%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW365+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 11:01:22 AM UTC 2026
% Result : Theorem 177.55s 35.94s
% Output : CNFRefutation 177.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 345
% Syntax : Number of formulae : 3888 (2457 unt; 0 typ; 0 def)
% Number of atoms : 20933 (8900 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 77480 (7225 ~;5542 |; 63 &;63732 @)
% ( 189 <=>; 729 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 552 ( 549 usr; 53 con; 0-7 aty)
% Number of variables : 15058 ( 0 ^;15022 !; 36 ?;15058 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Big__Operators_Ocomm__monoid__add__class_Osetsum,type,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum: $i > $i > $i ).
thf(tp_c_Big__Operators_Ocomm__monoid__big,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod,type,
c_Big__Operators_Ocomm__monoid__mult__class_Osetprod: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OInf__fin,type,
c_Big__Operators_Olattice_OInf__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice_OSup__fin,type,
c_Big__Operators_Olattice_OSup__fin: $i > $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OInf__fin,type,
c_Big__Operators_Olattice__class_OInf__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olattice__class_OSup__fin,type,
c_Big__Operators_Olattice__class_OSup__fin: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMax,type,
c_Big__Operators_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Big__Operators_Olinorder__class_OMin,type,
c_Big__Operators_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Big__Operators_Osemilattice__big,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i ).
thf(tp_c_COMBI,type,
c_COMBI: $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_OSuc__code__numeral,type,
c_Code__Numeral_OSuc__code__numeral: $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__case,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case: $i > $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Code__Numeral_Ocode__numeral_Ocode__numeral__size,type,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size: $i > $i ).
thf(tp_c_Code__Numeral_Odiv__mod__code__numeral,type,
c_Code__Numeral_Odiv__mod__code__numeral: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oint__of,type,
c_Code__Numeral_Oint__of: $i ).
thf(tp_c_Code__Numeral_Onat__of,type,
c_Code__Numeral_Onat__of: $i ).
thf(tp_c_Code__Numeral_Onat__of__aux,type,
c_Code__Numeral_Onat__of__aux: $i > $i > $i ).
thf(tp_c_Code__Numeral_Oof__nat,type,
c_Code__Numeral_Oof__nat: $i ).
thf(tp_c_Code__Numeral_Osubtract__code__numeral,type,
c_Code__Numeral_Osubtract__code__numeral: $i ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i > $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(tp_c_DSequence_Oempty,type,
c_DSequence_Oempty: $i > $i ).
thf(tp_c_DSequence_Osingle,type,
c_DSequence_Osingle: $i > $i ).
thf(tp_c_DSequence_Ounion,type,
c_DSequence_Ounion: $i > $i ).
thf(tp_c_Divides_Oadjust,type,
c_Divides_Oadjust: $i > $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int__rel,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat__rel,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg__rel,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(tp_c_Divides_OnegateSnd,type,
c_Divides_OnegateSnd: $i ).
thf(tp_c_Divides_Opdivmod,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg__rel,type,
c_Divides_OposDivAlg__rel: $i ).
thf(tp_c_Enum_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_Obij__betw,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
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_If,type,
c_If: $i > $i ).
thf(tp_c_Int_OAbs__Integ,type,
c_Int_OAbs__Integ: $i ).
thf(tp_c_Int_OBit0,type,
c_Int_OBit0: $i > $i ).
thf(tp_c_Int_OBit1,type,
c_Int_OBit1: $i > $i ).
thf(tp_c_Int_OInteg,type,
c_Int_OInteg: $i ).
thf(tp_c_Int_OMin,type,
c_Int_OMin: $i ).
thf(tp_c_Int_OPls,type,
c_Int_OPls: $i ).
thf(tp_c_Int_ORep__Integ,type,
c_Int_ORep__Integ: $i ).
thf(tp_c_Int_Oint__ge__less__than,type,
c_Int_Oint__ge__less__than: $i > $i ).
thf(tp_c_Int_Oint__ge__less__than2,type,
c_Int_Oint__ge__less__than2: $i > $i ).
thf(tp_c_Int_Ointrel,type,
c_Int_Ointrel: $i ).
thf(tp_c_Int_Oiszero,type,
c_Int_Oiszero: $i > $i > $o ).
thf(tp_c_Int_Onat,type,
c_Int_Onat: $i ).
thf(tp_c_Int_Onat__aux,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i ).
thf(tp_c_Int_Opred,type,
c_Int_Opred: $i > $i ).
thf(tp_c_Int_Oring__1__class_OInts,type,
c_Int_Oring__1__class_OInts: $i > $i ).
thf(tp_c_Int_Oring__1__class_Oof__int,type,
c_Int_Oring__1__class_Oof__int: $i > $i ).
thf(tp_c_Int_Osucc,type,
c_Int_Osucc: $i > $i ).
thf(tp_c_Lattices_Osemilattice__inf__class_Oinf,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(tp_c_Lattices_Osemilattice__sup__class_Osup,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(tp_c_Lazy__Sequence_Oanamorph,type,
c_Lazy__Sequence_Oanamorph: $i > $i > $i > $i ).
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_Oflat,type,
c_Lazy__Sequence_Oflat: $i > $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__rec,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec: $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_Omap,type,
c_Lazy__Sequence_Omap: $i > $i > $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_Oall__interval__nat,type,
c_List_Oall__interval__nat: $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__map,type,
c_New__DSequence_Opos__map: $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__not__seq,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(tp_c_New__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_Option_Othe,type,
c_Option_Othe: $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_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_Ostrict__mono,type,
c_Orderings_Oorder_Ostrict__mono: $i > $i > $i > $i > $o ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Partial__Function_Oflat__lub,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(tp_c_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_Quotient_OBabs,type,
c_Quotient_OBabs: $i > $i > $i > $i > $i ).
thf(tp_c_Quotient_ORespects,type,
c_Quotient_ORespects: $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_SY2454,type,
sK10_SY2454: $i > $i > $i ).
thf(tp_sK11_SY2834,type,
sK11_SY2834: $i > $i > $i > $i ).
thf(tp_sK12_SY3079,type,
sK12_SY3079: $i > $i > $i > $i ).
thf(tp_sK13_SY2244,type,
sK13_SY2244: $i > $i > $i ).
thf(tp_sK14_SY2349,type,
sK14_SY2349: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY2524,type,
sK15_SY2524: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY3016,type,
sK16_SY3016: $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_SY2937,type,
sK17_SY2937: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY3033,type,
sK18_SY3033: $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY1910,type,
sK19_SY1910: $i > $i > $i ).
thf(tp_sK1_SY2421,type,
sK1_SY2421: $i > $i > $i ).
thf(tp_sK20_SY2877,type,
sK20_SY2877: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK21_SY1914,type,
sK21_SY1914: $i > $i > $i > $i ).
thf(tp_sK22_SY3085,type,
sK22_SY3085: $i > $i > $i > $i ).
thf(tp_sK2_SY1378,type,
sK2_SY1378: $i > $i > $i ).
thf(tp_sK3_SY1456,type,
sK3_SY1456: $i > $i > $i ).
thf(tp_sK4_SY1809,type,
sK4_SY1809: $i > $i > $i ).
thf(tp_sK5_SY2494,type,
sK5_SY2494: $i > $i > $i ).
thf(tp_sK6_SY3073,type,
sK6_SY3073: $i > $i > $i ).
thf(tp_sK7_SY2628,type,
sK7_SY2628: $i > $i > $i > $i ).
thf(tp_sK8_SY2631,type,
sK8_SY2631: $i > $i > $i > $i ).
thf(tp_sK9_SY2674,type,
sK9_SY2674: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Code__Evaluation_Oterm,type,
tc_Code__Evaluation_Oterm: $i ).
thf(tp_tc_Code__Numeral_Ocode__numeral,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_tc_Com_Opname,type,
tc_Com_Opname: $i ).
