SV274: $i,SV391: $i,SV484: $i,SV548: $i,SV588: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
| ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6345]) ).
thf(6482,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6346]) ).
thf(6483,plain,
! [SV134: $i,SV276: $i,SV393: $i,SV486: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV486 @ SV393 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6347]) ).
thf(6484,plain,
! [SV136: $i,SV278: $i,SV394: $i,SV487: $i,SV550: $i,SV589: $i] :
( ( ( ( hAPP @ SV589 @ SV550 )
!= SV487 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SV589 ) @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6348]) ).
thf(6485,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6349]) ).
thf(6486,plain,
! [SV488: $i,SV137: $i,SV395: $i,SV279: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6349]) ).
thf(6487,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6350]) ).
thf(6488,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ~ ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6350]) ).
thf(6489,plain,
! [SV139: $i,SV281: $i,SV397: $i,SV490: $i,SV551: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6351]) ).
thf(6490,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i,SV552: $i,SV590: $i] :
( ( ! [SY1967: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1967 @ SV590 @ SV552 @ SV491 @ SV398 )
| ~ ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6352]) ).
thf(6491,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
| ( SV283 = SV141 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6353]) ).
thf(6492,plain,
! [SV399: $i,SV141: $i,SV283: $i] :
( ( ( SV283 != SV141 )
| ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6354]) ).
thf(6493,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6357]) ).
thf(6494,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) )
| ( SV403 = SV145 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6358]) ).
thf(6495,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ~ ( ~ ( ( SV592 != SV554 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 ) )
| ~ ( ~ ( ( SV592 != SV554 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6359]) ).
thf(6496,plain,
! [SV148: $i,SV290: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
= $true )
| ( ( SV290 = SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6361]) ).
thf(6497,plain,
! [SV148: $i,SV290: $i] :
( ( ( SV290 != SV148 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6498,plain,
! [SV9: $i,SV157: $i,SV296: $i,SV408: $i,SV496: $i,SV555: $i,SV593: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV593 @ SV555 @ SV496 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV593 @ SV408 @ SV555 ) @ SV296 ) @ SV157 ) ) @ SV9 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV593 @ SV408 @ SV496 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV408 @ SV555 @ SV496 ) @ SV157 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6363]) ).
thf(6499,plain,
! [SV11: $i,SV159: $i,SV298: $i,SV410: $i,SV498: $i,SV557: $i,SV594: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV594 @ SV557 @ SV498 @ SV410 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SV594 @ SV498 @ SV159 ) @ SV11 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV298 @ SV557 @ SV498 @ ( hAPP @ ( c_Fun_Ocomp @ SV594 @ SV557 @ SV298 @ SV410 ) @ SV159 ) ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6365]) ).
thf(6500,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i,SV595: $i] :
( ( ! [SY1968: $i,SY1969: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1969 @ SY1968 @ SV595 @ SV562 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SY1968 @ SV595 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6372]) ).
thf(6501,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 ) )
= $true )
| ( ( ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6373]) ).
thf(6502,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6374]) ).
thf(6503,plain,
! [SV38: $i,SV183: $i,SV310: $i,SV420: $i,SV505: $i,SV563: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $true )
| ( ( ~ ( ( SV420 != SV183 )
| ( SV310 != SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6375]) ).
thf(6504,plain,
! [SV311: $i,SV39: $i,SV421: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) ) )
= $false )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6376]) ).
thf(6505,plain,
! [SV40: $i,SV185: $i,SV312: $i,SV422: $i,SV506: $i,SV564: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV564 @ SV506 @ SV422 @ SV312 @ SV185 ) )
= $true )
| ( ( ( hAPP @ SV312 @ ( hAPP @ SV422 @ SV40 ) )
= SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6377]) ).
thf(6506,plain,
! [SV41: $i,SV186: $i,SV313: $i,SV423: $i,SV507: $i,SV565: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV565 @ SV507 @ SV423 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6378]) ).
thf(6507,plain,
! [SV43: $i,SV188: $i,SV314: $i,SV424: $i,SV508: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV508 ) @ ( hAPP @ SV424 @ SV314 ) ) @ SV188 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV43 ) @ SV314 ) @ ( hAPP @ ( c_Set_Ovimage @ SV43 @ SV508 @ SV424 ) @ SV188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6379]) ).
thf(6508,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6380]) ).
thf(6509,plain,
! [SV45: $i,SV190: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
= $false )
| ( ( SV190 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6381]) ).
thf(6510,plain,
! [SV45: $i,SV190: $i] :
( ( ( SV190 = SV45 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV190 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6382]) ).
thf(6511,plain,
! [SV48: $i,SV192: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
= $false )
| ( ( SV192 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6384]) ).
thf(6512,plain,
! [SV48: $i,SV192: $i] :
( ( ( SV192 = SV48 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV192 )
= ( hAPP @ c_Int_ORep__Integ @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6385]) ).
thf(6513,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6386]) ).
thf(6514,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ~ ( ~ ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6386]) ).
thf(6515,plain,
! [SV50: $i,SV428: $i,SV194: $i,SV318: $i] :
( ( ( ~ ( ( SV318 != SV194 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6387]) ).
thf(6516,plain,
! [SV51: $i,SV195: $i,SV319: $i,SV429: $i,SV511: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV511 @ SV429 ) @ SV319 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV195 @ SV51 @ SV511 ) @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6388]) ).
thf(6517,plain,
! [SV53: $i,SV197: $i,SV321: $i,SV430: $i,SV512: $i,SV567: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV567 @ SV512 @ SV430 @ SV321 @ SV197 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6389]) ).
thf(6518,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
| ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6390]) ).
thf(6519,plain,
! [SV431: $i,SV198: $i,SV54: $i,SV322: $i] :
( ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6391]) ).
thf(6520,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6392]) ).
thf(6521,plain,
! [SV56: $i,SV200: $i,SV324: $i,SV433: $i,SV513: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV513 ) @ SV433 ) @ ( hAPP @ ( c_Set_Ovimage @ SV513 @ SV324 @ SV200 ) @ SV56 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ ( hAPP @ SV200 @ SV433 ) ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6393]) ).
thf(6522,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6394]) ).
thf(6523,plain,
! [SV203: $i,SV59: $i,SV327: $i] :
( ( ( ~ ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6395]) ).
thf(6524,plain,
! [SV434: $i,SV204: $i,SV60: $i,SV328: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV60 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6396]) ).
thf(6525,plain,
! [SV61: $i,SV205: $i,SV329: $i,SV435: $i,SV514: $i,SV568: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV435 )
!= SV329 )
= $true )
| ( ( ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV435 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV329 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6397]) ).
thf(6526,plain,
! [SV62: $i,SV206: $i,SV330: $i,SV436: $i,SV515: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6398]) ).
thf(6527,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6399]) ).
thf(6528,plain,
! [SV66: $i,SV209: $i,SV597: $i,SV333: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV333 @ SV597 ) ) )
= $true )
| ( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6400]) ).
thf(6529,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i,SV569: $i,SV598: $i] :
( ( ! [SY1972: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1972 @ SV598 ) @ SV569 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SY1972 @ SV516 ) @ SV598 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6401]) ).
thf(6530,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6402]) ).
thf(6531,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6402]) ).
thf(6532,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i,SV518: $i,SV570: $i] :
( ( ( ~ ( ( SV570 != SV518 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SV518 @ SV69 ) @ SV570 )
= ( hAPP @ SV212 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6403]) ).
thf(6533,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
| ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6404]) ).
thf(6534,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV441: $i] :
( ( ~ ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) )
| ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6405]) ).
thf(6535,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i,SV519: $i,SV571: $i,SV599: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV599 @ SV571 @ SV519 @ SV442 @ SV338 @ SV214 )
| ( ( hAPP @ ( hAPP @ SV519 @ SV71 ) @ SV71 )
= SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6406]) ).
thf(6536,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) ) )
= $true )
| ( ( SV215 = SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6407]) ).
thf(6537,plain,
! [SV339: $i,SV72: $i,SV215: $i] :
( ( ( SV215 != SV72 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6408]) ).
thf(6538,plain,
! [SV73: $i,SV216: $i,SV340: $i,SV443: $i,SV520: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV520 @ SV443 @ SV340 ) @ SV216 ) @ SV73 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV340 @ SV73 ) @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6409]) ).
thf(6539,plain,
! [SV74: $i,SV217: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) )
= $false )
| ( ( SV217 = SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6410]) ).
thf(6540,plain,
! [SV74: $i,SV217: $i] :
( ( ( SV217 = SV74 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV217 )
= ( hAPP @ c_Nat_OSuc @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6411]) ).
thf(6541,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6412]) ).
thf(6542,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6412]) ).
thf(6543,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6414]) ).
thf(6544,plain,
! [SV446: $i,SV78: $i,SV344: $i,SV221: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6415]) ).
thf(6545,plain,
! [SV79: $i,SV222: $i,SV345: $i,SV447: $i,SV522: $i,SV572: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6416]) ).
thf(6546,plain,
! [SV81: $i,SV224: $i,SV347: $i,SV448: $i,SV523: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV448 ) @ SV347 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV224 @ SV81 @ SV523 ) @ SV347 ) @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6417]) ).
thf(6547,plain,
! [SV82: $i,SV573: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ SV225 @ SV573 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( c_Hilbert__Choice_OEps @ SV82 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6418]) ).
thf(6548,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) ) )
= $true )
| ( ( ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6419]) ).
thf(6549,plain,
! [SV349: $i,SV84: $i,SV227: $i] :
( ( ( ~ ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6420]) ).
thf(6550,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ~ ( ( SV574 != SV524 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 ) )
| ~ ( ~ ( ( SV574 != SV524 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6421]) ).
thf(6551,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6422]) ).
thf(6552,plain,
! [SV450: $i,SV525: $i,SV86: $i,SV351: $i,SV229: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6422]) ).
thf(6553,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i,SV526: $i,SV575: $i] :
( ( ( ~ ( ( SV575 != SV526 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV575 ) @ SV230 ) ) @ SV526 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV526 ) @ SV87 ) ) @ SV575 ) @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6423]) ).
thf(6554,plain,
! [SV88: $i,SV231: $i,SV353: $i,SV452: $i,SV527: $i,SV576: $i] :
( ( ( SV576
!= ( hAPP @ SV527 @ SV452 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SV576 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6424]) ).
thf(6555,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6425]) ).
thf(6556,plain,
! [SV453: $i,SV354: $i,SV89: $i,SV232: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6426]) ).
thf(6557,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
| ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6427]) ).
thf(6558,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6428]) ).
thf(6559,plain,
! [SV92: $i,SV234: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false )
| ( ( ! [SY921: $i,SY922: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) )
| ( ( hAPP @ SV92 @ SY921 )
= ( hAPP @ SV92 @ SY922 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY921 )
!= ( hAPP @ SV92 @ SY922 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY921 ) @ SY922 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6429]) ).
thf(6560,plain,
! [SV234: $i,SV92: $i] :
( ( ( ! [SY923: $i,SY924: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) )
| ( ( hAPP @ SV92 @ SY923 )
= ( hAPP @ SV92 @ SY924 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SY923 )
!= ( hAPP @ SV92 @ SY924 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY923 ) @ SY924 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6430]) ).
thf(6561,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) ) )
= $true )
| ( ( ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6431]) ).
thf(6562,plain,
! [SV356: $i,SV93: $i,SV235: $i] :
( ( ( ~ ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6432]) ).
thf(6563,plain,
! [SV455: $i,SV94: $i,SV236: $i,SV357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV455 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6433]) ).
thf(6564,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(6565,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6435]) ).
thf(6566,plain,
! [SV359: $i,SV238: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ SV238 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6436]) ).
thf(6567,plain,
! [SV97: $i,SV239: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false )
| ( ( ~ ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6437]) ).
thf(6568,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6438]) ).
thf(6569,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6439]) ).
thf(6570,plain,
! [SV457: $i,SV529: $i,SV98: $i,SV240: $i,SV360: $i] :
( ( ~ ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6439]) ).
thf(6571,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6440]) ).
thf(6572,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ~ ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6440]) ).
thf(6573,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6441]) ).
thf(6574,plain,
! [SV459: $i,SV531: $i,SV242: $i,SV100: $i,SV362: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6441]) ).
thf(6575,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
| ( SV243 = SV101 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6442]) ).
thf(6576,plain,
! [SV363: $i,SV460: $i,SV101: $i,SV243: $i] :
( ( ( SV243 != SV101 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6443]) ).
thf(6577,plain,
! [SV102: $i,SV244: $i,SV364: $i,SV461: $i,SV532: $i,SV578: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 ) )
= $true )
| ( ( ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6444]) ).
thf(6578,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i] :
( ( ! [SY1973: $i,SY1974: $i,SY1975: $i,SY1976: $i] :
( ( ( hAPP @ SY1976 @ ( hAPP @ SY1975 @ SY1974 ) )
!= ( hAPP @ SY1973 @ ( hAPP @ SV600 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1976 ) @ SY1975 ) @ SY1974 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SY1973 ) @ SV600 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6445]) ).
thf(6579,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i,SV534: $i,SV580: $i,SV601: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV601 @ SV580 @ SV534 @ SV463 ) @ SV366 )
!= SV246 )
| ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6446]) ).
thf(6580,plain,
! [SV105: $i,SV247: $i,SV367: $i,SV464: $i,SV535: $i,SV581: $i] :
( ( ( SV581 != SV535 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV581 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6447]) ).
thf(6581,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6448]) ).
thf(6582,plain,
! [SV465: $i,SV536: $i,SV248: $i,SV106: $i,SV368: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6448]) ).
thf(6583,plain,
! [SV107: $i,SV249: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
= $false )
| ( ( SV249 = SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6449]) ).
thf(6584,plain,
! [SV107: $i,SV249: $i] :
( ( ( SV249 = SV107 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV249 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6450]) ).
thf(6585,plain,
! [SV250: $i,SV108: $i,SV369: $i,SV466: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV108 ) ) )
= $true )
| ( ( SV250 = SV108 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV250 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6451]) ).