thf(tp_tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lazy__Sequence_Olazy__sequence,type,
tc_Lazy__Sequence_Olazy__sequence: $i > $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
thf(tp_tc_Nitpick_Opair__box,type,
tc_Nitpick_Opair__box: $i > $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_tc_sum,type,
tc_sum: $i > $i > $i ).
thf(tp_v_G,type,
v_G: $i ).
thf(tp_v_P,type,
v_P: $i > $i > $o ).
thf(tp_v_U,type,
v_U: $i ).
thf(tp_v_mgt,type,
v_mgt: $i > $i ).
thf(tp_v_mgt__call,type,
v_mgt__call: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(tp_v_pn,type,
v_pn: $i ).
thf(tp_v_wt,type,
v_wt: $i > $o ).
thf(1,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(2,axiom,
! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(3,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(4,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(5,axiom,
! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(6,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(7,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(8,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(9,axiom,
! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(10,axiom,
! [V_Pa_2: $i] :
( ~ ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(11,axiom,
! [V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) )
| ~ ( hBOOL @ V_Pa_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(12,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(13,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(16,axiom,
! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Q_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19,axiom,
! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(20,axiom,
! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(82,axiom,
class_Nat_Osize @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
thf(83,axiom,
class_Enum_Oenum @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
thf(84,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(85,axiom,
class_Groups_Ouminus @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
thf(86,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(87,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(88,axiom,
class_Orderings_Otop @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
thf(89,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(90,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(91,axiom,
class_Finite__Set_Ofinite @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
thf(92,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(93,axiom,
class_Lattices_Oboolean__algebra @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
thf(94,axiom,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
thf(95,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(96,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(97,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(98,axiom,
class_Lattices_Obounded__lattice__top @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
thf(99,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
thf(222,axiom,
! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).
thf(223,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(224,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(225,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(226,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(227,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
thf(228,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(229,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(230,axiom,
! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
thf(231,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(232,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(233,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
thf(238,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(239,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
thf(240,axiom,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
thf(379,axiom,
! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Respects__def) ).
thf(402,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ V_A_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).
thf(403,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).
thf(465,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__transp) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__symp) ).
thf(467,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/sandbox/benchmark/theBenchmark.p',fact_part__equivp__def) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',fact_sympE) ).
thf(506,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/sandbox/benchmark/theBenchmark.p',fact_transpE) ).
thf(525,axiom,
! [V_Pa_2: $i,T_b: $i] :
~ ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__empty) ).
thf(623,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/sandbox/benchmark/theBenchmark.p',fact_conversep__iff) ).
thf(624,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/sandbox/benchmark/theBenchmark.p',fact_conversep_Oequations) ).
thf(625,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/sandbox/benchmark/theBenchmark.p',fact_conversep_Ointros) ).
thf(626,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/sandbox/benchmark/theBenchmark.p',fact_conversepD) ).
thf(783,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(784,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(785,axiom,
! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(1039,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(1040,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(1064,axiom,
! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(1285,axiom,
! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1286,axiom,
! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(1287,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(1288,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(1289,axiom,
! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(1393,axiom,
! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(1394,axiom,
! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(1510,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1511,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(1512,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1567,axiom,
! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(1576,axiom,
! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1617,axiom,
! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1731,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/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1732,axiom,
! [T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).
thf(1733,axiom,
! [T_b: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1734,axiom,
! [T_b: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1737,axiom,
! [T_b: $i,V_c_2: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ V_c_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1759,axiom,
! [V_Pa_2: $i,T_b: $i,B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).
thf(1765,axiom,
! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(1778,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/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1779,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/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1833,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/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1834,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/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1835,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/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1836,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/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1862,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1882,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/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1883,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1884,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
thf(1946,axiom,
! [V_Pa_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
thf(1947,axiom,
! [V_Pa_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
thf(1949,axiom,
! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(2074,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).
thf(2075,axiom,
! [T_b: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).
thf(2123,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).
thf(2134,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/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(2137,axiom,
! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).
thf(2138,axiom,
! [V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).
thf(2154,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(2155,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(2160,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/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(2161,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/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(2162,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/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(2163,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/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(2168,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(2231,axiom,
! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
thf(2290,axiom,
! [T_b: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
thf(2291,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
thf(2466,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(2467,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(2468,axiom,
! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(2469,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(2585,axiom,
! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(2594,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(2595,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(2596,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(2597,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(2598,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(2599,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(2600,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(2622,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(2623,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(2624,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(2625,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(2626,axiom,
! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(2627,axiom,
! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(2643,axiom,
! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(2644,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(2669,axiom,
! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(2670,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(2746,axiom,
! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
thf(2747,axiom,
! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
thf(2748,axiom,
! [V_r_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
thf(2838,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).
thf(2873,axiom,
! [V_R_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(2895,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).
thf(2900,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
thf(2902,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2905,axiom,
! [T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).
thf(2967,axiom,
! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(2968,axiom,
! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(2969,axiom,
! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(2970,axiom,
! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(3024,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(3027,axiom,
! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= V_B_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(3028,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(3029,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
& ( V_B_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(3035,axiom,
! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(3036,axiom,
! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(3037,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(3038,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(3039,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(3040,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(3041,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(3059,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(3060,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(3061,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(3062,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(3063,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(3066,axiom,
! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(3067,axiom,
! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(3089,axiom,
! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(3090,axiom,
! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(3096,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(3097,axiom,
! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(3353,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/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(3364,axiom,
! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(3366,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/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(3367,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/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(3368,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/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(3397,axiom,
! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3398,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(3399,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(3400,axiom,
! [T_c: $i,T_b: $i,V_Pa_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(3401,axiom,
! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(3402,axiom,
! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(3403,axiom,
! [V_B_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(3406,axiom,
! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
thf(3591,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).
thf(3592,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
thf(3607,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).
thf(3611,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).
thf(3612,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).
thf(4373,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(4407,axiom,
! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).
thf(4411,axiom,
! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(4412,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).
thf(4413,axiom,
! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(4414,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(4415,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(4416,axiom,
! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(4431,axiom,
! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(4432,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(4433,axiom,
! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(4434,axiom,
! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(4472,axiom,
! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
( ( V_g_2
= ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
=> ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).
thf(4473,axiom,
! [V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
thf(4481,axiom,
! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).
thf(4516,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(4517,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(4519,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(4520,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(4522,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(4523,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(4524,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/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(4590,axiom,
! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_b_2 ) )
<=> ( V_a_2 = V_b_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
thf(4645,axiom,
! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ V_A_2 ) @ V_x_2 ) )
=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).
thf(4646,axiom,
! [V_x_2: $i,V_f_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
thf(4753,axiom,
! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
thf(4817,axiom,
! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
thf(4855,axiom,
! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
thf(4857,axiom,
! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
thf(4858,axiom,
! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).
thf(4859,axiom,
! [V_x_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) )
=> ( V_x_2 = V_z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).
thf(4876,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(4877,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(4878,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(4879,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(4880,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(4893,axiom,
! [V_A_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(4912,axiom,
! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(4913,axiom,
! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(4930,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(4931,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(5046,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).
thf(5053,axiom,
! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).
thf(5056,axiom,
! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(5057,axiom,
! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(5058,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(5063,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(5064,axiom,
! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(5065,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(5067,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(5068,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(5069,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(5073,axiom,
! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(5074,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(5075,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(5103,axiom,
! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(5104,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(5105,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(5106,axiom,
! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(5107,axiom,
! [V_x: $i,T_a: $i] :
( ( class_Orderings_Obot @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
thf(5110,axiom,
! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(5111,axiom,
! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(5112,axiom,
! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(5113,axiom,
! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(5114,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(5115,axiom,
! [V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(5116,axiom,
! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(5117,axiom,
! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5118,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5119,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5120,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5122,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(5123,axiom,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(5124,axiom,
! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(5125,axiom,
! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(5126,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(5127,axiom,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(5128,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(5129,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(5130,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(5131,axiom,
! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(5132,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(5133,axiom,
! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(5134,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(5138,axiom,
! [V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(5140,axiom,
! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(5141,axiom,
! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(5142,axiom,
! [V_x_2: $i,T_b: $i] :
( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(5153,axiom,
! [V_x_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
| ( V_A_2
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(5155,axiom,
! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(5156,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(5157,axiom,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( V_b_2 = V_a_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(5158,axiom,
! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( V_b_2 = V_a_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(5159,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(5160,axiom,
! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
thf(5161,axiom,
! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
thf(5162,axiom,
! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(5163,axiom,
! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(5164,axiom,
! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(5165,axiom,
! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
thf(5166,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
thf(5167,axiom,
! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
thf(5168,axiom,
! [V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
thf(5169,axiom,
! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
thf(5170,axiom,
! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(5171,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(5172,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(5173,axiom,
! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(5174,axiom,
! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( V_a_2 = V_c_2 )
& ( V_b_2 = V_d_2 ) )
| ( ( V_a_2 = V_d_2 )
& ( V_b_2 = V_c_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(5175,axiom,
! [V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( V_a_2 = V_b_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(5176,axiom,
! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
thf(5180,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(5181,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(5182,axiom,
! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(5183,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/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(5184,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/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(5185,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/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(5186,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/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(5187,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/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(5188,axiom,
! [V_A_2: $i,T_b: $i] :
( ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(5189,axiom,
! [V_A_2: $i,T_b: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(5190,axiom,
! [V_c_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(5191,axiom,
! [V_a_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(5193,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(5194,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(5195,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(5196,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(5197,axiom,
! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(5198,axiom,
! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(5199,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(5200,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(5201,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/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(5204,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/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(5205,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/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(5206,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/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(5207,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/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(5208,axiom,
! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(5209,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/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(5210,axiom,
! [V_a_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(5211,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/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(5212,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/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(5213,axiom,
! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(5215,axiom,
! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
thf(5216,axiom,
! [V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(5217,axiom,
! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(5222,axiom,
! [V_G_2: $i,V_ts_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ V_ts_2 ) @ V_G_2 ) )
=> ( v_P @ V_G_2 @ V_ts_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
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/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(5224,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ v_G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(5231,conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(5232,negated_conjecture,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5231]) ).
thf(5233,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ) )
= $false ),
inference(unfold_def,[status(thm)],[5232]) ).
thf(5234,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(5235,plain,
( ( ! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(5236,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(5237,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(5238,plain,
( ( ! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(5239,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(5240,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(5241,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(5242,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(5243,plain,
( ( ! [V_Pa_2: $i] :
( ~ ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(5244,plain,
( ( ! [V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) )
| ~ ( hBOOL @ V_Pa_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(5245,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(5246,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(5247,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(5248,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(5249,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5250,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5251,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5252,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(5253,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5254,plain,
( ( class_Nat_Osize @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(5255,plain,
( ( class_Enum_Oenum @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(5256,plain,
( ( class_Groups_Ominus @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(5257,plain,
( ( class_Groups_Ouminus @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(5258,plain,
( ( class_Orderings_Obot @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(5259,plain,
( ( class_Orderings_Oord @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(5260,plain,
( ( class_Orderings_Otop @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(5261,plain,
( ( class_Orderings_Oorder @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(5262,plain,
( ( class_Lattices_Olattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(5263,plain,
( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(5264,plain,
( ( class_Orderings_Opreorder @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(5265,plain,
( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(5266,plain,
( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(5267,plain,
( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(5268,plain,
( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(5269,plain,
( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(5270,plain,
( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(5271,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(5272,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(5273,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(5274,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(5275,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(5276,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(5277,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(5278,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(5279,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(5280,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(5281,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(5282,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(5283,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(5284,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(5285,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(5286,plain,
( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(5287,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(5288,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ V_A_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(5289,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(5290,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)],[465]) ).
thf(5291,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)],[466]) ).
thf(5292,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)],[467]) ).
thf(5293,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)],[503]) ).
thf(5294,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)],[506]) ).
thf(5295,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
~ ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(5296,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)],[623]) ).
thf(5297,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)],[624]) ).
thf(5298,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)],[625]) ).
thf(5299,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)],[626]) ).
thf(5300,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)],[783]) ).
thf(5301,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)],[784]) ).
thf(5302,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)],[785]) ).
thf(5303,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)],[1039]) ).
thf(5304,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)],[1040]) ).
thf(5305,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)],[1064]) ).
thf(5306,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)],[1285]) ).
thf(5307,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1286]) ).
thf(5308,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)],[1287]) ).
thf(5309,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)],[1288]) ).
thf(5310,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)],[1289]) ).
thf(5311,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)],[1393]) ).
thf(5312,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)],[1394]) ).
thf(5313,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)],[1510]) ).
thf(5314,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)],[1511]) ).
thf(5315,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)],[1512]) ).
thf(5316,plain,
( ( ! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1567]) ).
thf(5317,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)],[1576]) ).
thf(5318,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)],[1617]) ).
thf(5319,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)],[1731]) ).
thf(5320,plain,
( ( ! [T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1732]) ).
thf(5321,plain,
( ( ! [T_b: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1733]) ).
thf(5322,plain,
( ( ! [T_b: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1734]) ).
thf(5323,plain,
( ( ! [T_b: $i,V_c_2: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1737]) ).
thf(5324,plain,
( ( ! [V_Pa_2: $i,T_b: $i,B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1759]) ).
thf(5325,plain,
( ( ! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1765]) ).
thf(5326,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)],[1778]) ).
thf(5327,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)],[1779]) ).
thf(5328,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)],[1833]) ).
thf(5329,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)],[1834]) ).
thf(5330,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)],[1835]) ).
thf(5331,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)],[1836]) ).
thf(5332,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)],[1862]) ).
thf(5333,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)],[1882]) ).
thf(5334,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1883]) ).
thf(5335,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)],[1884]) ).
thf(5336,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1946]) ).
thf(5337,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1947]) ).
thf(5338,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1949]) ).
thf(5339,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2074]) ).
thf(5340,plain,
( ( ! [T_b: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2075]) ).
thf(5341,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2123]) ).
thf(5342,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)],[2134]) ).
thf(5343,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2137]) ).
thf(5344,plain,
( ( ! [V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2138]) ).
thf(5345,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)],[2154]) ).
thf(5346,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)],[2155]) ).
thf(5347,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)],[2160]) ).
thf(5348,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)],[2161]) ).
thf(5349,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)],[2162]) ).
thf(5350,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)],[2163]) ).
thf(5351,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)],[2168]) ).
thf(5352,plain,
( ( ! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2231]) ).
thf(5353,plain,
( ( ! [T_b: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2290]) ).
thf(5354,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2291]) ).
thf(5355,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2466]) ).
thf(5356,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2467]) ).
thf(5357,plain,
( ( ! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2468]) ).
thf(5358,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2469]) ).
thf(5359,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2585]) ).
thf(5360,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[2594]) ).
thf(5361,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2595]) ).
thf(5362,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2596]) ).
thf(5363,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2597]) ).
thf(5364,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2598]) ).
thf(5365,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2599]) ).
thf(5366,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2600]) ).
thf(5367,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2622]) ).
thf(5368,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2623]) ).
thf(5369,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2624]) ).
thf(5370,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2625]) ).
thf(5371,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2626]) ).
thf(5372,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2627]) ).
thf(5373,plain,
( ( ! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2643]) ).
thf(5374,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2644]) ).
thf(5375,plain,
( ( ! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2669]) ).
thf(5376,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2670]) ).
thf(5377,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2746]) ).
thf(5378,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2747]) ).
thf(5379,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2748]) ).
thf(5380,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2838]) ).
thf(5381,plain,
( ( ! [V_R_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2873]) ).
thf(5382,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2895]) ).
thf(5383,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2900]) ).
thf(5384,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)],[2902]) ).
thf(5385,plain,
( ( ! [T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2905]) ).
thf(5386,plain,
( ( ! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2967]) ).