thf(6586,plain,
! [SV109: $i,SV251: $i,SV370: $i,SV467: $i,SV537: $i,SV582: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV582 ) @ SV537 ) @ SV467 ) ) )
= $true )
| ( ( ( SV370
!= ( hAPP @ SV251 @ SV537 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SV582 @ SV109 @ SV251 ) @ SV467 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6452]) ).
thf(6587,plain,
! [SV110: $i,SV252: $i,SV371: $i,SV468: $i,SV538: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV538 @ SV468 @ SV371 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV252 ) @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6453]) ).
thf(6588,plain,
! [SV111: $i,SV253: $i,SV372: $i,SV469: $i,SV539: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV539 ) @ SV469 ) @ SV372 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV253 ) @ ( hAPP @ SV111 @ SV469 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV539 @ SV253 @ SV111 ) @ SV372 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6454]) ).
thf(6589,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
| ~ ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6455]) ).
thf(6590,plain,
! [SV113: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $false )
| ( ( ~ ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6456]) ).
thf(6591,plain,
! [SV113: $i,SV255: $i] :
( ( ( ~ ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6457]) ).
thf(6592,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
| ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6458]) ).
thf(6593,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6459]) ).
thf(6594,plain,
! [SV375: $i,SV472: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) ) )
= $false )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(6595,plain,
! [SV473: $i,SV116: $i,SV376: $i,SV258: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV473 ) @ SV116 ) )
= $true )
| ( ( SV473 = SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6461]) ).
thf(6596,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
| ( SV377 = SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6462]) ).
thf(6597,plain,
! [SV259: $i,SV474: $i,SV117: $i,SV377: $i] :
( ( ( SV377 != SV117 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6463]) ).
thf(6598,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i,SV584: $i,SV602: $i] :
( ( ! [SY1977: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1977 @ SV602 @ SV584 @ SV541 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SV602 @ SV584 @ SV260 ) @ SV118 ) )
| ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6464]) ).
thf(6599,plain,
! [SV119: $i,SV261: $i,SV379: $i,SV476: $i,SV542: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV542 @ SV476 ) @ SV379 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV261 @ SV119 @ SV542 ) @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6465]) ).
thf(6600,plain,
! [SV120: $i,SV262: $i,SV380: $i,SV477: $i,SV543: $i] :
( ( ( ( hAPP @ SV543 @ SV477 )
= SV380 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV262 @ SV120 @ SV543 @ SV477 @ SV380 )
= SV543 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6466]) ).
thf(6601,plain,
! [SV121: $i,SV263: $i,SV381: $i,SV478: $i,SV544: $i,SV585: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV585 @ SV544 @ SV478 @ SV381 @ SV263 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV544 ) @ ( hAPP @ SV478 @ SV121 ) ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6467]) ).
thf(6602,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6468]) ).
thf(6603,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ~ ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6468]) ).
thf(6604,plain,
! [SV123: $i,SV265: $i,SV383: $i,SV480: $i,SV546: $i] :
( ( ( c_Predicate_Otransp @ SV546 @ SV480 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6469]) ).
thf(6605,plain,
! [SV481: $i,SV124: $i,SV266: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV481 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6470]) ).
thf(6606,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( ~ ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) ) )
= $true )
| ( ( ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6471]) ).
thf(6607,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( ~ ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) ) )
= $true )
| ( ( ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6472]) ).
thf(6608,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
!= SV126 )
= $true )
| ( ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6473]) ).
thf(6609,plain,
! [SV126: $i,SV386: $i,SV268: $i] :
( ( ( SV268
!= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6474]) ).
thf(6610,plain,
! [SV127: $i,SV586: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP @ SV269 @ SV586 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV269 @ ( c_Hilbert__Choice_OEps @ SV127 @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6475]) ).
thf(6611,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6476]) ).
thf(6612,plain,
! [SV387: $i,SV270: $i,SV128: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV128 @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6477]) ).
thf(6613,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i,SV547: $i,SV587: $i,SV603: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6478]) ).
thf(6614,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6479]) ).
thf(6615,plain,
! [SV483: $i,SV389: $i,SV130: $i,SV272: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6480]) ).
thf(6616,plain,
! [SV132: $i,SV274: $i,SV391: $i,SV484: $i,SV548: $i,SV588: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 ) )
= $true )
| ( ( ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6481]) ).
thf(6617,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6482]) ).
thf(6618,plain,
! [SV549: $i,SV133: $i,SV485: $i,SV275: $i,SV392: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6482]) ).
thf(6619,plain,
! [SV486: $i,SV134: $i,SV276: $i,SV393: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV486 @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6483]) ).
thf(6620,plain,
! [SV136: $i,SV278: $i,SV394: $i,SV487: $i,SV550: $i,SV589: $i] :
( ( ( ( hAPP @ SV589 @ SV550 )
!= SV487 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SV589 ) @ SV278 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6484]) ).
thf(6621,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6485]) ).
thf(6622,plain,
! [SV488: $i,SV137: $i,SV395: $i,SV279: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6486]) ).
thf(6623,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
| ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6487]) ).
thf(6624,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6488]) ).
thf(6625,plain,
! [SV139: $i,SV281: $i,SV397: $i,SV490: $i,SV551: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6489]) ).
thf(6626,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i,SV552: $i,SV590: $i,SV604: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
| ~ ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6490]) ).
thf(6627,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
!= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
= $true )
| ( ( SV283 = SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6491]) ).
thf(6628,plain,
! [SV399: $i,SV141: $i,SV283: $i] :
( ( ( SV283 != SV141 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6492]) ).
thf(6629,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(6630,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6494]) ).
thf(6631,plain,
! [SV287: $i,SV493: $i,SV145: $i,SV403: $i] :
( ( ( SV403 = SV145 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6494]) ).
thf(6632,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ~ ( ( SV592 != SV554 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 ) )
| ~ ( ~ ( ( SV592 != SV554 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6495]) ).
thf(6633,plain,
! [SV148: $i,SV290: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
= $false )
| ( ( SV290 = SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(6634,plain,
! [SV148: $i,SV290: $i] :
( ( ( SV290 = SV148 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV290 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6497]) ).
thf(6635,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i,SV595: $i,SV605: $i] :
( ( ! [SY1979: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1979 @ SV605 @ SV595 @ SV562 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SV605 @ SV595 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6500]) ).
thf(6636,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false )
| ( ( ! [SY1553: $i] :
( ~ ! [SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1554 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1554 ) )
| ! [SY1555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1555 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1553 @ SY1555 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6501]) ).
thf(6637,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ! [SY1556: $i] :
( ~ ! [SY1557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1557 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1557 ) )
| ! [SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1558 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SY1556 @ SY1558 ) ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(6638,plain,
! [SV38: $i,SV183: $i,SV310: $i,SV420: $i,SV505: $i,SV563: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false )
| ( ( ~ ( ( SV420 != SV183 )
| ( SV310 != SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(6639,plain,
! [SV311: $i,SV39: $i,SV421: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) ) )
= $false )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6504]) ).
thf(6640,plain,
! [SV421: $i,SV39: $i,SV311: $i,SV184: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) ) )
= $false )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6504]) ).
thf(6641,plain,
! [SV40: $i,SV185: $i,SV312: $i,SV422: $i,SV506: $i,SV564: $i] :
( ( ( c_Typedef_Otype__definition @ SV564 @ SV506 @ SV422 @ SV312 @ SV185 )
= $false )
| ( ( ( hAPP @ SV312 @ ( hAPP @ SV422 @ SV40 ) )
= SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6505]) ).
thf(6642,plain,
! [SV41: $i,SV186: $i,SV313: $i,SV423: $i,SV507: $i,SV565: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV565 @ SV507 @ SV423 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ SV41 ) )
= ( hAPP @ ( hAPP @ SV423 @ SV186 ) @ ( hAPP @ ( hAPP @ SV423 @ SV313 ) @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6506]) ).
thf(6643,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
| ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(6644,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
| ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6513]) ).
thf(6645,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ~ ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6514]) ).
thf(6646,plain,
! [SV50: $i,SV428: $i,SV194: $i,SV318: $i] :
( ( ( SV318 != SV194 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6515]) ).
thf(6647,plain,
! [SV53: $i,SV197: $i,SV321: $i,SV430: $i,SV512: $i,SV567: $i] :
( ( ( c_Typedef_Otype__definition @ SV567 @ SV512 @ SV430 @ SV321 @ SV197 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) )
| ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6517]) ).
thf(6648,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) ) )
= $true )
| ( ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6518]) ).
thf(6649,plain,
! [SV431: $i,SV198: $i,SV54: $i,SV322: $i] :
( ( ( ~ ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6519]) ).
thf(6650,plain,
! [SV199: $i,SV55: $i,SV323: $i,SV432: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6520]) ).
thf(6651,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1592 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1592 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6522]) ).
thf(6652,plain,
! [SV203: $i,SV59: $i,SV327: $i] :
( ( ( ! [SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SY1593 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SY1593 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6523]) ).
thf(6653,plain,
! [SV434: $i,SV204: $i,SV60: $i,SV328: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV328 @ SV60 ) @ SV204 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV60 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV434 @ SV328 ) @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6524]) ).
thf(6654,plain,
! [SV61: $i,SV205: $i,SV329: $i,SV435: $i,SV514: $i,SV568: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV435 )
= SV329 )
= $false )
| ( ( ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV435 ) @ SV61 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV329 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(6655,plain,
! [SV515: $i,SV62: $i,SV206: $i,SV330: $i,SV436: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6526]) ).
thf(6656,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6527]) ).
thf(6657,plain,
! [SV66: $i,SV209: $i,SV597: $i,SV333: $i] :
( ( ( hBOOL @ ( hAPP @ SV333 @ SV597 ) )
= $false )
| ( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
| ( hBOOL @ ( hAPP @ SV333 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6528]) ).
thf(6658,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i,SV569: $i,SV598: $i,SV606: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV606 @ SV598 ) @ SV569 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SV606 @ SV516 ) @ SV598 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6529]) ).
thf(6659,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6530]) ).
thf(6660,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6531]) ).
thf(6661,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i,SV518: $i,SV570: $i] :
( ( ( SV570 != SV518 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SV518 @ SV69 ) @ SV570 )
= ( hAPP @ SV212 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6532]) ).
thf(6662,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 ) )
= $true )
| ( ( ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6533]) ).
thf(6663,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV441: $i] :
( ( ( ~ ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6534]) ).
thf(6664,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i,SV519: $i,SV571: $i,SV599: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV599 @ SV571 @ SV519 @ SV442 @ SV338 @ SV214 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV519 @ SV71 ) @ SV71 )
= SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6535]) ).
thf(6665,plain,
! [SV72: $i,SV215: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
= $false )
| ( ( SV215 = SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6536]) ).
thf(6666,plain,
! [SV339: $i,SV72: $i,SV215: $i] :
( ( ( SV215 = SV72 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV339 ) @ SV215 ) @ ( hAPP @ c_fequal @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6537]) ).
thf(6667,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6541]) ).
thf(6668,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6542]) ).
thf(6669,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6543]) ).
thf(6670,plain,
! [SV446: $i,SV78: $i,SV344: $i,SV221: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6544]) ).
thf(6671,plain,
! [SV79: $i,SV222: $i,SV345: $i,SV447: $i,SV522: $i,SV572: $i] :
( ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6545]) ).
thf(6672,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $false )
| ( ( ! [SY1632: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1632 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1632 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6548]) ).
thf(6673,plain,
! [SV349: $i,SV84: $i,SV227: $i] :
( ( ( ! [SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SY1633 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SY1633 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6549]) ).
thf(6674,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ~ ( ( SV574 != SV524 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6550]) ).
thf(6675,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ~ ( ~ ( ( SV574 != SV524 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6550]) ).
thf(6676,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6551]) ).
thf(6677,plain,
! [SV450: $i,SV525: $i,SV86: $i,SV351: $i,SV229: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6552]) ).
thf(6678,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i,SV526: $i,SV575: $i] :
( ( ( SV575 != SV526 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV575 ) @ SV230 ) ) @ SV526 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV526 ) @ SV87 ) ) @ SV575 ) @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6553]) ).
thf(6679,plain,
! [SV88: $i,SV231: $i,SV353: $i,SV452: $i,SV527: $i,SV576: $i] :
( ( ( SV576
= ( hAPP @ SV527 @ SV452 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SV576 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6554]) ).
thf(6680,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6555]) ).
thf(6681,plain,
! [SV453: $i,SV354: $i,SV89: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6556]) ).
thf(6682,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) ) )
= $true )
| ( ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6557]) ).
thf(6683,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ( ~ ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6684,plain,
! [SV234: $i,SV607: $i,SV92: $i] :
( ( ( ! [SY1980: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SY1980 ) )
| ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SY1980 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SY1980 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SY1980 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6559]) ).
thf(6685,plain,
! [SV234: $i,SV92: $i] :
( ( ( ! [SY1981: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ SY1981 ) )
| ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ SY1981 ) ) )
| ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ SY1981 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ SY1981 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6560]) ).
thf(6686,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $false )
| ( ( ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1647 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1647 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6561]) ).
thf(6687,plain,
! [SV356: $i,SV93: $i,SV235: $i] :
( ( ( ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY1648 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SY1648 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6562]) ).
thf(6688,plain,
! [SV455: $i,SV94: $i,SV236: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV236 ) @ SV94 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV94 ) @ SV236 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV455 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6563]) ).
thf(6689,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6564]) ).
thf(6690,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6564]) ).
thf(6691,plain,
! [SV96: $i,SV238: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(6692,plain,
! [SV359: $i,SV238: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ SV238 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV359 ) @ SV238 ) @ ( hAPP @ ( c_Set_OCollect @ SV359 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6566]) ).
thf(6693,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) )
| ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6567]) ).
thf(6694,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) )
| ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6568]) ).
thf(6695,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
| ( ( hAPP @ SV360 @ SV240 )
= SV98 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6569]) ).
thf(6696,plain,
! [SV457: $i,SV529: $i,SV98: $i,SV240: $i,SV360: $i] :
( ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
| ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6570]) ).