thf(5387,plain,
( ( ! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2968]) ).
thf(5388,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2969]) ).
thf(5389,plain,
( ( ! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2970]) ).
thf(5390,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3024]) ).
thf(5391,plain,
( ( ! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= V_B_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[3027]) ).
thf(5392,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[3028]) ).
thf(5393,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
& ( V_B_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3029]) ).
thf(5394,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3035]) ).
thf(5395,plain,
( ( ! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3036]) ).
thf(5396,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3037]) ).
thf(5397,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3038]) ).
thf(5398,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3039]) ).
thf(5399,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3040]) ).
thf(5400,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3041]) ).
thf(5401,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[3059]) ).
thf(5402,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3060]) ).
thf(5403,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3061]) ).
thf(5404,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3062]) ).
thf(5405,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3063]) ).
thf(5406,plain,
( ( ! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3066]) ).
thf(5407,plain,
( ( ! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3067]) ).
thf(5408,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3089]) ).
thf(5409,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3090]) ).
thf(5410,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3096]) ).
thf(5411,plain,
( ( ! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3097]) ).
thf(5412,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)],[3353]) ).
thf(5413,plain,
( ( ! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3364]) ).
thf(5414,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)],[3366]) ).
thf(5415,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)],[3367]) ).
thf(5416,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)],[3368]) ).
thf(5417,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)],[3397]) ).
thf(5418,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)],[3398]) ).
thf(5419,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)],[3399]) ).
thf(5420,plain,
( ( ! [T_c: $i,T_b: $i,V_Pa_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3400]) ).
thf(5421,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3401]) ).
thf(5422,plain,
( ( ! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3402]) ).
thf(5423,plain,
( ( ! [V_B_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3403]) ).
thf(5424,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3406]) ).
thf(5425,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3591]) ).
thf(5426,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[3592]) ).
thf(5427,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3607]) ).
thf(5428,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3611]) ).
thf(5429,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3612]) ).
thf(5430,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)],[4373]) ).
thf(5431,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4407]) ).
thf(5432,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)],[4411]) ).
thf(5433,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)],[4412]) ).
thf(5434,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)],[4413]) ).
thf(5435,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)],[4414]) ).
thf(5436,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)],[4415]) ).
thf(5437,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)],[4416]) ).
thf(5438,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4431]) ).
thf(5439,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4432]) ).
thf(5440,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4433]) ).
thf(5441,plain,
( ( ! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4434]) ).
thf(5442,plain,
( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
( ( V_g_2
= ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
=> ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4472]) ).
thf(5443,plain,
( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4473]) ).
thf(5444,plain,
( ( ! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4481]) ).
thf(5445,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)],[4516]) ).
thf(5446,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)],[4517]) ).
thf(5447,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)],[4519]) ).
thf(5448,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)],[4520]) ).
thf(5449,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)],[4522]) ).
thf(5450,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)],[4523]) ).
thf(5451,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)],[4524]) ).
thf(5452,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_b_2 ) )
<=> ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4590]) ).
thf(5453,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ V_A_2 ) @ V_x_2 ) )
=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4645]) ).
thf(5454,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4646]) ).
thf(5455,plain,
( ( ! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4753]) ).
thf(5456,plain,
( ( ! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4817]) ).
thf(5457,plain,
( ( ! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4855]) ).
thf(5458,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4857]) ).
thf(5459,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4858]) ).
thf(5460,plain,
( ( ! [V_x_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) )
=> ( V_x_2 = V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4859]) ).
thf(5461,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4876]) ).
thf(5462,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4877]) ).
thf(5463,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4878]) ).
thf(5464,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4879]) ).
thf(5465,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4880]) ).
thf(5466,plain,
( ( ! [V_A_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4893]) ).
thf(5467,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4912]) ).
thf(5468,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4913]) ).
thf(5469,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)],[4930]) ).
thf(5470,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4931]) ).
thf(5471,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5046]) ).
thf(5472,plain,
( ( ! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5053]) ).
thf(5473,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5056]) ).
thf(5474,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5057]) ).
thf(5475,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5058]) ).
thf(5476,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5063]) ).
thf(5477,plain,
( ( ! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5064]) ).
thf(5478,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5065]) ).
thf(5479,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5067]) ).
thf(5480,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5068]) ).
thf(5481,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5069]) ).
thf(5482,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)],[5073]) ).
thf(5483,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)],[5074]) ).
thf(5484,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5075]) ).
thf(5485,plain,
( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5103]) ).
thf(5486,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5104]) ).
thf(5487,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5105]) ).
thf(5488,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5106]) ).
thf(5489,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Obot @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5107]) ).
thf(5490,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5110]) ).
thf(5491,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5111]) ).
thf(5492,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5112]) ).
thf(5493,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5113]) ).
thf(5494,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5114]) ).
thf(5495,plain,
( ( ! [V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5115]) ).
thf(5496,plain,
( ( ! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5116]) ).
thf(5497,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)],[5117]) ).
thf(5498,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)],[5118]) ).
thf(5499,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[5119]) ).
thf(5500,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5120]) ).
thf(5501,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5122]) ).
thf(5502,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5123]) ).
thf(5503,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5124]) ).
thf(5504,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5125]) ).
thf(5505,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5126]) ).
thf(5506,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5127]) ).
thf(5507,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5128]) ).
thf(5508,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5129]) ).
thf(5509,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5130]) ).
thf(5510,plain,
( ( ! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5131]) ).
thf(5511,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5132]) ).
thf(5512,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5133]) ).
thf(5513,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5134]) ).
thf(5514,plain,
( ( ! [V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5138]) ).
thf(5515,plain,
( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5140]) ).
thf(5516,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5141]) ).
thf(5517,plain,
( ( ! [V_x_2: $i,T_b: $i] :
( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5142]) ).
thf(5518,plain,
( ( ! [V_x_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
| ( V_A_2
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5153]) ).
thf(5519,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5155]) ).
thf(5520,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5156]) ).
thf(5521,plain,
( ( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( V_b_2 = V_a_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5157]) ).
thf(5522,plain,
( ( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( V_b_2 = V_a_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5158]) ).
thf(5523,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5159]) ).
thf(5524,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5160]) ).
thf(5525,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5161]) ).
thf(5526,plain,
( ( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5162]) ).
thf(5527,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5163]) ).
thf(5528,plain,
( ( ! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5164]) ).
thf(5529,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5165]) ).
thf(5530,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5166]) ).
thf(5531,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5167]) ).
thf(5532,plain,
( ( ! [V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5168]) ).
thf(5533,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5169]) ).
thf(5534,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5170]) ).
thf(5535,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5171]) ).
thf(5536,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5172]) ).
thf(5537,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5173]) ).
thf(5538,plain,
( ( ! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( V_a_2 = V_c_2 )
& ( V_b_2 = V_d_2 ) )
| ( ( V_a_2 = V_d_2 )
& ( V_b_2 = V_c_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5174]) ).
thf(5539,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5175]) ).
thf(5540,plain,
( ( ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5176]) ).
thf(5541,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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)],[5180]) ).
thf(5542,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5181]) ).
thf(5543,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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)],[5182]) ).
thf(5544,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)],[5183]) ).
thf(5545,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)],[5184]) ).
thf(5546,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)],[5185]) ).
thf(5547,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)],[5186]) ).
thf(5548,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)],[5187]) ).
thf(5549,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5188]) ).
thf(5550,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5189]) ).
thf(5551,plain,
( ( ! [V_c_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5190]) ).
thf(5552,plain,
( ( ! [V_a_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5191]) ).
thf(5553,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5193]) ).
thf(5554,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5194]) ).
thf(5555,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5195]) ).
thf(5556,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5196]) ).
thf(5557,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5197]) ).
thf(5558,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5198]) ).
thf(5559,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)],[5199]) ).
thf(5560,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)],[5200]) ).
thf(5561,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)],[5201]) ).
thf(5562,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)],[5204]) ).
thf(5563,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)],[5205]) ).
thf(5564,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)],[5206]) ).
thf(5565,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)],[5207]) ).
thf(5566,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5208]) ).
thf(5567,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)],[5209]) ).
thf(5568,plain,
( ( ! [V_a_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5210]) ).
thf(5569,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)],[5211]) ).
thf(5570,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)],[5212]) ).
thf(5571,plain,
( ( ! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5213]) ).
thf(5572,plain,
( ( ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5215]) ).
thf(5573,plain,
( ( ! [V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5216]) ).
thf(5574,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5217]) ).
thf(5575,plain,
( ( ! [V_G_2: $i,V_ts_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ V_ts_2 ) @ V_G_2 ) )
=> ( v_P @ V_G_2 @ V_ts_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5222]) ).
thf(5576,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(5577,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ v_G ) )
= $true ),
inference(unfold_def,[status(thm)],[5224]) ).
thf(5578,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5233]) ).
thf(5579,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ v_G ) )
= $true ),
inference(copy,[status(thm)],[5577]) ).
thf(5580,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)],[5576]) ).
thf(5581,plain,
( ( ! [V_G_2: $i,V_ts_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ V_ts_2 ) @ V_G_2 ) )
=> ( v_P @ V_G_2 @ V_ts_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5575]) ).
thf(5582,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5574]) ).
thf(5583,plain,
( ( ! [V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5573]) ).
thf(5584,plain,
( ( ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5572]) ).
thf(5585,plain,
( ( ! [V_c_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5571]) ).
thf(5586,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)],[5570]) ).
thf(5587,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)],[5569]) ).
thf(5588,plain,
( ( ! [V_a_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5568]) ).
thf(5589,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)],[5567]) ).
thf(5590,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5566]) ).
thf(5591,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)],[5565]) ).
thf(5592,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)],[5564]) ).
thf(5593,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)],[5563]) ).
thf(5594,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)],[5562]) ).
thf(5595,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)],[5561]) ).
thf(5596,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)],[5560]) ).
thf(5597,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)],[5559]) ).
thf(5598,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5558]) ).
thf(5599,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5557]) ).
thf(5600,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5556]) ).
thf(5601,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5555]) ).
thf(5602,plain,
( ( ! [T_b: $i,V_B_2: $i,V_A_2: $i] :
( ( V_A_2 = V_B_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5554]) ).
thf(5603,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5553]) ).
thf(5604,plain,
( ( ! [V_a_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_a_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5552]) ).
thf(5605,plain,
( ( ! [V_c_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_c_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5551]) ).
thf(5606,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ? [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5550]) ).
thf(5607,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5549]) ).
thf(5608,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)],[5548]) ).
thf(5609,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)],[5547]) ).
thf(5610,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)],[5546]) ).
thf(5611,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)],[5545]) ).
thf(5612,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)],[5544]) ).
thf(5613,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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)],[5543]) ).
thf(5614,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5542]) ).
thf(5615,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ 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)],[5541]) ).
thf(5616,plain,
( ( ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5540]) ).
thf(5617,plain,
( ( ! [V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5539]) ).
thf(5618,plain,
( ( ! [V_d_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_c_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_d_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( V_a_2 = V_c_2 )
& ( V_b_2 = V_d_2 ) )
| ( ( V_a_2 = V_d_2 )
& ( V_b_2 = V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5538]) ).
thf(5619,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5537]) ).
thf(5620,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5536]) ).
thf(5621,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5535]) ).
thf(5622,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5534]) ).
thf(5623,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5533]) ).
thf(5624,plain,
( ( ! [V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5532]) ).
thf(5625,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5531]) ).
thf(5626,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5530]) ).
thf(5627,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ T_b ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5529]) ).
thf(5628,plain,
( ( ! [V_a_2: $i,V_D_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_C_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_D_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5528]) ).
thf(5629,plain,
( ( ! [V_b_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_b_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5527]) ).
thf(5630,plain,
( ( ! [V_a_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5526]) ).
thf(5631,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_c ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ ( hAPP @ V_f_2 @ V_a_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5525]) ).
thf(5632,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Oimage @ T_b @ T_c @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5524]) ).
thf(5633,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) )
<=> ? [B_AA: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ B_AA ) @ V_A_2 ) )
& ( V_B_2
= ( hAPP @ ( c_Set_Oimage @ T_c @ T_b @ V_f_2 ) @ B_AA ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5523]) ).
thf(5634,plain,
( ( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( V_b_2 = V_a_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5522]) ).
thf(5635,plain,
( ( ! [V_a_2: $i,V_b_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_b_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
<=> ( V_b_2 = V_a_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5521]) ).
thf(5636,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_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5520]) ).
thf(5637,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ V_B_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5519]) ).
thf(5638,plain,
( ( ! [V_x_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
| ( V_A_2
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5518]) ).
thf(5639,plain,
( ( ! [V_x_2: $i,T_b: $i] :
( ( c_Set_Othe__elem @ T_b @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ) )
= $true ),
inference(copy,[status(thm)],[5517]) ).
thf(5640,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5516]) ).
thf(5641,plain,
( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[5515]) ).
thf(5642,plain,
( ( ! [V_x_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5514]) ).
thf(5643,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5513]) ).
thf(5644,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( V_x_2 = V_y_2 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5512]) ).
thf(5645,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( V_x = V_y )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5511]) ).
thf(5646,plain,
( ( ! [V_x_2: $i,V_y_2: $i,T_b: $i] :
( ( class_Orderings_Oorder @ T_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_y_2 ) @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_b ) @ V_x_2 ) @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5510]) ).
thf(5647,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_c ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5509]) ).
thf(5648,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( V_a = V_b )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_b ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5508]) ).
thf(5649,plain,
( ( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Orderings_Oord @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_b ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_a ) @ V_c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5507]) ).
thf(5650,plain,
( ( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_b ) @ V_a ) )
=> ( ( V_b = V_c )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_c ) @ V_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5506]) ).
thf(5651,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5505]) ).
thf(5652,plain,
( ( ! [V_z: $i,V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Opreorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_z ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5504]) ).
thf(5653,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( V_x = V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5503]) ).
thf(5654,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( class_Orderings_Oorder @ T_a )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_z ) @ V_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5502]) ).
thf(5655,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( class_Orderings_Olinorder @ T_a )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_x ) @ V_y ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ V_y ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5501]) ).
thf(5656,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5500]) ).
thf(5657,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5499]) ).
thf(5658,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)],[5498]) ).
thf(5659,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)],[5497]) ).
thf(5660,plain,
( ( ! [V_Q_2: $i,T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5496]) ).
thf(5661,plain,
( ( ! [V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Q_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5495]) ).
thf(5662,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5494]) ).
thf(5663,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[5493]) ).
thf(5664,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_m = V_n )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[5492]) ).
thf(5665,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5491]) ).
thf(5666,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_m ) @ V_n ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ V_n ) @ V_m ) )
=> ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[5490]) ).
thf(5667,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( class_Orderings_Obot @ T_a )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5489]) ).
thf(5668,plain,
( ( ! [V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
<=> ! [B_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ B_x ) ) @ ( hAPP @ V_g_2 @ B_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5488]) ).
thf(5669,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5487]) ).
thf(5670,plain,
( ( ! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( class_Orderings_Oord @ T_c )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ T_c ) ) @ V_f_2 ) @ V_g_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ T_c ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) @ ( hAPP @ V_g_2 @ V_x_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5486]) ).
thf(5671,plain,
( ( ! [V_x_2: $i,T_c: $i,T_b: $i] :
( ( class_Orderings_Obot @ T_b )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ T_b ) ) @ V_x_2 )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[5485]) ).
thf(5672,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5484]) ).
thf(5673,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)],[5483]) ).
thf(5674,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)],[5482]) ).
thf(5675,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5481]) ).
thf(5676,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5480]) ).
thf(5677,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_A_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5479]) ).
thf(5678,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
= V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5478]) ).
thf(5679,plain,
( ( ! [V_B_2: $i,V_D_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_D_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5477]) ).
thf(5680,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5476]) ).