thf(6697,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
| ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6571]) ).
thf(6698,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6572]) ).
thf(6699,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6573]) ).
thf(6700,plain,
! [SV459: $i,SV531: $i,SV242: $i,SV100: $i,SV362: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6574]) ).
thf(6701,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
= $true )
| ( ( SV243 = SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6575]) ).
thf(6702,plain,
! [SV363: $i,SV460: $i,SV101: $i,SV243: $i] :
( ( ( SV243 != SV101 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6576]) ).
thf(6703,plain,
! [SV102: $i,SV244: $i,SV364: $i,SV461: $i,SV532: $i,SV578: $i] :
( ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false )
| ( ( ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6577]) ).
thf(6704,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i] :
( ( ! [SY1982: $i,SY1983: $i,SY1984: $i] :
( ( ( hAPP @ SY1984 @ ( hAPP @ SY1983 @ SY1982 ) )
!= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1984 ) @ SY1983 ) @ SY1982 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6578]) ).
thf(6705,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i,SV534: $i,SV580: $i,SV601: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV601 @ SV580 @ SV534 @ SV463 ) @ SV366 )
!= SV246 )
= $true )
| ( ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6579]) ).
thf(6706,plain,
! [SV105: $i,SV247: $i,SV367: $i,SV464: $i,SV535: $i,SV581: $i] :
( ( ( SV581 = SV535 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV581 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV464 @ SV367 @ SV247 ) @ SV105 ) @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6580]) ).
thf(6707,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6581]) ).
thf(6708,plain,
! [SV465: $i,SV536: $i,SV248: $i,SV106: $i,SV368: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6582]) ).
thf(6709,plain,
! [SV250: $i,SV108: $i,SV369: $i,SV466: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV108 ) )
= $false )
| ( ( SV250 = SV108 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV466 @ SV369 ) @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6585]) ).
thf(6710,plain,
! [SV109: $i,SV251: $i,SV370: $i,SV467: $i,SV537: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV582 ) @ SV537 ) @ SV467 ) )
= $false )
| ( ( ( SV370
!= ( hAPP @ SV251 @ SV537 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SV582 @ SV109 @ SV251 ) @ SV467 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6586]) ).
thf(6711,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6589]) ).
thf(6712,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ~ ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6589]) ).
thf(6713,plain,
! [SV113: $i,SV255: $i] :
( ( ( ! [SY1417: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1417 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6590]) ).
thf(6714,plain,
! [SV113: $i,SV255: $i] :
( ( ( ! [SY1418: $i] :
~ ( hBOOL @ ( hAPP @ SV255 @ SY1418 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6591]) ).
thf(6715,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) ) )
= $true )
| ( ( ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6592]) ).
thf(6716,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ( ~ ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6593]) ).
thf(6717,plain,
! [SV375: $i,SV472: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) ) )
= $false )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6594]) ).
thf(6718,plain,
! [SV472: $i,SV375: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) ) )
= $false )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6594]) ).
thf(6719,plain,
! [SV473: $i,SV116: $i,SV376: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV376 ) @ SV116 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV258 ) @ SV473 ) @ SV116 ) )
= $true )
| ( ( SV473 = SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6595]) ).
thf(6720,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
= $true )
| ( ( SV377 = SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6596]) ).
thf(6721,plain,
! [SV259: $i,SV474: $i,SV117: $i,SV377: $i] :
( ( ( SV377 != SV117 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6597]) ).
thf(6722,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i,SV584: $i,SV602: $i,SV609: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV609 @ SV602 @ SV584 @ SV541 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SV602 @ SV584 @ SV260 ) @ SV118 ) )
| ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6598]) ).
thf(6723,plain,
! [SV121: $i,SV263: $i,SV381: $i,SV478: $i,SV544: $i,SV585: $i] :
( ( ( c_Typedef_Otype__definition @ SV585 @ SV544 @ SV478 @ SV381 @ SV263 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV544 ) @ ( hAPP @ SV478 @ SV121 ) ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6601]) ).
thf(6724,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
| ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6602]) ).
thf(6725,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6603]) ).
thf(6726,plain,
! [SV546: $i,SV123: $i,SV265: $i,SV383: $i,SV480: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV546 @ SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6604]) ).
thf(6727,plain,
! [SV481: $i,SV124: $i,SV266: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV266 ) @ SV124 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV384 @ SV124 ) @ SV266 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV481 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6605]) ).
thf(6728,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( ! [SY1717: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1717 ) ) )
= $false )
| ( ( ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6606]) ).
thf(6729,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( ! [SY1720: $i,SY1721: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1720 ) @ SY1721 ) ) ) )
= $false )
| ( ( ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6607]) ).
thf(6730,plain,
! [SV126: $i,SV268: $i,SV386: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 )
= $false )
| ( ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6608]) ).
thf(6731,plain,
! [SV126: $i,SV386: $i,SV268: $i] :
( ( ( SV268
= ( hAPP @ ( c_List_Orev @ SV386 ) @ SV126 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV386 ) @ SV268 )
= SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6609]) ).
thf(6732,plain,
! [SV128: $i,SV270: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6611]) ).
thf(6733,plain,
! [SV387: $i,SV270: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV270 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV387 ) @ SV270 ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6612]) ).
thf(6734,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i,SV547: $i,SV587: $i,SV603: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6613]) ).
thf(6735,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6614]) ).
thf(6736,plain,
! [SV483: $i,SV389: $i,SV130: $i,SV272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6615]) ).
thf(6737,plain,
! [SV132: $i,SV274: $i,SV391: $i,SV484: $i,SV548: $i,SV588: $i] :
( ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false )
| ( ( ~ ( ( SV274 != SV132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6616]) ).
thf(6738,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6617]) ).
thf(6739,plain,
! [SV549: $i,SV133: $i,SV485: $i,SV275: $i,SV392: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6618]) ).
thf(6740,plain,
! [SV486: $i,SV134: $i,SV276: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV276 ) @ SV134 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV393 @ SV134 ) @ SV276 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV486 @ SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6619]) ).
thf(6741,plain,
! [SV136: $i,SV278: $i,SV394: $i,SV487: $i,SV550: $i,SV589: $i] :
( ( ( ( hAPP @ SV589 @ SV550 )
= SV487 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SV589 ) @ SV278 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6620]) ).
thf(6742,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6621]) ).
thf(6743,plain,
! [SV488: $i,SV137: $i,SV395: $i,SV279: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6622]) ).
thf(6744,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) ) )
= $true )
| ( ( ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6623]) ).
thf(6745,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ( ~ ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6624]) ).
thf(6746,plain,
! [SV551: $i,SV139: $i,SV281: $i,SV397: $i,SV490: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6625]) ).
thf(6747,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i,SV552: $i,SV590: $i,SV604: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6626]) ).
thf(6748,plain,
! [SV141: $i,SV283: $i,SV399: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
= $false )
| ( ( SV283 = SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6627]) ).
thf(6749,plain,
! [SV399: $i,SV141: $i,SV283: $i] :
( ( ( SV283 = SV141 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV399 ) @ SV283 )
= ( hAPP @ ( c_List_Orev @ SV399 ) @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6628]) ).
thf(6750,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6629]) ).
thf(6751,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6629]) ).
thf(6752,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6630]) ).
thf(6753,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ~ ( ( SV592 != SV554 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6632]) ).
thf(6754,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ~ ( ~ ( ( SV592 != SV554 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6632]) ).
thf(6755,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i,SV595: $i,SV605: $i,SV610: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV610 @ SV605 @ SV595 @ SV562 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SV605 @ SV595 @ SV308 ) @ SV181 ) )
| ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6635]) ).
thf(6756,plain,
! [SV37: $i,SV611: $i,SV182: $i,SV309: $i] :
( ( ( ~ ! [SY1986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1986 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1986 ) )
| ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6636]) ).
thf(6757,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ! [SY1988: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1988 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SY1988 ) )
| ! [SY1989: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1989 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SY1989 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6637]) ).
thf(6758,plain,
! [SV505: $i,SV563: $i,SV38: $i,SV310: $i,SV183: $i,SV420: $i] :
( ( ( ( SV420 != SV183 )
| ( SV310 != SV38 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6638]) ).
thf(6759,plain,
! [SV311: $i,SV39: $i,SV421: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6639]) ).
thf(6760,plain,
! [SV421: $i,SV39: $i,SV311: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6640]) ).
thf(6761,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6643]) ).
thf(6762,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ~ ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6643]) ).
thf(6763,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true )
| ( ( ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6644]) ).
thf(6764,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6645]) ).
thf(6765,plain,
! [SV50: $i,SV428: $i,SV194: $i,SV318: $i] :
( ( ( SV318 = SV194 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ SV50 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV428 ) @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV428 ) @ SV194 ) @ SV50 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6646]) ).
thf(6766,plain,
! [SV567: $i,SV321: $i,SV430: $i,SV197: $i,SV53: $i,SV512: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) ) )
= $true )
| ( ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV567 @ SV512 @ SV430 @ SV321 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6647]) ).
thf(6767,plain,
! [SV54: $i,SV198: $i,SV322: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $false )
| ( ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6648]) ).
thf(6768,plain,
! [SV431: $i,SV198: $i,SV54: $i,SV322: $i] :
( ( ( ( SV322 = SV54 )
| ( hBOOL @ ( hAPP @ SV198 @ SV54 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6649]) ).
thf(6769,plain,
! [SV199: $i,SV55: $i,SV323: $i,SV432: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6650]) ).
thf(6770,plain,
! [SV203: $i,SV59: $i,SV612: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SV612 ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ SV612 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6651]) ).
thf(6771,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ ( sK5_SY1593 @ SV203 @ SV59 @ SV327 ) ) @ SV59 ) )
| ( hBOOL @ ( hAPP @ SV203 @ ( sK5_SY1593 @ SV203 @ SV59 @ SV327 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6652]) ).
thf(6772,plain,
! [SV329: $i,SV514: $i,SV61: $i,SV435: $i,SV568: $i,SV205: $i] :
( ( ( SV205
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV435 ) @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV329 ) @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV435 )
= SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6654]) ).
thf(6773,plain,
! [SV515: $i,SV62: $i,SV206: $i,SV330: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6655]) ).
thf(6774,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6656]) ).
thf(6775,plain,
! [SV437: $i,SV332: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6656]) ).
thf(6776,plain,
! [SV597: $i,SV333: $i,SV66: $i,SV209: $i] :
( ( ( SV209
!= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV333 @ SV209 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV333 @ SV597 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6657]) ).
thf(6777,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i,SV569: $i,SV598: $i,SV606: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV606 @ SV598 ) @ SV569 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SV606 @ SV516 ) @ SV598 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6658]) ).
thf(6778,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6659]) ).
thf(6779,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6660]) ).
thf(6780,plain,
! [SV69: $i,SV212: $i,SV336: $i,SV440: $i,SV518: $i,SV570: $i] :
( ( ( SV570 = SV518 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV440 @ SV336 @ SV212 @ SV518 @ SV69 ) @ SV570 )
= ( hAPP @ SV212 @ SV570 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6661]) ).
thf(6781,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false )
| ( ( ! [SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1806 ) @ SV70 ) )
| ! [SY1807: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1807 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1806 )
!= ( hAPP @ SV213 @ SY1807 ) )
| ( SY1806 = SY1807 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6662]) ).
thf(6782,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV441: $i] :
( ( ( ! [SY1808: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1808 ) @ SV70 ) )
| ! [SY1809: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1809 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SY1808 )
!= ( hAPP @ SV213 @ SY1809 ) )
| ( SY1808 = SY1809 ) ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6663]) ).
thf(6783,plain,
! [SV71: $i,SV214: $i,SV338: $i,SV442: $i,SV519: $i,SV571: $i,SV599: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV599 @ SV571 @ SV519 @ SV442 @ SV338 @ SV214 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV519 @ SV71 ) @ SV71 )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6664]) ).
thf(6784,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6667]) ).
thf(6785,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6668]) ).
thf(6786,plain,
! [SV78: $i,SV221: $i,SV344: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6669]) ).
thf(6787,plain,
! [SV446: $i,SV78: $i,SV344: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV221 @ SV344 ) @ SV78 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV446 ) @ SV344 ) @ ( c_SetInterval_Oord_OlessThan @ SV446 @ SV221 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6670]) ).
thf(6788,plain,
! [SV522: $i,SV447: $i,SV79: $i,SV345: $i,SV222: $i,SV572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6671]) ).
thf(6789,plain,
! [SV349: $i,SV84: $i,SV613: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV613 ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV613 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6672]) ).
thf(6790,plain,
! [SV84: $i,SV349: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ ( sK6_SY1633 @ SV349 @ SV84 @ SV227 ) ) @ SV84 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ ( sK6_SY1633 @ SV349 @ SV84 @ SV227 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6673]) ).
thf(6791,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( SV574 != SV524 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6674]) ).
thf(6792,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ~ ( ( SV574 != SV524 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6675]) ).
thf(6793,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6676]) ).
thf(6794,plain,
! [SV450: $i,SV525: $i,SV86: $i,SV351: $i,SV229: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6677]) ).
thf(6795,plain,
! [SV87: $i,SV230: $i,SV352: $i,SV451: $i,SV526: $i,SV575: $i] :
( ( ( SV575 = SV526 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV575 ) @ SV230 ) ) @ SV526 ) @ SV87 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV451 @ SV352 ) @ SV526 ) @ SV87 ) ) @ SV575 ) @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6678]) ).
thf(6796,plain,
! [SV527: $i,SV576: $i,SV88: $i,SV231: $i,SV452: $i,SV353: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SV576 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) )
= $true )
| ( ( SV576
= ( hAPP @ SV527 @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6679]) ).
thf(6797,plain,
! [SV89: $i,SV232: $i,SV354: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(6798,plain,
! [SV453: $i,SV354: $i,SV89: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV89 ) @ SV354 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV453 ) @ SV354 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV453 @ SV232 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6681]) ).
thf(6799,plain,
! [SV90: $i,SV233: $i,SV355: $i,SV454: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $false )
| ( ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6682]) ).
thf(6800,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ( ( SV355 = SV233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6683]) ).