thf(5681,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5475]) ).
thf(5682,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5474]) ).
thf(5683,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5473]) ).
thf(5684,plain,
( ( ! [V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5472]) ).
thf(5685,plain,
( ( ! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ V_F_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5471]) ).
thf(5686,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5470]) ).
thf(5687,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)],[5469]) ).
thf(5688,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_z_2 ) )
= $true ),
inference(copy,[status(thm)],[5468]) ).
thf(5689,plain,
( ( ! [V_a2_2: $i,V_a1_2: $i,T_c: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ T_b @ T_c @ V_a1_2 @ V_a2_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_a2_2 ) )
= $true ),
inference(copy,[status(thm)],[5467]) ).
thf(5690,plain,
( ( ! [V_A_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5466]) ).
thf(5691,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5465]) ).
thf(5692,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5464]) ).
thf(5693,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5463]) ).
thf(5694,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
| ( V_A_2 = V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5462]) ).
thf(5695,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
& ( V_A_2 != V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5461]) ).
thf(5696,plain,
( ( ! [V_x_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) )
=> ( V_x_2 = V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5460]) ).
thf(5697,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5459]) ).
thf(5698,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ T_b @ T_c @ V_f_2 @ V_z_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_z_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5458]) ).
thf(5699,plain,
( ( ! [T_b: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[5457]) ).
thf(5700,plain,
( ( ! [V_f_2: $i,T_c: $i,T_b: $i] : ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5456]) ).
thf(5701,plain,
( ( ! [V_A_2: $i,V_B_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_B_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( c_Fun_Oinj__on @ T_b @ T_c @ V_f_2 @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5455]) ).
thf(5702,plain,
( ( ! [V_x_2: $i,V_f_2: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5454]) ).
thf(5703,plain,
( ( ! [V_x_2: $i,V_A_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ V_A_2 ) @ V_x_2 ) )
=> ( V_A_2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5453]) ).
thf(5704,plain,
( ( ! [V_b_2: $i,V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ T_b @ V_f_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_b_2 ) )
<=> ( V_a_2 = V_b_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5452]) ).
thf(5705,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)],[5451]) ).
thf(5706,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)],[5450]) ).
thf(5707,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)],[5449]) ).
thf(5708,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)],[5448]) ).
thf(5709,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)],[5447]) ).
thf(5710,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)],[5446]) ).
thf(5711,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)],[5445]) ).
thf(5712,plain,
( ( ! [V_z_2: $i,V_g_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ T_b @ T_c @ V_f_2 ) @ V_g_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) )
= $true ),
inference(copy,[status(thm)],[5444]) ).
thf(5713,plain,
( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ) )
= $true ),
inference(copy,[status(thm)],[5443]) ).
thf(5714,plain,
( ( ! [V_a_2: $i,V_f_2: $i,T_b: $i,V_g_2: $i] :
( ( V_g_2
= ( c_Finite__Set_Ofold1 @ T_b @ V_f_2 ) )
=> ( ( hAPP @ V_g_2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= V_a_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5442]) ).
thf(5715,plain,
( ( ! [V_w: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_w ) ) )
= $true ),
inference(copy,[status(thm)],[5441]) ).
thf(5716,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[5440]) ).
thf(5717,plain,
( ( ! [V_k: $i,V_j: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_j ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_j ) @ V_k ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_i ) @ V_k ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5439]) ).
thf(5718,plain,
( ( ! [V_w: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_z ) @ V_w ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ V_w ) @ V_z ) )
=> ( V_z = V_w ) ) ) )
= $true ),
inference(copy,[status(thm)],[5438]) ).
thf(5719,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)],[5437]) ).
thf(5720,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)],[5436]) ).
thf(5721,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)],[5435]) ).
thf(5722,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)],[5434]) ).
thf(5723,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)],[5433]) ).
thf(5724,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)],[5432]) ).
thf(5725,plain,
( ( ! [V_z_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ T_c @ T_b @ V_f_2 ) @ V_z_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= V_z_2 ) )
= $true ),
inference(copy,[status(thm)],[5431]) ).
thf(5726,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)],[5430]) ).
thf(5727,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5429]) ).
thf(5728,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5428]) ).
thf(5729,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5427]) ).
thf(5730,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5426]) ).
thf(5731,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) )
<=> ( V_A_2 = V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5425]) ).
thf(5732,plain,
( ( ! [V_y_2: $i,V_x_2: $i,T_c: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_x_2 ) @ V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5424]) ).
thf(5733,plain,
( ( ! [V_B_2: $i,T_b: $i,V_A_2: $i] :
( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ T_b @ T_b ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5423]) ).
thf(5734,plain,
( ( ! [V_Q_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5422]) ).
thf(5735,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_Q_2: $i,V_Pa_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_Pa_2 ) @ V_Q_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_Pa_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5421]) ).
thf(5736,plain,
( ( ! [T_c: $i,T_b: $i,V_Pa_2: $i] :
( ! [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
<=> ! [B_a: $i,B_b: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ B_a ) @ B_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5420]) ).
thf(5737,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)],[5419]) ).
thf(5738,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)],[5418]) ).
thf(5739,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)],[5417]) ).
thf(5740,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)],[5416]) ).
thf(5741,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)],[5415]) ).
thf(5742,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)],[5414]) ).
thf(5743,plain,
( ( ! [V_R2_2: $i,V_R1_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_R1_2 ) @ V_R2_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R2_2 ) ) @ ( c_Wellfounded_Oaccp @ T_b @ V_R1_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5413]) ).
thf(5744,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)],[5412]) ).
thf(5745,plain,
( ( ! [T_b: $i,V_A_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5411]) ).
thf(5746,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5410]) ).
thf(5747,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5409]) ).
thf(5748,plain,
( ( ! [V_B_2: $i,V_a_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5408]) ).
thf(5749,plain,
( ( ! [V_A_2: $i,T_b: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5407]) ).
thf(5750,plain,
( ( ! [V_B_2: $i,T_b: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5406]) ).
thf(5751,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5405]) ).
thf(5752,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5404]) ).
thf(5753,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5403]) ).
thf(5754,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5402]) ).
thf(5755,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5401]) ).
thf(5756,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5400]) ).
thf(5757,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5399]) ).
thf(5758,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5398]) ).
thf(5759,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5397]) ).
thf(5760,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5396]) ).
thf(5761,plain,
( ( ! [V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5395]) ).
thf(5762,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5394]) ).
thf(5763,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ( ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
& ( V_B_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5393]) ).
thf(5764,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5392]) ).
thf(5765,plain,
( ( ! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= V_B_2 ) )
= $true ),
inference(copy,[status(thm)],[5391]) ).
thf(5766,plain,
( ( ! [V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5390]) ).
thf(5767,plain,
( ( ! [T_c: $i,T_b: $i,V_A_2: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5389]) ).
thf(5768,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5388]) ).
thf(5769,plain,
( ( ! [V_A_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_B_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5387]) ).
thf(5770,plain,
( ( ! [V_B_2: $i,T_c: $i,T_b: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5386]) ).
thf(5771,plain,
( ( ! [T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5385]) ).
thf(5772,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)],[5384]) ).
thf(5773,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5383]) ).
thf(5774,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_OPow @ T_b ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5382]) ).
thf(5775,plain,
( ( ! [V_R_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_OImage @ T_c @ T_b @ V_R_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5381]) ).
thf(5776,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ T_b @ V_A_2 ) ) @ ( c_Predicate_OPowp @ T_b @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5380]) ).
thf(5777,plain,
( ( ! [V_r_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5379]) ).
thf(5778,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5378]) ).
thf(5779,plain,
( ( ! [V_r_2: $i,V_A_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ T_b ) @ V_A_2 ) @ V_r_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5377]) ).
thf(5780,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ~ ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5376]) ).
thf(5781,plain,
( ( ! [T_b: $i,V_B_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) )
=> ( ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5375]) ).
thf(5782,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5374]) ).
thf(5783,plain,
( ( ! [V_B_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_B_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5373]) ).
thf(5784,plain,
( ( ! [V_D_2: $i,V_B_2: $i,V_C_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_D_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_D_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5372]) ).
thf(5785,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_C_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_A_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_C_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5371]) ).
thf(5786,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5370]) ).
thf(5787,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5369]) ).
thf(5788,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5368]) ).
thf(5789,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5367]) ).
thf(5790,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_B_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5366]) ).
thf(5791,plain,
( ( ! [V_x_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_A_2 @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5365]) ).
thf(5792,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) @ V_C_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5364]) ).
thf(5793,plain,
( ( ! [V_C_2: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_C_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_C_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5363]) ).
thf(5794,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5362]) ).
thf(5795,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5361]) ).
thf(5796,plain,
( ( ! [V_A_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_A_2 )
= V_A_2 ) )
= $true ),
inference(copy,[status(thm)],[5360]) ).
thf(5797,plain,
( ( ! [V_B_2: $i,V_A_2: $i,V_a_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_A_2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ V_B_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5359]) ).
thf(5798,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5358]) ).
thf(5799,plain,
( ( ! [T_c: $i,T_b: $i,V_B_2: $i,V_y_2: $i,V_x_2: $i,V_A_2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5357]) ).
thf(5800,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_B_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5356]) ).
thf(5801,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_B_2: $i,V_A_2: $i,T_c: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) @ V_A_2 ) @ V_B_2 ) @ V_x_2 ) @ V_y_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ V_A_2 @ V_x_2 ) @ V_y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5355]) ).
thf(5802,plain,
( ( ! [V_A_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5354]) ).
thf(5803,plain,
( ( ! [T_b: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5353]) ).
thf(5804,plain,
( ( ! [V_x_2: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_x_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5352]) ).
thf(5805,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)],[5351]) ).
thf(5806,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)],[5350]) ).
thf(5807,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)],[5349]) ).
thf(5808,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)],[5348]) ).
thf(5809,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)],[5347]) ).
thf(5810,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)],[5346]) ).
thf(5811,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)],[5345]) ).
thf(5812,plain,
( ( ! [V_f_2: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Set_Ovimage @ T_b @ T_c @ V_f_2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5344]) ).
thf(5813,plain,
( ( ! [V_f_2: $i,T_c: $i,V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_A_2 ) ) @ ( hAPP @ ( c_Set_Ovimage @ T_c @ T_b @ V_f_2 ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5343]) ).
thf(5814,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)],[5342]) ).
thf(5815,plain,
( ( ! [V_A_2: $i,V_B_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_B_2 ) @ V_A_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5341]) ).
thf(5816,plain,
( ( ! [T_b: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
= $true ),
inference(copy,[status(thm)],[5340]) ).
thf(5817,plain,
( ( ! [V_B_2: $i,V_A_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ V_A_2 ) @ V_B_2 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_A_2 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ T_b @ tc_HOL_Obool ) @ V_B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5339]) ).
thf(5818,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= V_Pa_2 ) )
= $true ),
inference(copy,[status(thm)],[5338]) ).
thf(5819,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5337]) ).
thf(5820,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_Pa_2 ) )
<=> ! [B_x: $i] :
~ ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5336]) ).
thf(5821,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)],[5335]) ).
thf(5822,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5334]) ).
thf(5823,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)],[5333]) ).
thf(5824,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)],[5332]) ).
thf(5825,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)],[5331]) ).
thf(5826,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)],[5330]) ).
thf(5827,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)],[5329]) ).
thf(5828,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)],[5328]) ).
thf(5829,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)],[5327]) ).
thf(5830,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)],[5326]) ).
thf(5831,plain,
( ( ! [V_p_2: $i,V_r_2: $i,T_b: $i] :
( ( c_Wellfounded_OwfP @ T_b @ V_r_2 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ T_b @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) @ V_p_2 ) @ V_r_2 ) )
=> ( c_Wellfounded_OwfP @ T_b @ V_p_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5325]) ).
thf(5832,plain,
( ( ! [V_Pa_2: $i,T_b: $i,B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5324]) ).
thf(5833,plain,
( ( ! [T_b: $i,V_c_2: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( ( V_c_2
= ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ V_c_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5323]) ).
thf(5834,plain,
( ( ! [T_b: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) )
<=> ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5322]) ).
thf(5835,plain,
( ( ! [T_b: $i,V_Pa_2: $i] :
( ? [B_x1: $i] : ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x1 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5321]) ).
thf(5836,plain,
( ( ! [T_b: $i,V_x_2: $i,V_Pa_2: $i] :
( ( hBOOL @ ( hAPP @ V_Pa_2 @ V_x_2 ) )
=> ( hBOOL @ ( hAPP @ V_Pa_2 @ ( c_Hilbert__Choice_OEps @ T_b @ V_Pa_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5320]) ).
thf(5837,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)],[5319]) ).
thf(5838,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)],[5318]) ).
thf(5839,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)],[5317]) ).
thf(5840,plain,
( ( ! [V_r_2: $i,T_b: $i] : ( c_Relation_Ototal__on @ T_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_r_2 ) )
= $true ),
inference(copy,[status(thm)],[5316]) ).
thf(5841,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)],[5315]) ).
thf(5842,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)],[5314]) ).
thf(5843,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)],[5313]) ).
thf(5844,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)],[5312]) ).
thf(5845,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)],[5311]) ).
thf(5846,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)],[5310]) ).
thf(5847,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)],[5309]) ).
thf(5848,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)],[5308]) ).
thf(5849,plain,
( ( ! [V_ts_2: $i,V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_ts_2 ) )
<=> ? [B_us: $i] :
( ( ( V_xs_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ B_us ) )
& ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ys_2 )
= V_ts_2 ) )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ B_us )
= V_zs_2 )
& ( V_ys_2
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ B_us ) @ V_ts_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5307]) ).
thf(5850,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)],[5306]) ).
thf(5851,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)],[5305]) ).
thf(5852,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)],[5304]) ).
thf(5853,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)],[5303]) ).
thf(5854,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)],[5302]) ).
thf(5855,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)],[5301]) ).
thf(5856,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)],[5300]) ).
thf(5857,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)],[5299]) ).
thf(5858,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)],[5298]) ).
thf(5859,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)],[5297]) ).
thf(5860,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)],[5296]) ).
thf(5861,plain,
( ( ! [V_Pa_2: $i,T_b: $i] :
~ ? [B_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ T_b ) @ B_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) )
& ( hBOOL @ ( hAPP @ V_Pa_2 @ B_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5862,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)],[5294]) ).
thf(5863,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)],[5293]) ).
thf(5864,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)],[5292]) ).
thf(5865,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)],[5291]) ).
thf(5866,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)],[5290]) ).
thf(5867,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) @ V_A_2 )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5868,plain,
( ( ! [V_A_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Obij__betw @ T_b @ T_c @ V_f_2 @ V_A_2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_c @ tc_HOL_Obool ) ) )
=> ( V_A_2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5869,plain,
( ( ! [V_x_2: $i,V_R_2: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ T_b @ V_R_2 ) @ V_x_2 ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ V_R_2 @ V_x_2 ) @ V_x_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5870,plain,
( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5871,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ T_1 )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(5872,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ T_1 )
=> ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(5873,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ T_1 )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(5874,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ T_1 )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5282]) ).
thf(5875,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ T_1 )
=> ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(5876,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Finite__Set_Ofinite @ T_2 )
& ( class_Finite__Set_Ofinite @ T_1 ) )
=> ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5280]) ).
thf(5877,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ T_1 )
=> ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5279]) ).
thf(5878,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ T_1 )
=> ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5278]) ).
thf(5879,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ T_1 )
=> ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5277]) ).
thf(5880,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oord @ T_1 )
=> ( class_Orderings_Oord @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5276]) ).
thf(5881,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ T_1 )
=> ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5275]) ).
thf(5882,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ouminus @ T_1 )
=> ( class_Groups_Ouminus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5274]) ).