thf(6801,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
| ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SV614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6684]) ).
thf(6802,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
| ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6685]) ).
thf(6803,plain,
! [SV356: $i,SV93: $i,SV615: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV615 ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV615 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6686]) ).
thf(6804,plain,
! [SV93: $i,SV356: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ ( sK8_SY1648 @ SV356 @ SV93 @ SV235 ) ) @ SV93 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ ( sK8_SY1648 @ SV356 @ SV93 @ SV235 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6687]) ).
thf(6805,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6689]) ).
thf(6806,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6690]) ).
thf(6807,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6693]) ).
thf(6808,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6693]) ).
thf(6809,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) ) )
= $true )
| ( ( ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6694]) ).
thf(6810,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
!= SV360 )
= $true )
| ( ( ( hAPP @ SV360 @ SV240 )
= SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6695]) ).
thf(6811,plain,
! [SV457: $i,SV529: $i,SV98: $i,SV240: $i,SV360: $i] :
( ( ( ( hAPP @ SV360 @ SV240 )
!= SV98 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6696]) ).
thf(6812,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true )
| ( ( ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6697]) ).
thf(6813,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( ~ ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6698]) ).
thf(6814,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6699]) ).
thf(6815,plain,
! [SV459: $i,SV531: $i,SV242: $i,SV100: $i,SV362: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6700]) ).
thf(6816,plain,
! [SV101: $i,SV243: $i,SV363: $i,SV460: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
= $false )
| ( ( SV243 = SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6701]) ).
thf(6817,plain,
! [SV363: $i,SV460: $i,SV101: $i,SV243: $i] :
( ( ( SV243 = SV101 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV243 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV460 ) @ SV363 ) @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6702]) ).
thf(6818,plain,
! [SV532: $i,SV364: $i,SV578: $i,SV102: $i,SV244: $i,SV461: $i] :
( ( ( ( hAPP @ SV461 @ SV244 )
!= ( hAPP @ SV461 @ SV102 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6703]) ).
thf(6819,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i,SV616: $i] :
( ( ! [SY1990: $i,SY1991: $i] :
( ( ( hAPP @ SY1991 @ ( hAPP @ SY1990 @ SV616 ) )
!= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1991 ) @ SY1990 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6704]) ).
thf(6820,plain,
! [SV104: $i,SV246: $i,SV366: $i,SV463: $i,SV534: $i,SV580: $i,SV601: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV601 @ SV580 @ SV534 @ SV463 ) @ SV366 )
= SV246 )
= $false )
| ( ( ( hAPP @ SV463 @ ( hAPP @ SV366 @ SV104 ) )
= ( hAPP @ SV246 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6705]) ).
thf(6821,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6707]) ).
thf(6822,plain,
! [SV465: $i,SV536: $i,SV248: $i,SV106: $i,SV368: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6708]) ).
thf(6823,plain,
! [SV467: $i,SV582: $i,SV109: $i,SV537: $i,SV251: $i,SV370: $i] :
( ( ( SV370
!= ( hAPP @ SV251 @ SV537 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SV582 @ SV109 @ SV251 ) @ SV467 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV582 ) @ SV537 ) @ SV467 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6710]) ).
thf(6824,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
| ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6711]) ).
thf(6825,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6712]) ).
thf(6826,plain,
! [SV113: $i,SV255: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV255 @ ( sK9_SY1417 @ SV113 @ SV255 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6713]) ).
thf(6827,plain,
! [SV113: $i,SV617: $i,SV255: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV255 @ SV617 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6714]) ).
thf(6828,plain,
! [SV114: $i,SV256: $i,SV374: $i,SV471: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $false )
| ( ( ~ ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6715]) ).
thf(6829,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ( ~ ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6716]) ).
thf(6830,plain,
! [SV375: $i,SV472: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6717]) ).
thf(6831,plain,
! [SV472: $i,SV375: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6718]) ).
thf(6832,plain,
! [SV117: $i,SV259: $i,SV377: $i,SV474: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
= $false )
| ( ( SV377 = SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6720]) ).
thf(6833,plain,
! [SV259: $i,SV474: $i,SV117: $i,SV377: $i] :
( ( ( SV377 = SV117 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV377 ) @ SV259 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV474 ) @ SV117 ) @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6721]) ).
thf(6834,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i,SV584: $i,SV602: $i,SV609: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV609 @ SV602 @ SV584 @ SV541 ) @ SV475 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SV602 @ SV584 @ SV260 ) @ SV118 ) )
= $true )
| ( ( ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6722]) ).
thf(6835,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) ) )
= $true )
| ( ( ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6724]) ).
thf(6836,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ( ~ ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6725]) ).
thf(6837,plain,
! [SV546: $i,SV123: $i,SV265: $i,SV383: $i,SV480: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV546 @ SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6726]) ).
thf(6838,plain,
! [SV267: $i,SV125: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ ( sK10_SY1717 @ SV125 @ SV267 @ SV385 ) ) )
= $false )
| ( ( ! [SY1718: $i,SY1719: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SY1718 ) @ SY1719 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6728]) ).
thf(6839,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( ! [SY1992: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ ( sK11_SY1720 @ SV125 @ SV267 @ SV385 ) ) @ SY1992 ) ) ) )
= $false )
| ( ( ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6729]) ).
thf(6840,plain,
! [SV129: $i,SV271: $i,SV388: $i,SV482: $i,SV547: $i,SV587: $i,SV603: $i] :
( ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6734]) ).
thf(6841,plain,
! [SV130: $i,SV272: $i,SV389: $i,SV483: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6735]) ).
thf(6842,plain,
! [SV483: $i,SV389: $i,SV130: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV272 @ SV130 ) @ SV389 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV483 ) @ SV389 ) @ ( c_SetInterval_Oord_OatLeast @ SV483 @ SV272 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6736]) ).
thf(6843,plain,
! [SV548: $i,SV484: $i,SV391: $i,SV588: $i,SV132: $i,SV274: $i] :
( ( ( ~ ( ( SV274 != SV132 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6737]) ).
thf(6844,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6738]) ).
thf(6845,plain,
! [SV549: $i,SV133: $i,SV485: $i,SV275: $i,SV392: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6739]) ).
thf(6846,plain,
! [SV589: $i,SV550: $i,SV136: $i,SV278: $i,SV487: $i,SV394: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SV589 ) @ SV278 ) ) )
= $true )
| ( ( ( hAPP @ SV589 @ SV550 )
= SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6741]) ).
thf(6847,plain,
! [SV137: $i,SV279: $i,SV395: $i,SV488: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6742]) ).
thf(6848,plain,
! [SV488: $i,SV137: $i,SV395: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV279 @ SV395 ) @ SV137 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV488 ) @ SV395 ) @ ( c_SetInterval_Oord_OatMost @ SV488 @ SV279 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6743]) ).
thf(6849,plain,
! [SV138: $i,SV280: $i,SV396: $i,SV489: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $false )
| ( ( ~ ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6744]) ).
thf(6850,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ( ~ ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6745]) ).
thf(6851,plain,
! [SV551: $i,SV139: $i,SV281: $i,SV397: $i,SV490: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6746]) ).
thf(6852,plain,
! [SV140: $i,SV282: $i,SV398: $i,SV491: $i,SV552: $i,SV590: $i,SV604: $i] :
( ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6747]) ).
thf(6853,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6750]) ).
thf(6854,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6751]) ).
thf(6855,plain,
! [SV145: $i,SV287: $i,SV403: $i,SV493: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ SV287 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV493 ) @ SV403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV493 ) @ SV145 ) @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6752]) ).
thf(6856,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( SV592 != SV554 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6753]) ).
thf(6857,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ~ ( ( SV592 != SV554 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6754]) ).
thf(6858,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i,SV595: $i,SV605: $i,SV610: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV610 @ SV605 @ SV595 @ SV562 ) @ SV504 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SV605 @ SV595 @ SV308 ) @ SV181 ) )
= $true )
| ( ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6755]) ).
thf(6859,plain,
! [SV37: $i,SV611: $i,SV182: $i,SV309: $i] :
( ( ( ~ ! [SY1986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1986 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1986 ) ) )
= $true )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6756]) ).
thf(6860,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ! [SY1988: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1988 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SY1988 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6757]) ).
thf(6861,plain,
! [SV182: $i,SV37: $i,SV309: $i] :
( ( ( ! [SY1989: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1989 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SY1989 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6757]) ).
thf(6862,plain,
! [SV38: $i,SV310: $i,SV505: $i,SV563: $i,SV183: $i,SV420: $i] :
( ( ( SV420 != SV183 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6758]) ).
thf(6863,plain,
! [SV183: $i,SV420: $i,SV505: $i,SV563: $i,SV38: $i,SV310: $i] :
( ( ( SV310 != SV38 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6758]) ).
thf(6864,plain,
! [SV311: $i,SV39: $i,SV421: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6759]) ).
thf(6865,plain,
! [SV421: $i,SV39: $i,SV311: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6760]) ).
thf(6866,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
| ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6761]) ).
thf(6867,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[6762]) ).
thf(6868,plain,
! [SV49: $i,SV193: $i,SV317: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false )
| ( ( ~ ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6763]) ).
thf(6869,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6764]) ).
thf(6870,plain,
! [SV567: $i,SV321: $i,SV430: $i,SV197: $i,SV53: $i,SV512: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV512 ) @ SV53 ) @ SV197 ) )
= $false )
| ( ( ( hAPP @ SV430 @ ( hAPP @ SV321 @ SV53 ) )
= SV53 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV567 @ SV512 @ SV430 @ SV321 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6766]) ).
thf(6871,plain,
! [SV431: $i,SV198: $i,SV54: $i,SV322: $i] :
( ( ( SV322 = SV54 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV198 @ SV54 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6767]) ).
thf(6872,plain,
! [SV198: $i,SV431: $i,SV54: $i,SV322: $i] :
( ( ( SV322 = SV54 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6768]) ).
thf(6873,plain,
! [SV322: $i,SV431: $i,SV54: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ SV198 @ SV54 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV431 ) @ SV322 ) @ SV198 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6768]) ).
thf(6874,plain,
! [SV199: $i,SV55: $i,SV323: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6769]) ).
thf(6875,plain,
! [SV203: $i,SV59: $i,SV612: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SV612 ) @ SV59 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV203 @ SV612 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6770]) ).
thf(6876,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ ( sK5_SY1593 @ SV203 @ SV59 @ SV327 ) ) @ SV59 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6771]) ).
thf(6877,plain,
! [SV327: $i,SV59: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ SV203 @ ( sK5_SY1593 @ SV203 @ SV59 @ SV327 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6771]) ).
thf(6878,plain,
! [SV329: $i,SV514: $i,SV61: $i,SV435: $i,SV568: $i,SV205: $i] :
( ( ( SV205
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV435 ) @ SV61 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV205 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV329 ) @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV568 ) @ SV514 ) @ SV435 )
= SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6772]) ).
thf(6879,plain,
! [SV515: $i,SV330: $i,SV62: $i,SV206: $i,SV436: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6773]) ).
thf(6880,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6774]) ).
thf(6881,plain,
! [SV437: $i,SV332: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6775]) ).
thf(6882,plain,
! [SV597: $i,SV333: $i,SV66: $i,SV209: $i] :
( ( ( SV209
= ( c_Hilbert__Choice_OEps @ SV66 @ SV333 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV333 @ SV209 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV333 @ SV597 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6776]) ).
thf(6883,plain,
! [SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV516: $i,SV569: $i,SV598: $i,SV606: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV606 @ SV598 ) @ SV569 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SV606 @ SV516 ) @ SV598 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6777]) ).
thf(6884,plain,
! [SV68: $i,SV211: $i,SV335: $i,SV439: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6778]) ).
thf(6885,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6779]) ).
thf(6886,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV618: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
| ! [SY1993: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1993 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SY1993 ) )
| ( SV618 = SY1993 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6781]) ).
thf(6887,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) )
| ! [SY1994: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1994 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
!= ( hAPP @ SV213 @ SY1994 ) )
| ( ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 )
= SY1994 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6782]) ).
thf(6888,plain,
! [SV75: $i,SV218: $i,SV341: $i,SV444: $i,SV521: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6784]) ).
thf(6889,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6785]) ).
thf(6890,plain,
! [SV522: $i,SV447: $i,SV79: $i,SV345: $i,SV222: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
| ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6788]) ).
thf(6891,plain,
! [SV349: $i,SV84: $i,SV613: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV613 ) @ SV84 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV613 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6789]) ).
thf(6892,plain,
! [SV84: $i,SV349: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ ( sK6_SY1633 @ SV349 @ SV84 @ SV227 ) ) @ SV84 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6790]) ).
thf(6893,plain,
! [SV84: $i,SV227: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ ( sK6_SY1633 @ SV349 @ SV84 @ SV227 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6790]) ).
thf(6894,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( SV574 != SV524 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6791]) ).
thf(6895,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( ~ ( ( SV574 != SV524 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6792]) ).
thf(6896,plain,
! [SV86: $i,SV229: $i,SV351: $i,SV450: $i,SV525: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6793]) ).
thf(6897,plain,
! [SV450: $i,SV525: $i,SV86: $i,SV351: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ ( hAPP @ SV351 @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV525 @ SV450 @ SV351 ) @ SV229 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6794]) ).
thf(6898,plain,
! [SV527: $i,SV576: $i,SV88: $i,SV231: $i,SV452: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV353 ) @ SV452 ) @ SV231 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV88 ) @ SV576 ) @ ( hAPP @ ( c_Set_Oimage @ SV353 @ SV88 @ SV527 ) @ SV231 ) ) )
= $true )
| ( ( SV576
= ( hAPP @ SV527 @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6796]) ).
thf(6899,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ( SV355 = SV233 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6799]) ).
thf(6900,plain,
! [SV90: $i,SV454: $i,SV233: $i,SV355: $i] :
( ( ( SV355 = SV233 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6800]) ).
thf(6901,plain,
! [SV233: $i,SV90: $i,SV355: $i,SV454: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ SV90 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV454 ) @ SV355 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV454 ) @ SV233 ) @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6800]) ).
thf(6902,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
| ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) ) )
| ~ ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SV614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6801]) ).
thf(6903,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
| ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6802]) ).
thf(6904,plain,
! [SV356: $i,SV93: $i,SV615: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV615 ) @ SV93 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV615 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6803]) ).
thf(6905,plain,
! [SV93: $i,SV356: $i,SV235: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ ( sK8_SY1648 @ SV356 @ SV93 @ SV235 ) ) @ SV93 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6804]) ).
thf(6906,plain,
! [SV93: $i,SV235: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ ( sK8_SY1648 @ SV356 @ SV93 @ SV235 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6804]) ).
thf(6907,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6805]) ).
thf(6908,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6806]) ).
thf(6909,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6807]) ).
thf(6910,plain,
! [SV239: $i,SV97: $i] :
( ( ( ! [SY941: $i,SY942: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY941 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY942 ) @ SY942 ) ) )
| ( ( hAPP @ SV97 @ SY941 )
!= ( hAPP @ SV97 @ SY942 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY941 ) @ SY942 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6808]) ).
thf(6911,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) ) )
= $false )
| ( ( ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6809]) ).
thf(6912,plain,
! [SV98: $i,SV240: $i,SV360: $i,SV457: $i,SV529: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 )
= $false )
| ( ( ( hAPP @ SV360 @ SV240 )
= SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6810]) ).
thf(6913,plain,
! [SV457: $i,SV529: $i,SV98: $i,SV240: $i,SV360: $i] :
( ( ( ( hAPP @ SV360 @ SV240 )
= SV98 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV529 @ SV457 @ SV360 @ SV240 @ SV98 )
= SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6811]) ).
thf(6914,plain,
! [SV99: $i,SV241: $i,SV361: $i,SV458: $i,SV530: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false )
| ( ( ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6812]) ).
thf(6915,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( ~ ( ( SV458 != SV241 )
| ( SV361 != SV99 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6813]) ).
thf(6916,plain,
! [SV100: $i,SV242: $i,SV362: $i,SV459: $i,SV531: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6814]) ).
thf(6917,plain,
! [SV459: $i,SV531: $i,SV242: $i,SV100: $i,SV362: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV100 ) @ SV242 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV531 @ SV459 @ SV362 ) @ SV242 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6815]) ).
thf(6918,plain,
! [SV532: $i,SV364: $i,SV578: $i,SV102: $i,SV244: $i,SV461: $i] :
( ( ( ( hAPP @ SV461 @ SV244 )
= ( hAPP @ SV461 @ SV102 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6818]) ).
thf(6919,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i,SV616: $i,SV619: $i] :
( ( ! [SY1995: $i] :
( ( ( hAPP @ SY1995 @ ( hAPP @ SV619 @ SV616 ) )
!= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SY1995 ) @ SV619 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6819]) ).
thf(6920,plain,
! [SV106: $i,SV248: $i,SV368: $i,SV465: $i,SV536: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6821]) ).
thf(6921,plain,
! [SV465: $i,SV536: $i,SV248: $i,SV106: $i,SV368: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV368 @ SV106 ) @ SV248 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV536 @ SV465 @ SV368 ) @ SV248 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(6922,plain,
! [SV467: $i,SV582: $i,SV109: $i,SV537: $i,SV251: $i,SV370: $i] :
( ( ( SV370
= ( hAPP @ SV251 @ SV537 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV109 ) @ SV370 ) @ ( hAPP @ ( c_Set_Oimage @ SV582 @ SV109 @ SV251 ) @ SV467 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV582 ) @ SV537 ) @ SV467 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6823]) ).
thf(6923,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true )
| ( ( ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6824]) ).
thf(6924,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( ~ ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6825]) ).
thf(6925,plain,
! [SV113: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ SV255 @ ( sK9_SY1417 @ SV113 @ SV255 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6826]) ).
thf(6926,plain,
! [SV113: $i,SV617: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP @ SV255 @ SV617 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV255 @ ( c_Hilbert__Choice_OEps @ SV113 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6827]) ).
thf(6927,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ( ! [SY1421: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1421 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6828]) ).
thf(6928,plain,
! [SV374: $i,SV471: $i,SV114: $i,SV256: $i] :
( ( ( ! [SY1422: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SY1422 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6829]) ).
thf(6929,plain,
! [SV375: $i,SV472: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6830]) ).
thf(6930,plain,
! [SV472: $i,SV375: $i,SV115: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6831]) ).
thf(6931,plain,
! [SV118: $i,SV260: $i,SV378: $i,SV475: $i,SV541: $i,SV584: $i,SV602: $i,SV609: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV609 @ SV602 @ SV584 @ SV541 ) @ SV475 )
= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SV602 @ SV584 @ SV260 ) @ SV118 ) )
= $false )
| ( ( ! [SY1934: $i] :
( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SY1934 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SY1934 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6834]) ).
thf(6932,plain,
! [SV122: $i,SV264: $i,SV382: $i,SV479: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false )
| ( ( ~ ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6835]) ).
thf(6933,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ( ~ ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6836]) ).
thf(6934,plain,
! [SV546: $i,SV383: $i,SV123: $i,SV265: $i,SV480: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV546 @ SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6837]) ).
thf(6935,plain,
! [SV620: $i,SV125: $i,SV267: $i,SV385: $i] :
( ( ( ! [SY1996: $i] : ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SV620 ) @ SY1996 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( sK10_SY1717 @ SV125 @ SV267 @ SV385 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6838]) ).
thf(6936,plain,
! [SV125: $i,SV267: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ ( sK11_SY1720 @ SV125 @ SV267 @ SV385 ) ) @ ( sK13_SY1992 @ SV125 @ SV267 @ SV385 ) ) ) )
= $false )
| ( ( ! [SY1722: $i] : ( hBOOL @ ( hAPP @ SV385 @ SY1722 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6839]) ).
thf(6937,plain,
! [SV547: $i,SV603: $i,SV482: $i,SV129: $i,SV388: $i,SV271: $i,SV587: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6840]) ).
thf(6938,plain,
! [SV548: $i,SV484: $i,SV391: $i,SV588: $i,SV132: $i,SV274: $i] :
( ( ( SV274 != SV132 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(6939,plain,
! [SV133: $i,SV275: $i,SV392: $i,SV485: $i,SV549: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(6940,plain,
! [SV549: $i,SV133: $i,SV485: $i,SV275: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV392 ) @ ( hAPP @ SV275 @ SV485 ) ) @ SV133 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV549 ) @ SV485 ) @ ( hAPP @ ( c_Set_Ovimage @ SV549 @ SV392 @ SV275 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(6941,plain,
! [SV589: $i,SV550: $i,SV136: $i,SV278: $i,SV487: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV394 ) @ SV487 ) @ SV278 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV136 ) @ SV550 ) @ ( hAPP @ ( c_Set_Ovimage @ SV136 @ SV394 @ SV589 ) @ SV278 ) ) )
= $true )
| ( ( ( hAPP @ SV589 @ SV550 )
= SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6846]) ).
thf(6942,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ( ! [SY1491: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1491 ) @ SV138 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6849]) ).
thf(6943,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV280: $i] :
( ( ( ! [SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SY1492 ) @ SV138 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6850]) ).
thf(6944,plain,
! [SV551: $i,SV397: $i,SV139: $i,SV281: $i,SV490: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6851]) ).
thf(6945,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV140: $i,SV282: $i,SV552: $i] :
( ( ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
| ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6946,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6853]) ).
thf(6947,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6854]) ).
thf(6948,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( SV592 != SV554 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6856]) ).
thf(6949,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( ~ ( ( SV592 != SV554 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6857]) ).
thf(6950,plain,
! [SV36: $i,SV181: $i,SV308: $i,SV419: $i,SV504: $i,SV562: $i,SV595: $i,SV605: $i,SV610: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV610 @ SV605 @ SV595 @ SV562 ) @ SV504 )
= ( hAPP @ ( c_Fun_Ocomp @ SV419 @ SV605 @ SV595 @ SV308 ) @ SV181 ) )
= $false )
| ( ( ( hAPP @ SV562 @ ( hAPP @ SV504 @ SV36 ) )
= ( hAPP @ SV308 @ ( hAPP @ SV181 @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6858]) ).
thf(6951,plain,
! [SV37: $i,SV611: $i,SV182: $i,SV309: $i] :
( ( ( ! [SY1986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1986 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1986 ) ) )
= $false )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6859]) ).
thf(6952,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ! [SY1988: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1988 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SY1988 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6860]) ).
thf(6953,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK14_SY1989 @ SV182 @ SV37 @ SV309 ) ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ ( sK14_SY1989 @ SV182 @ SV37 @ SV309 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6861]) ).
thf(6954,plain,
! [SV38: $i,SV310: $i,SV505: $i,SV563: $i,SV183: $i,SV420: $i] :
( ( ( SV420 = SV183 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6862]) ).
thf(6955,plain,
! [SV183: $i,SV420: $i,SV505: $i,SV563: $i,SV38: $i,SV310: $i] :
( ( ( SV310 = SV38 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV420 ) @ SV310 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV563 @ SV505 ) @ SV183 ) @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6863]) ).
thf(6956,plain,
! [SV311: $i,SV39: $i,SV421: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6864]) ).
thf(6957,plain,
! [SV421: $i,SV39: $i,SV311: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV311 ) @ SV39 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV184 ) @ SV421 ) @ SV39 ) )
= $true )
| ( ( SV421 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6865]) ).
thf(6958,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) ) )
= $true )
| ( ( ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6866]) ).
thf(6959,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ( ~ ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6867]) ).
thf(6960,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ! [SY1904: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1904 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1904 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1904 ) @ SV49 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6868]) ).
thf(6961,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ! [SY1905: $i] :
~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SY1905 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SY1905 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SY1905 ) @ SV49 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6869]) ).
thf(6962,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
| ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6874]) ).
thf(6963,plain,
! [SV203: $i,SV59: $i,SV612: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ SV612 ) @ SV59 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV203 @ SV612 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6875]) ).
thf(6964,plain,
! [SV59: $i,SV203: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV327 ) @ ( sK5_SY1593 @ SV203 @ SV59 @ SV327 ) ) @ SV59 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ SV327 @ SV203 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6876]) ).
thf(6965,plain,
! [SV515: $i,SV330: $i,SV62: $i,SV206: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV206 ) @ SV62 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV62 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV436 @ SV330 ) @ SV206 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV515 @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6879]) ).
thf(6966,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(6967,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6881]) ).
thf(6968,plain,
! [SV598: $i,SV606: $i,SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV569: $i,SV516: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SV606 @ SV516 ) @ SV598 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV606 @ SV598 ) @ SV569 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6883]) ).
thf(6969,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6884]) ).
thf(6970,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6885]) ).
thf(6971,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV618: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) ) )
= $true )
| ( ( ! [SY1993: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1993 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SY1993 ) )
| ( SV618 = SY1993 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6886]) ).
thf(6972,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6887]) ).
thf(6973,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV441: $i] :
( ( ( ! [SY1994: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1994 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
!= ( hAPP @ SV213 @ SY1994 ) )
| ( ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 )
= SY1994 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6887]) ).
thf(6974,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6888]) ).
thf(6975,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6889]) ).
thf(6976,plain,
! [SV522: $i,SV222: $i,SV447: $i,SV345: $i,SV79: $i,SV572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6890]) ).
thf(6977,plain,
! [SV349: $i,SV84: $i,SV613: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ SV613 ) @ SV84 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV613 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6891]) ).
thf(6978,plain,
! [SV84: $i,SV349: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV227 @ ( sK6_SY1633 @ SV349 @ SV84 @ SV227 ) ) @ SV84 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV349 @ SV227 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6892]) ).
thf(6979,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( SV574 = SV524 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6894]) ).
thf(6980,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( SV574 != SV524 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6895]) ).
thf(6981,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
| ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6902]) ).
thf(6982,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SV614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6902]) ).
thf(6983,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6903]) ).
thf(6984,plain,
! [SV356: $i,SV93: $i,SV615: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV615 ) @ SV93 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV615 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6904]) ).
thf(6985,plain,
! [SV93: $i,SV356: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ ( sK8_SY1648 @ SV356 @ SV93 @ SV235 ) ) @ SV93 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV356 @ SV235 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6905]) ).
thf(6986,plain,
! [SV95: $i,SV237: $i,SV358: $i,SV456: $i,SV528: $i,SV577: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6907]) ).
thf(6987,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6908]) ).
thf(6988,plain,
! [SV239: $i,SV97: $i] :
( ( ( ! [SY940: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY940 ) @ SY940 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6909]) ).
thf(6989,plain,
! [SV239: $i,SV621: $i,SV97: $i] :
( ( ( ! [SY1997: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SY1997 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY1997 ) @ SY1997 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SY1997 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY1997 ) @ SY1997 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SY1997 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SY1997 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6910]) ).
thf(6990,plain,
! [SV239: $i,SV97: $i] :
( ( ( ! [SY943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY943 ) @ SY943 ) ) )
= $true )
| ( ( ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6911]) ).
thf(6991,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6914]) ).
thf(6992,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( ( SV458 != SV241 )
| ( SV361 != SV99 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6915]) ).
thf(6993,plain,
! [SV532: $i,SV461: $i,SV102: $i,SV364: $i,SV244: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true )
| ( ( ( hAPP @ SV461 @ SV244 )
= ( hAPP @ SV461 @ SV102 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6918]) ).
thf(6994,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i,SV616: $i,SV619: $i,SV622: $i] :
( ( ( ( hAPP @ SV622 @ ( hAPP @ SV619 @ SV616 ) )
!= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SV622 ) @ SV619 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6919]) ).
thf(6995,plain,
! [SV112: $i,SV254: $i,SV373: $i,SV470: $i,SV540: $i,SV583: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false )
| ( ( ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6923]) ).
thf(6996,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( ~ ( ( SV470 != SV254 )
| ( SV373 != SV112 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6924]) ).
thf(6997,plain,
! [SV471: $i,SV374: $i,SV114: $i,SV256: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ ( sK15_SY1421 @ SV374 @ SV471 @ SV114 @ SV256 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6927]) ).
thf(6998,plain,
! [SV374: $i,SV471: $i,SV623: $i,SV114: $i,SV256: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SV623 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6928]) ).
thf(6999,plain,
! [SV375: $i,SV472: $i,SV115: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6929]) ).
thf(7000,plain,
! [SV472: $i,SV375: $i,SV115: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV375 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV257 ) @ SV115 ) @ SV472 ) )
= $true )
| ( ( SV472 = SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6930]) ).
thf(7001,plain,
! [SV378: $i,SV584: $i,SV602: $i,SV609: $i,SV118: $i,SV260: $i,SV624: $i,SV475: $i,SV541: $i] :
( ( ( ( hAPP @ SV541 @ ( hAPP @ SV475 @ SV624 ) )
= ( hAPP @ SV260 @ ( hAPP @ SV118 @ SV624 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV609 @ SV602 @ SV584 @ SV541 ) @ SV475 )
= ( hAPP @ ( c_Fun_Ocomp @ SV378 @ SV602 @ SV584 @ SV260 ) @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6931]) ).
thf(7002,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ( ! [SY1863: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1863 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1863 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6932]) ).
thf(7003,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV382: $i] :
( ( ( ! [SY1864: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SY1864 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SY1864 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6933]) ).
thf(7004,plain,
! [SV546: $i,SV383: $i,SV123: $i,SV265: $i,SV480: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV265 ) @ SV123 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV123 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV480 @ SV383 ) @ SV265 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV546 @ SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6934]) ).
thf(7005,plain,
! [SV625: $i,SV620: $i,SV125: $i,SV267: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ SV620 ) @ SV625 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( sK10_SY1717 @ SV125 @ SV267 @ SV385 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6935]) ).
thf(7006,plain,
! [SV125: $i,SV267: $i,SV626: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ SV626 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV267 @ SV125 ) @ ( sK11_SY1720 @ SV125 @ SV267 @ SV385 ) ) @ ( sK13_SY1992 @ SV125 @ SV267 @ SV385 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6936]) ).
thf(7007,plain,
! [SV547: $i,SV603: $i,SV482: $i,SV129: $i,SV388: $i,SV271: $i,SV587: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
| ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6937]) ).
thf(7008,plain,
! [SV548: $i,SV484: $i,SV391: $i,SV588: $i,SV132: $i,SV274: $i] :
( ( ( SV274 = SV132 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6938]) ).
thf(7009,plain,
! [SV138: $i,SV489: $i,SV396: $i,SV280: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ ( sK16_SY1491 @ SV396 @ SV489 @ SV138 @ SV280 ) ) @ SV138 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6942]) ).
thf(7010,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV627: $i,SV280: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SV627 ) @ SV138 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6943]) ).
thf(7011,plain,
! [SV551: $i,SV397: $i,SV139: $i,SV281: $i,SV490: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV281 ) @ SV139 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV139 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV490 @ SV397 ) @ SV281 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV551 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6944]) ).
thf(7012,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV140: $i,SV282: $i,SV552: $i] :
( ( ( ~ ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6945]) ).
thf(7013,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV552: $i,SV140: $i,SV282: $i] :
( ( ( ~ ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6945]) ).
thf(7014,plain,
! [SV144: $i,SV286: $i,SV402: $i,SV492: $i,SV553: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6946]) ).
thf(7015,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6947]) ).
thf(7016,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( SV592 = SV554 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6948]) ).
thf(7017,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( SV592 != SV554 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6949]) ).
thf(7018,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) )
= $false )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6951]) ).
thf(7019,plain,
! [SV37: $i,SV182: $i,SV628: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV628 ) @ SV182 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SV628 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6952]) ).
thf(7020,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK14_SY1989 @ SV182 @ SV37 @ SV309 ) ) @ SV37 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6953]) ).
thf(7021,plain,
! [SV182: $i,SV37: $i,SV309: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ ( sK14_SY1989 @ SV182 @ SV37 @ SV309 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6953]) ).
thf(7022,plain,
! [SV44: $i,SV189: $i,SV315: $i,SV425: $i,SV509: $i,SV566: $i,SV596: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false )
| ( ( ~ ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6958]) ).
thf(7023,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ( ~ ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6959]) ).
thf(7024,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6960]) ).
thf(7025,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6961]) ).
thf(7026,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6962]) ).
thf(7027,plain,
! [SV323: $i,SV432: $i,SV55: $i,SV199: $i] :
( ( ( ~ ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[6962]) ).
thf(7028,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6966]) ).
thf(7029,plain,
! [SV437: $i,SV332: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6966]) ).
thf(7030,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6967]) ).
thf(7031,plain,
! [SV437: $i,SV332: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6967]) ).
thf(7032,plain,
! [SV598: $i,SV606: $i,SV67: $i,SV210: $i,SV334: $i,SV438: $i,SV569: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV516 @ SV569 ) @ SV438 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV334 @ SV210 @ SV67 @ SV606 @ SV516 ) @ SV598 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV606 @ SV598 ) @ SV569 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6968]) ).
thf(7033,plain,
! [SV68: $i,SV517: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6969]) ).
thf(7034,plain,
! [SV211: $i,SV517: $i,SV68: $i,SV439: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6969]) ).
thf(7035,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6970]) ).
thf(7036,plain,
! [SV337: $i,SV213: $i,SV70: $i,SV618: $i,SV441: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( ! [SY1993: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SY1993 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SY1993 ) )
| ( SV618 = SY1993 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6971]) ).
thf(7037,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6972]) ).
thf(7038,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) )
| ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
!= ( hAPP @ SV213 @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
| ( ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 )
= ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[6973]) ).
thf(7039,plain,
! [SV75: $i,SV521: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6974]) ).
thf(7040,plain,
! [SV218: $i,SV521: $i,SV75: $i,SV444: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6974]) ).
thf(7041,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6975]) ).
thf(7042,plain,
! [SV522: $i,SV222: $i,SV447: $i,SV345: $i,SV79: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6976]) ).
thf(7043,plain,
! [SV85: $i,SV228: $i,SV350: $i,SV449: $i,SV524: $i,SV574: $i] :
( ( ( SV574 = SV524 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV449 @ SV350 @ SV228 @ SV524 @ SV85 ) @ SV574 )
= ( hAPP @ SV228 @ SV574 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6980]) ).
thf(7044,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
| ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6981]) ).
thf(7045,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SV614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6982]) ).
thf(7046,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6983]) ).
thf(7047,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6986]) ).
thf(7048,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6987]) ).
thf(7049,plain,
! [SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK20_SY940 @ SV239 @ SV97 ) ) @ ( sK20_SY940 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[6988]) ).
thf(7050,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6989]) ).
thf(7051,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) ) )
= $true )
| ( ( ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6990]) ).
thf(7052,plain,
! [SV99: $i,SV361: $i,SV530: $i,SV241: $i,SV458: $i] :
( ( ( SV458 != SV241 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6991]) ).
thf(7053,plain,
! [SV241: $i,SV458: $i,SV530: $i,SV99: $i,SV361: $i] :
( ( ( SV361 != SV99 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6991]) ).
thf(7054,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( SV458 != SV241 )
= $true )
| ( ( SV361 != SV99 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6992]) ).
thf(7055,plain,
! [SV532: $i,SV461: $i,SV102: $i,SV364: $i,SV244: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
| ( SV244 = SV102 ) )
= $true )
| ( ( ( hAPP @ SV461 @ SV244 )
= ( hAPP @ SV461 @ SV102 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6993]) ).
thf(7056,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i,SV616: $i,SV619: $i,SV622: $i] :
( ( ( ( hAPP @ SV622 @ ( hAPP @ SV619 @ SV616 ) )
!= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SV622 ) @ SV619 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6994]) ).
thf(7057,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6995]) ).
thf(7058,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( ( SV470 != SV254 )
| ( SV373 != SV112 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6996]) ).
thf(7059,plain,
! [SV471: $i,SV374: $i,SV114: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ ( sK15_SY1421 @ SV374 @ SV471 @ SV114 @ SV256 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6997]) ).
thf(7060,plain,
! [SV374: $i,SV471: $i,SV623: $i,SV114: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV256 @ SV114 ) @ SV623 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV471 @ SV374 @ SV256 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6998]) ).
thf(7061,plain,
! [SV122: $i,SV479: $i,SV264: $i,SV545: $i,SV382: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7002]) ).
thf(7062,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV632: $i,SV382: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SV632 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7003]) ).
thf(7063,plain,
! [SV547: $i,SV603: $i,SV271: $i,SV482: $i,SV388: $i,SV129: $i,SV587: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7007]) ).
thf(7064,plain,
! [SV548: $i,SV484: $i,SV132: $i,SV391: $i,SV274: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true )
| ( ( SV274 = SV132 )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7008]) ).
thf(7065,plain,
! [SV138: $i,SV489: $i,SV396: $i,SV280: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ ( sK16_SY1491 @ SV396 @ SV489 @ SV138 @ SV280 ) ) @ SV138 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7009]) ).
thf(7066,plain,
! [SV396: $i,SV489: $i,SV138: $i,SV627: $i,SV280: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV280 @ SV627 ) @ SV138 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV396 @ SV280 ) @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7010]) ).
thf(7067,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV140: $i,SV282: $i,SV552: $i] :
( ( ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
| ( SV282 = SV140 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7012]) ).
thf(7068,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV552: $i,SV140: $i,SV282: $i] :
( ( ( ( SV282 != SV140 )
| ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7013]) ).
thf(7069,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7014]) ).
thf(7070,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7015]) ).
thf(7071,plain,
! [SV146: $i,SV288: $i,SV404: $i,SV494: $i,SV554: $i,SV592: $i] :
( ( ( SV592 = SV554 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV494 @ SV404 @ SV288 @ SV554 @ SV146 ) @ SV592 )
= ( hAPP @ SV288 @ SV592 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7017]) ).
thf(7072,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) ) )
= $false )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7018]) ).
thf(7073,plain,
! [SV182: $i,SV37: $i,SV611: $i,SV309: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) )
= $false )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7018]) ).
thf(7074,plain,
! [SV37: $i,SV182: $i,SV628: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV628 ) @ SV182 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SV628 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7019]) ).
thf(7075,plain,
! [SV37: $i,SV182: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK14_SY1989 @ SV182 @ SV37 @ SV309 ) ) @ SV37 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7020]) ).
thf(7076,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ( ! [SY1787: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1787 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1787 ) @ SV44 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7022]) ).
thf(7077,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV189: $i,SV425: $i] :
( ( ( ! [SY1788: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SY1788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SY1788 ) @ SV44 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7023]) ).
thf(7078,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7024]) ).
thf(7079,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7025]) ).
thf(7080,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
| ( SV199 = SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7026]) ).
thf(7081,plain,
! [SV323: $i,SV432: $i,SV55: $i,SV199: $i] :
( ( ( ( SV199 != SV55 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7027]) ).
thf(7082,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7028]) ).
thf(7083,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7030]) ).
thf(7084,plain,
! [SV68: $i,SV517: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7033]) ).
thf(7085,plain,
! [SV211: $i,SV517: $i,SV68: $i,SV439: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7034]) ).
thf(7086,plain,
! [SV517: $i,SV68: $i,SV439: $i,SV211: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7035]) ).
thf(7087,plain,
! [SV337: $i,SV618: $i,SV213: $i,SV70: $i,SV633: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV633 ) @ SV70 ) )
| ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SV633 ) )
| ( SV618 = SV633 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7036]) ).
thf(7088,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7038]) ).
thf(7089,plain,
! [SV441: $i,SV70: $i,SV337: $i,SV213: $i] :
( ( ( ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
!= ( hAPP @ SV213 @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
| ( ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 )
= ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7038]) ).
thf(7090,plain,
! [SV75: $i,SV521: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7039]) ).
thf(7091,plain,
! [SV218: $i,SV521: $i,SV75: $i,SV444: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7040]) ).
thf(7092,plain,
! [SV521: $i,SV75: $i,SV444: $i,SV218: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7041]) ).
thf(7093,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV79: $i,SV222: $i,SV447: $i] :
( ( ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
| ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7042]) ).
thf(7094,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) ) )
= $true )
| ( ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7044]) ).
thf(7095,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ SV607 )
!= ( hAPP @ SV92 @ SV614 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7045]) ).
thf(7096,plain,
! [SV234: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7046]) ).
thf(7097,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7046]) ).
thf(7098,plain,
! [SV95: $i,SV456: $i,SV577: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7047]) ).
thf(7099,plain,
! [SV237: $i,SV358: $i,SV577: $i,SV95: $i,SV528: $i,SV456: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7047]) ).
thf(7100,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7048]) ).
thf(7101,plain,
! [SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK20_SY940 @ SV239 @ SV97 ) ) @ ( sK20_SY940 @ SV239 @ SV97 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7049]) ).
thf(7102,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7050]) ).
thf(7103,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( ~ ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7051]) ).
thf(7104,plain,
! [SV99: $i,SV361: $i,SV530: $i,SV241: $i,SV458: $i] :
( ( ( SV458 = SV241 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7052]) ).
thf(7105,plain,
! [SV241: $i,SV458: $i,SV530: $i,SV99: $i,SV361: $i] :
( ( ( SV361 = SV99 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7053]) ).
thf(7106,plain,
! [SV530: $i,SV99: $i,SV361: $i,SV241: $i,SV458: $i] :
( ( ( SV458 = SV241 )
= $false )
| ( ( SV361 != SV99 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7054]) ).
thf(7107,plain,
! [SV532: $i,SV461: $i,SV244: $i,SV364: $i,SV102: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) ) )
= $true )
| ( ( SV244 = SV102 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
= $false )
| ( ( ( hAPP @ SV461 @ SV244 )
= ( hAPP @ SV461 @ SV102 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7055]) ).
thf(7108,plain,
! [SV103: $i,SV245: $i,SV365: $i,SV462: $i,SV533: $i,SV579: $i,SV600: $i,SV608: $i,SV616: $i,SV619: $i,SV622: $i] :
( ( ( ( hAPP @ SV622 @ ( hAPP @ SV619 @ SV616 ) )
= ( hAPP @ SV608 @ ( hAPP @ SV600 @ SV579 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV533 @ SV462 @ SV365 @ SV622 ) @ SV619 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV245 @ SV462 @ SV103 @ SV608 ) @ SV600 ) @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7056]) ).
thf(7109,plain,
! [SV112: $i,SV373: $i,SV540: $i,SV583: $i,SV254: $i,SV470: $i] :
( ( ( SV470 != SV254 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7057]) ).
thf(7110,plain,
! [SV254: $i,SV470: $i,SV540: $i,SV583: $i,SV112: $i,SV373: $i] :
( ( ( SV373 != SV112 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7057]) ).
thf(7111,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( SV470 != SV254 )
= $true )
| ( ( SV373 != SV112 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7058]) ).
thf(7112,plain,
! [SV122: $i,SV479: $i,SV264: $i,SV545: $i,SV382: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7061]) ).
thf(7113,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV632: $i,SV382: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SV632 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7062]) ).
thf(7114,plain,
! [SV547: $i,SV603: $i,SV271: $i,SV482: $i,SV388: $i,SV129: $i,SV587: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7063]) ).
thf(7115,plain,
! [SV548: $i,SV484: $i,SV132: $i,SV391: $i,SV274: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
| ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) ) )
= $true )
| ( ( SV274 = SV132 )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7064]) ).
thf(7116,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV140: $i,SV282: $i,SV552: $i] :
( ( ( ( hAPP @ SV552 @ SV282 )
!= ( hAPP @ SV552 @ SV140 ) )
= $true )
| ( ( SV282 = SV140 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7067]) ).
thf(7117,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV552: $i,SV140: $i,SV282: $i] :
( ( ( SV282 != SV140 )
= $true )
| ( ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7068]) ).
thf(7118,plain,
! [SV144: $i,SV402: $i,SV591: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7069]) ).
thf(7119,plain,
! [SV286: $i,SV492: $i,SV591: $i,SV144: $i,SV553: $i,SV402: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7069]) ).
thf(7120,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7070]) ).
thf(7121,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) )
= $true )
| ( ( ! [SY1987: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SY1987 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SY1987 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7072]) ).
thf(7122,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV634: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV634 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV634 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7073]) ).
thf(7123,plain,
! [SV37: $i,SV182: $i,SV628: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV628 ) @ SV182 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ ( sK4_SY1556 @ SV37 @ SV182 @ SV309 ) @ SV628 )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7074]) ).
thf(7124,plain,
! [SV315: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV189: $i,SV425: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) @ SV44 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[7076]) ).
thf(7125,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV635: $i,SV189: $i,SV425: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7077]) ).
thf(7126,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
!= SV49 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7078]) ).
thf(7127,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ~ ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7079]) ).
thf(7128,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV629: $i,SV427: $i,SV510: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7079]) ).
thf(7129,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( SV199 = SV55 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7080]) ).
thf(7130,plain,
! [SV323: $i,SV432: $i,SV55: $i,SV199: $i] :
( ( ( SV199 != SV55 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7081]) ).
thf(7131,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7082]) ).
thf(7132,plain,
! [SV332: $i,SV437: $i,SV65: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV208 ) @ SV65 ) @ SV332 ) )
= $true )
| ( ( SV437 = SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7083]) ).
thf(7133,plain,
! [SV517: $i,SV211: $i,SV68: $i,SV439: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV439 ) @ SV68 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV335 @ SV211 ) @ SV439 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV517 ) @ SV439 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV517 @ SV335 @ SV211 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7086]) ).
thf(7134,plain,
! [SV337: $i,SV618: $i,SV213: $i,SV70: $i,SV633: $i,SV441: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV633 ) @ SV70 ) ) )
= $true )
| ( ( ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SV633 ) )
| ( SV618 = SV633 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7087]) ).
thf(7135,plain,
! [SV70: $i,SV213: $i,SV337: $i,SV441: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) @ SV70 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7088]) ).
thf(7136,plain,
! [SV441: $i,SV70: $i,SV337: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
!= ( hAPP @ SV213 @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7089]) ).
thf(7137,plain,
! [SV441: $i,SV70: $i,SV213: $i,SV337: $i] :
( ( ( ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 )
= ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7089]) ).
thf(7138,plain,
! [SV521: $i,SV218: $i,SV75: $i,SV444: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV444 ) @ SV75 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV218 ) @ SV444 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV521 ) @ SV444 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV521 @ SV341 @ SV218 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7092]) ).
thf(7139,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV79: $i,SV222: $i,SV447: $i] :
( ( ( ~ ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7093]) ).
thf(7140,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV447: $i,SV79: $i,SV222: $i] :
( ( ( ~ ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7093]) ).
thf(7141,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
= $false )
| ( ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7094]) ).
thf(7142,plain,
! [SV234: $i,SV614: $i,SV607: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ SV607 )
= ( hAPP @ SV92 @ SV614 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV607 ) @ SV614 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7095]) ).
thf(7143,plain,
! [SV234: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7096]) ).
thf(7144,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
= $false )
| ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7097]) ).
thf(7145,plain,
! [SV95: $i,SV456: $i,SV577: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7098]) ).
thf(7146,plain,
! [SV237: $i,SV358: $i,SV577: $i,SV95: $i,SV528: $i,SV456: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7099]) ).
thf(7147,plain,
! [SV577: $i,SV95: $i,SV456: $i,SV528: $i,SV237: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7100]) ).
thf(7148,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7102]) ).
thf(7149,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7102]) ).
thf(7150,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( ! [SY944: $i,SY945: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY944 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY945 ) @ SY945 ) ) )
| ( ( hAPP @ SV97 @ SY944 )
!= ( hAPP @ SV97 @ SY945 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY944 ) @ SY945 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7103]) ).
thf(7151,plain,
! [SV530: $i,SV241: $i,SV458: $i,SV99: $i,SV361: $i] :
( ( ( SV361 = SV99 )
= $false )
| ( ( SV458 = SV241 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV458 ) @ SV361 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV530 ) @ SV241 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7106]) ).
thf(7152,plain,
! [SV532: $i,SV461: $i,SV244: $i,SV364: $i,SV102: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV102 ) @ SV364 ) )
= $false )
| ( ( SV244 = SV102 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV578 ) @ SV244 ) @ SV364 ) )
= $false )
| ( ( ( hAPP @ SV461 @ SV244 )
= ( hAPP @ SV461 @ SV102 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV578 @ SV532 @ SV461 @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7107]) ).
thf(7153,plain,
! [SV112: $i,SV373: $i,SV540: $i,SV583: $i,SV254: $i,SV470: $i] :
( ( ( SV470 = SV254 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7109]) ).
thf(7154,plain,
! [SV254: $i,SV470: $i,SV540: $i,SV583: $i,SV112: $i,SV373: $i] :
( ( ( SV373 = SV112 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7110]) ).
thf(7155,plain,
! [SV540: $i,SV583: $i,SV112: $i,SV373: $i,SV254: $i,SV470: $i] :
( ( ( SV470 = SV254 )
= $false )
| ( ( SV373 != SV112 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7111]) ).
thf(7156,plain,
! [SV122: $i,SV479: $i,SV264: $i,SV545: $i,SV382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7112]) ).
thf(7157,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV632: $i,SV382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) )
| ( SV479
!= ( hAPP @ SV264 @ SV632 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7113]) ).
thf(7158,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV129: $i,SV271: $i,SV482: $i] :
( ( ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
| ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7114]) ).
thf(7159,plain,
! [SV548: $i,SV274: $i,SV484: $i,SV391: $i,SV132: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) ) )
= $true )
| ( ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
= $false )
| ( ( SV274 = SV132 )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7115]) ).
thf(7160,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV140: $i,SV282: $i,SV552: $i] :
( ( ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) )
= $false )
| ( ( SV282 = SV140 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7116]) ).
thf(7161,plain,
! [SV398: $i,SV491: $i,SV590: $i,SV604: $i,SV552: $i,SV140: $i,SV282: $i] :
( ( ( SV282 = SV140 )
= $false )
| ( ( ( hAPP @ SV552 @ SV282 )
= ( hAPP @ SV552 @ SV140 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV604 @ SV590 @ SV552 @ SV491 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7117]) ).
thf(7162,plain,
! [SV144: $i,SV402: $i,SV591: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7118]) ).
thf(7163,plain,
! [SV286: $i,SV492: $i,SV591: $i,SV144: $i,SV553: $i,SV402: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7119]) ).
thf(7164,plain,
! [SV591: $i,SV144: $i,SV402: $i,SV553: $i,SV286: $i,SV492: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7120]) ).
thf(7165,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV636: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV636 ) @ SV37 ) )
| ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV636 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7121]) ).
thf(7166,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV634: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV634 ) @ SV37 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV634 )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7122]) ).
thf(7167,plain,
! [SV315: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) @ SV44 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7124]) ).
thf(7168,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV635: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7125]) ).
thf(7169,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
!= SV49 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7126]) ).
thf(7170,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7127]) ).
thf(7171,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV629: $i,SV427: $i,SV510: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7128]) ).
thf(7172,plain,
! [SV55: $i,SV199: $i,SV323: $i,SV432: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
= $false )
| ( ( SV199 = SV55 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7129]) ).
thf(7173,plain,
! [SV323: $i,SV432: $i,SV55: $i,SV199: $i] :
( ( ( SV199 = SV55 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV55 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV432 ) @ SV323 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7130]) ).
thf(7174,plain,
! [SV337: $i,SV618: $i,SV213: $i,SV70: $i,SV633: $i,SV441: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV633 ) @ SV70 ) )
= $false )
| ( ( ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SV633 ) )
| ( SV618 = SV633 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7134]) ).
thf(7175,plain,
! [SV441: $i,SV70: $i,SV337: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ ( sK12_SY1808 @ SV337 @ SV213 @ SV70 @ SV441 ) )
= ( hAPP @ SV213 @ ( sK19_SY1994 @ SV337 @ SV213 @ SV70 @ SV441 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7136]) ).
thf(7176,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV79: $i,SV222: $i,SV447: $i] :
( ( ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
| ( SV222 = SV79 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7139]) ).
thf(7177,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV447: $i,SV79: $i,SV222: $i] :
( ( ( ( SV222 != SV79 )
| ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7140]) ).
thf(7178,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7143]) ).
thf(7179,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7144]) ).
thf(7180,plain,
! [SV234: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7144]) ).
thf(7181,plain,
! [SV577: $i,SV237: $i,SV358: $i,SV95: $i,SV528: $i,SV456: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV456 @ SV528 ) @ SV95 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV237 ) @ SV528 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV577 ) @ SV528 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV577 @ SV456 @ SV358 @ SV237 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7147]) ).
thf(7182,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7148]) ).
thf(7183,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7149]) ).
thf(7184,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ! [SY1998: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ SY1998 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY1998 ) @ SY1998 ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ SY1998 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SY1998 ) @ SY1998 ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ SY1998 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ SY1998 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7150]) ).
thf(7185,plain,
! [SV540: $i,SV583: $i,SV254: $i,SV470: $i,SV112: $i,SV373: $i] :
( ( ( SV373 = SV112 )
= $false )
| ( ( SV470 = SV254 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV470 ) @ SV373 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV583 @ SV540 ) @ SV254 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7155]) ).
thf(7186,plain,
! [SV122: $i,SV479: $i,SV264: $i,SV545: $i,SV382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) @ SV122 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7156]) ).
thf(7187,plain,
! [SV382: $i,SV122: $i,SV545: $i,SV264: $i,SV479: $i] :
( ( ( SV479
!= ( hAPP @ SV264 @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7156]) ).
thf(7188,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV632: $i,SV382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) ) )
= $true )
| ( ( SV479
!= ( hAPP @ SV264 @ SV632 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7157]) ).
thf(7189,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV129: $i,SV271: $i,SV482: $i] :
( ( ( ~ ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7158]) ).
thf(7190,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV482: $i,SV129: $i,SV271: $i] :
( ( ( ~ ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7158]) ).
thf(7191,plain,
! [SV548: $i,SV274: $i,SV484: $i,SV391: $i,SV132: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
= $false )
| ( ( ( hAPP @ SV484 @ SV274 )
!= ( hAPP @ SV484 @ SV132 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
= $false )
| ( ( SV274 = SV132 )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7159]) ).
thf(7192,plain,
! [SV591: $i,SV286: $i,SV492: $i,SV144: $i,SV553: $i,SV402: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV402 @ SV553 ) @ SV144 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV492 @ SV286 ) @ SV553 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV591 ) @ SV553 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV591 @ SV492 @ SV402 @ SV286 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7164]) ).
thf(7193,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV636: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV636 ) @ SV37 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV636 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7165]) ).
thf(7194,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV634: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV634 ) @ SV37 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV634 )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7166]) ).
thf(7195,plain,
! [SV315: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) @ SV44 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7167]) ).
thf(7196,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV635: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7168]) ).
thf(7197,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7169]) ).
thf(7198,plain,
! [SV427: $i,SV193: $i,SV317: $i,SV49: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
!= SV49 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7169]) ).
thf(7199,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( SV427
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7170]) ).
thf(7200,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV629: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
!= SV193 )
= $true )
| ( ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7171]) ).
thf(7201,plain,
! [SV337: $i,SV70: $i,SV441: $i,SV633: $i,SV618: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ SV618 )
!= ( hAPP @ SV213 @ SV633 ) )
= $true )
| ( ( SV618 = SV633 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV633 ) @ SV70 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7174]) ).
thf(7202,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV79: $i,SV222: $i,SV447: $i] :
( ( ( ( hAPP @ SV447 @ SV222 )
!= ( hAPP @ SV447 @ SV79 ) )
= $true )
| ( ( SV222 = SV79 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7176]) ).
thf(7203,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV447: $i,SV79: $i,SV222: $i] :
( ( ( SV222 != SV79 )
= $true )
| ( ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7177]) ).
thf(7204,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
!= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7178]) ).
thf(7205,plain,
! [SV234: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7178]) ).
thf(7206,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7179]) ).
thf(7207,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7182]) ).
thf(7208,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7183]) ).
thf(7209,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7184]) ).
thf(7210,plain,
! [SV122: $i,SV479: $i,SV264: $i,SV545: $i,SV382: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) @ SV122 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7186]) ).
thf(7211,plain,
! [SV382: $i,SV122: $i,SV545: $i,SV264: $i,SV479: $i] :
( ( ( SV479
= ( hAPP @ SV264 @ ( sK21_SY1863 @ SV545 @ SV264 @ SV479 @ SV122 @ SV382 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7187]) ).
thf(7212,plain,
! [SV545: $i,SV264: $i,SV479: $i,SV122: $i,SV632: $i,SV382: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) )
= $false )
| ( ( SV479
!= ( hAPP @ SV264 @ SV632 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7188]) ).
thf(7213,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV129: $i,SV271: $i,SV482: $i] :
( ( ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
| ( SV271 = SV129 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7189]) ).
thf(7214,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV482: $i,SV129: $i,SV271: $i] :
( ( ( ( SV271 != SV129 )
| ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7190]) ).
thf(7215,plain,
! [SV548: $i,SV391: $i,SV588: $i,SV132: $i,SV274: $i,SV484: $i] :
( ( ( ( hAPP @ SV484 @ SV274 )
= ( hAPP @ SV484 @ SV132 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV132 ) @ SV391 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV274 ) @ SV391 ) )
= $false )
| ( ( SV274 = SV132 )
= $true )
| ( ( c_Fun_Oinj__on @ SV588 @ SV548 @ SV484 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7191]) ).
thf(7216,plain,
! [SV182: $i,SV611: $i,SV37: $i,SV636: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ SV636 ) @ SV37 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV309 @ SV611 @ SV636 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_Hoare__Mirabelle_Otriple @ SV309 ) ) @ ( sK17_SY1986 @ SV37 @ SV611 @ SV182 @ SV309 ) ) @ SV182 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV309 @ SV182 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7193]) ).
thf(7217,plain,
! [SV315: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7195]) ).
thf(7218,plain,
! [SV425: $i,SV189: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV315: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) @ SV44 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7195]) ).
thf(7219,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV635: $i,SV189: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7196]) ).
thf(7220,plain,
! [SV317: $i,SV49: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7197]) ).
thf(7221,plain,
! [SV427: $i,SV193: $i,SV317: $i,SV49: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7198]) ).
thf(7222,plain,
! [SV49: $i,SV317: $i,SV629: $i,SV193: $i,SV510: $i,SV427: $i] :
( ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
!= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7199]) ).
thf(7223,plain,
! [SV49: $i,SV317: $i,SV193: $i,SV629: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
= SV193 )
= $false )
| ( ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7200]) ).
thf(7224,plain,
! [SV337: $i,SV70: $i,SV441: $i,SV633: $i,SV618: $i,SV213: $i] :
( ( ( ( hAPP @ SV213 @ SV618 )
= ( hAPP @ SV213 @ SV633 ) )
= $false )
| ( ( SV618 = SV633 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV633 ) @ SV70 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV441 ) @ SV618 ) @ SV70 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV441 @ SV337 @ SV213 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7201]) ).
thf(7225,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV79: $i,SV222: $i,SV447: $i] :
( ( ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) )
= $false )
| ( ( SV222 = SV79 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7202]) ).
thf(7226,plain,
! [SV522: $i,SV345: $i,SV572: $i,SV447: $i,SV79: $i,SV222: $i] :
( ( ( SV222 = SV79 )
= $false )
| ( ( ( hAPP @ SV447 @ SV222 )
= ( hAPP @ SV447 @ SV79 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV79 ) @ SV345 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV572 ) @ SV222 ) @ SV345 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV572 @ SV522 @ SV447 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7203]) ).
thf(7227,plain,
! [SV234: $i,SV92: $i] :
( ( ( ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) )
= ( hAPP @ SV92 @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ ( sK3_SY923 @ SV234 @ SV92 ) ) @ ( sK7_SY1981 @ SV234 @ SV92 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV234 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7204]) ).
thf(7228,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7207]) ).
thf(7229,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7208]) ).
thf(7230,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7209]) ).
thf(7231,plain,
! [SV545: $i,SV122: $i,SV382: $i,SV632: $i,SV264: $i,SV479: $i] :
( ( ( SV479
= ( hAPP @ SV264 @ SV632 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV382 ) @ SV632 ) @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV545 ) @ SV479 ) @ ( hAPP @ ( c_Set_Oimage @ SV382 @ SV545 @ SV264 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7212]) ).
thf(7232,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV129: $i,SV271: $i,SV482: $i] :
( ( ( ( hAPP @ SV482 @ SV271 )
!= ( hAPP @ SV482 @ SV129 ) )
= $true )
| ( ( SV271 = SV129 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7213]) ).
thf(7233,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV482: $i,SV129: $i,SV271: $i] :
( ( ( SV271 != SV129 )
= $true )
| ( ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7214]) ).
thf(7234,plain,
! [SV315: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV189: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7217]) ).
thf(7235,plain,
! [SV425: $i,SV189: $i,SV44: $i,SV596: $i,SV566: $i,SV509: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ ( sK22_SY1787 @ SV509 @ SV566 @ SV596 @ SV44 @ SV315 @ SV189 @ SV425 ) ) @ SV44 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7218]) ).
thf(7236,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV44: $i,SV315: $i,SV635: $i,SV189: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7219]) ).
thf(7237,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) )
= $false )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7220]) ).
thf(7238,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
| ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7221]) ).
thf(7239,plain,
! [SV193: $i,SV427: $i,SV49: $i,SV317: $i,SV629: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV317 )
= SV49 )
= $false )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV629 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7222]) ).
thf(7240,plain,
! [SV193: $i,SV427: $i,SV49: $i,SV629: $i,SV510: $i,SV317: $i] :
( ( ( SV317
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV629 ) @ SV49 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV629 )
= SV193 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7223]) ).
thf(7241,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7228]) ).
thf(7242,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
| ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7229]) ).
thf(7243,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7230]) ).
thf(7244,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV129: $i,SV271: $i,SV482: $i] :
( ( ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) )
= $false )
| ( ( SV271 = SV129 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7232]) ).
thf(7245,plain,
! [SV547: $i,SV603: $i,SV388: $i,SV587: $i,SV482: $i,SV129: $i,SV271: $i] :
( ( ( SV271 = SV129 )
= $false )
| ( ( ( hAPP @ SV482 @ SV271 )
= ( hAPP @ SV482 @ SV129 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV129 ) @ SV388 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV587 ) @ SV271 ) @ SV388 ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV603 @ SV587 @ SV547 @ SV482 @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7233]) ).
thf(7246,plain,
! [SV509: $i,SV566: $i,SV596: $i,SV189: $i,SV425: $i,SV44: $i,SV635: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV315 @ SV635 ) @ SV44 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV425 @ SV189 ) @ SV635 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV596 @ SV566 @ SV509 @ SV425 @ SV315 ) @ SV189 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7236]) ).
thf(7247,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
= $false )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7237]) ).
thf(7248,plain,
! [SV427: $i,SV193: $i,SV49: $i,SV510: $i,SV317: $i] :
( ( ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) )
= $false )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7237]) ).
thf(7249,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
!= SV193 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7238]) ).
thf(7250,plain,
! [SV427: $i,SV193: $i,SV49: $i,SV510: $i,SV317: $i] :
( ( ( SV317
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7238]) ).
thf(7251,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7241]) ).
thf(7252,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7241]) ).
thf(7253,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7242]) ).
thf(7254,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7243]) ).
thf(7255,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
= SV193 )
= $true )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7247]) ).
thf(7256,plain,
! [SV427: $i,SV193: $i,SV49: $i,SV510: $i,SV317: $i] :
( ( ( SV317
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) )
= $true )
| ( ( SV427
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7248]) ).
thf(7257,plain,
! [SV193: $i,SV317: $i,SV49: $i,SV427: $i,SV510: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) )
= SV193 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7249]) ).
thf(7258,plain,
! [SV427: $i,SV193: $i,SV49: $i,SV510: $i,SV317: $i] :
( ( ( SV317
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV49 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ ( sK18_SY1904 @ SV49 @ SV317 @ SV193 @ SV510 @ SV427 ) ) @ SV317 )
= SV49 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV427 ) @ SV317 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV510 ) @ SV193 ) @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7250]) ).
thf(7259,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7251]) ).
thf(7260,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ SV621 )
= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7252]) ).
thf(7261,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7253]) ).
thf(7262,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7254]) ).
thf(7263,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7254]) ).
thf(7264,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7259]) ).
thf(7265,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7261]) ).
thf(7266,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7262]) ).
thf(7267,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7263]) ).
thf(7268,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7264]) ).
thf(7269,plain,
! [SV239: $i,SV621: $i,SV630: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7264]) ).
thf(7270,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7265]) ).
thf(7271,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7266]) ).
thf(7272,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7267]) ).
thf(7273,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7268]) ).
thf(7274,plain,
! [SV239: $i,SV621: $i,SV630: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7269]) ).
thf(7275,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7270]) ).
thf(7276,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7271]) ).
thf(7277,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7271]) ).
thf(7278,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7272]) ).
thf(7279,plain,
! [SV239: $i,SV621: $i,SV630: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
= $false )
| ( ( ( hAPP @ SV97 @ SV621 )
!= ( hAPP @ SV97 @ SV630 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7275]) ).
thf(7280,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7276]) ).
thf(7281,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7278]) ).
thf(7282,plain,
! [SV239: $i,SV630: $i,SV621: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ SV621 )
= ( hAPP @ SV97 @ SV630 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV630 ) @ SV630 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV621 ) @ SV630 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7279]) ).
thf(7283,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7280]) ).
thf(7284,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7281]) ).
thf(7285,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7283]) ).
thf(7286,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7283]) ).
thf(7287,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $true )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7284]) ).
thf(7288,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7285]) ).
thf(7289,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7286]) ).
thf(7290,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7287]) ).
thf(7291,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7288]) ).
thf(7292,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7290]) ).
thf(7293,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7291]) ).
thf(7294,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7291]) ).
thf(7295,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7292]) ).
thf(7296,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7293]) ).
thf(7297,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7294]) ).
thf(7298,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7295]) ).
thf(7299,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7295]) ).
thf(7300,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7298]) ).
thf(7301,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
| ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7300]) ).
thf(7302,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7301]) ).
thf(7303,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
!= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7301]) ).
thf(7304,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7302]) ).
thf(7305,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7303]) ).
thf(7306,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7304]) ).
thf(7307,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7306]) ).
thf(7308,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7306]) ).
thf(7309,plain,
! [SV631: $i,SV239: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7307]) ).
thf(7310,plain,
! [SV239: $i,SV631: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) ) )
= $false )
| ( ( ( hAPP @ SV97 @ ( sK23_SY944 @ SV239 @ SV631 @ SV97 ) )
= ( hAPP @ SV97 @ ( sK24_SY1998 @ SV631 @ SV239 @ SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV97 @ SV631 ) @ SV631 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV239 @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7308]) ).
thf(7311,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5520,7310,7309,7305,7299,7297,7296,7289,7282,7277,7274,7273,7260,7258,7257,7256,7255,7246,7245,7244,7240,7239,7235,7234,7231,7227,7226,7225,7224,7216,7215,7211,7210,7206,7205,7194,7192,7185,7181,7180,7175,7173,7172,7163,7162,7161,7160,7154,7153,7152,7151,7146,7145,7142,7141,7138,7137,7135,7133,7132,7131,7123,7108,7105,7104,7101,7091,7090,7085,7084,7075,7071,7066,7065,7060,7059,7043,7037,7032,7031,7029,7021,7016,7011,7006,7005,7004,7001,7000,6999,6985,6984,6979,6978,6977,6965,6964,6963,6957,6956,6955,6954,6950,6941,6940,6939,6926,6925,6922,6921,6920,6917,6916,6913,6912,6906,6901,6900,6899,6898,6897,6896,6893,6882,6878,6877,6873,6872,6871,6870,6855,6848,6847,6842,6841,6833,6832,6820,6817,6816,6798,6797,6795,6787,6786,6783,6780,6765,6749,6748,6740,6733,6732,6731,6730,6727,6723,6719,6709,6706,6692,6691,6688,6666,6665,6653,6642,6641,6634,6633,6631,6610,6600,6599,6588,6587,6584,6583,6547,6546,6540,6539,6538,6521,6516,6512,6511,6510,6509,6507,6499,6498,6413,6383,6371,6370,6369,6368,6367,6366,6364,6360,6356,6355,6286,6283,6268,6262,6261,6256,6237,6232,6227,6212,6208,6157,6115,6107,6105,6104,6103,6102,6100,6099,6098,6094,6092,6091,6085,6084,6026,5970,5953,5946,5944,5858,5841,5814,5813,5804,5803,5802,5683,5671,5664,5532]) ).
thf(7312,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[7311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW298+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n005.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 16:53:45 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.06/21.42 .....................................
% 106.06/21.42
% 106.06/21.42 No.of.Axioms: 150
% 106.06/21.42
% 106.06/21.42 Length.of.Defs: 0
% 106.06/21.42
% 106.06/21.42 Contains.Choice.Funs: false
% 106.06/21.42 .................................................................................................................................................................
% 106.06/21.42
% 106.06/21.42 ********************************
% 106.06/21.42 * All subproblems solved! *
% 106.06/21.42 ********************************
% 106.06/21.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:151,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:291,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7311,loop_count:0,foatp_calls:1,translation:fof_full)
% 106.06/21.42
% 106.06/21.42 %**** Beginning of derivation protocol ****
% 106.06/21.42 % SZS output start CNFRefutation
% See solution above
% 106.06/21.45
% 106.06/21.45 %**** End of derivation protocol ****
% 106.06/21.45 %**** no. of clauses in derivation: 2238 ****
% 106.06/21.45 %**** clause counter: 7311 ****
% 106.06/21.45
% 106.06/21.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:151,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:291,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7311,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------