thf(5883,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Groups_Ominus @ T_1 )
=> ( class_Groups_Ominus @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5273]) ).
thf(5884,plain,
( ( ! [T_1: $i,T_2: $i] :
( ( ( class_Enum_Oenum @ T_2 )
& ( class_Enum_Oenum @ T_1 ) )
=> ( class_Enum_Oenum @ ( tc_fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5272]) ).
thf(5885,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5271]) ).
thf(5886,plain,
( ( class_Lattices_Obounded__lattice__top @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5270]) ).
thf(5887,plain,
( ( class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5269]) ).
thf(5888,plain,
( ( class_Lattices_Osemilattice__sup @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5268]) ).
thf(5889,plain,
( ( class_Lattices_Osemilattice__inf @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5267]) ).
thf(5890,plain,
( ( class_Lattices_Odistrib__lattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5266]) ).
thf(5891,plain,
( ( class_Lattices_Oboolean__algebra @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5265]) ).
thf(5892,plain,
( ( class_Orderings_Opreorder @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5264]) ).
thf(5893,plain,
( ( class_Finite__Set_Ofinite @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5263]) ).
thf(5894,plain,
( ( class_Lattices_Olattice @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5262]) ).
thf(5895,plain,
( ( class_Orderings_Oorder @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5261]) ).
thf(5896,plain,
( ( class_Orderings_Otop @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5260]) ).
thf(5897,plain,
( ( class_Orderings_Oord @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5259]) ).
thf(5898,plain,
( ( class_Orderings_Obot @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5258]) ).
thf(5899,plain,
( ( class_Groups_Ouminus @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5257]) ).
thf(5900,plain,
( ( class_Groups_Ominus @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5256]) ).
thf(5901,plain,
( ( class_Enum_Oenum @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5255]) ).
thf(5902,plain,
( ( class_Nat_Osize @ tc_HOL_Obool )
= $true ),
inference(copy,[status(thm)],[5254]) ).
thf(5903,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5253]) ).
thf(5904,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)],[5252]) ).
thf(5905,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_Pa_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5251]) ).
thf(5906,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5250]) ).
thf(5907,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_Pa_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_Pa_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_Pa_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5249]) ).
thf(5908,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)],[5248]) ).
thf(5909,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)],[5247]) ).
thf(5910,plain,
( ( ~ ( hBOOL @ c_fFalse ) )
= $true ),
inference(copy,[status(thm)],[5246]) ).
thf(5911,plain,
( ( hBOOL @ c_fTrue )
= $true ),
inference(copy,[status(thm)],[5245]) ).
thf(5912,plain,
( ( ! [V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) )
| ~ ( hBOOL @ V_Pa_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5244]) ).
thf(5913,plain,
( ( ! [V_Pa_2: $i] :
( ~ ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ c_fNot @ V_Pa_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5243]) ).
thf(5914,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5242]) ).
thf(5915,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5241]) ).
thf(5916,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5240]) ).
thf(5917,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5239]) ).
thf(5918,plain,
( ( ! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5238]) ).
thf(5919,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ V_Pa_2 ) @ V_Q_2 ) )
| ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5237]) ).
thf(5920,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ( hBOOL @ V_Pa_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5236]) ).
thf(5921,plain,
( ( ! [V_Pa_2: $i,V_Q_2: $i] :
( ~ ( hBOOL @ V_Q_2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5235]) ).
thf(5922,plain,
( ( ! [V_Q_2: $i,V_Pa_2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ V_Pa_2 ) @ V_Q_2 ) )
| ~ ( hBOOL @ V_Pa_2 )
| ( hBOOL @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5234]) ).
thf(5923,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ) ) )
= $true ),
inference(copy,[status(thm)],[5578]) ).
thf(5924,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)],[5808]) ).
thf(5925,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5749]) ).
thf(5926,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Obot @ SX2 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ SX2 ) ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5671]) ).
thf(5927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SX3 @ SX2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SX3 @ SX2 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5704]) ).
thf(5928,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5729]) ).
thf(5929,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5686]) ).
thf(5930,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5717]) ).
thf(5931,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5629]) ).
thf(5932,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5622]) ).
thf(5933,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)],[5726]) ).
thf(5934,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)],[5809]) ).
thf(5935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5664]) ).
thf(5936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Otop @ SX1 )
| ( class_Orderings_Otop @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5879]) ).
thf(5937,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5636]) ).
thf(5938,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX0 @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5734]) ).
thf(5939,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5657]) ).
thf(5940,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX0 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5815]) ).
thf(5941,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)],[5710]) ).
thf(5942,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)],[5843]) ).
thf(5943,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Wellfounded_OwfP @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) @ SX0 ) @ SX1 ) )
| ( c_Wellfounded_OwfP @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5831]) ).
thf(5944,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)],[5609]) ).
thf(5945,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5619]) ).
thf(5946,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5790]) ).
thf(5947,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)],[5594]) ).
thf(5948,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5800]) ).
thf(5949,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5666]) ).
thf(5950,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5654]) ).
thf(5951,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX1 != SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( ( SX1 != SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5695]) ).
thf(5952,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)],[5736]) ).
thf(5953,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)],[5673]) ).
thf(5954,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Predicate_Oreflp @ SX2 @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5823]) ).
thf(5955,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)],[5827]) ).
thf(5956,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)],[5720]) ).
thf(5957,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SX2 ) @ SX1 ) ) @ ( hAPP @ ( c_Set_OPow @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5774]) ).
thf(5958,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SX1 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5820]) ).
thf(5959,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5801]) ).
thf(5960,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5694]) ).
thf(5961,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)],[5863]) ).
thf(5962,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5643]) ).
thf(5963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SX1 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5873]) ).
thf(5964,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5841]) ).
thf(5965,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( v_P @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5581]) ).
thf(5966,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5735]) ).
thf(5967,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5661]) ).
thf(5968,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5626]) ).
thf(5969,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5760]) ).
thf(5970,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)],[5737]) ).
thf(5971,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5615]) ).
thf(5972,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)],[5866]) ).
thf(5973,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5653]) ).
thf(5974,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)],[5706]) ).
thf(5975,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SX2 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5869]) ).
thf(5976,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5842]) ).
thf(5977,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)],[5724]) ).
thf(5978,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)],[5862]) ).
thf(5979,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)],[5742]) ).
thf(5980,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)],[5608]) ).
thf(5981,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)],[5837]) ).
thf(5982,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Opreorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5652]) ).
thf(5983,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SX3 @ SX2 @ SX1 ) @ SX0 ) )
| ( SX1
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5703]) ).
thf(5984,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5761]) ).
thf(5985,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5606]) ).
thf(5986,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)],[5592]) ).
thf(5987,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)],[5811]) ).
thf(5988,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SX1 @ SX4 @ SX0 ) @ SX3 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SX1 @ SX4 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5813]) ).
thf(5989,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)],[5825]) ).
thf(5990,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SX1 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5874]) ).
thf(5991,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)],[5836]) ).
thf(5992,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5646]) ).
thf(5993,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)],[5856]) ).
thf(5994,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX3 @ SX1 ) @ SX0 ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX3 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5625]) ).
thf(5995,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( ~ ( ( SX1 != SX0 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) )
| ( SX1 = SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5644]) ).
thf(5996,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Olattice @ SX1 )
| ( class_Lattices_Olattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5877]) ).
thf(5997,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( class_Enum_Oenum @ SX1 )
| ~ ( class_Enum_Oenum @ SX0 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5884]) ).
thf(5998,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)],[5810]) ).
thf(5999,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5679]) ).
thf(6000,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)],[5847]) ).
thf(6001,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)],[5826]) ).
thf(6002,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)],[5848]) ).
thf(6003,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5798]) ).
thf(6004,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5627]) ).
thf(6005,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX0 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5770]) ).
thf(6006,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX5 ) @ SX0 ) )
| ( SX3
!= ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX5 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ ( hAPP @ ( c_Set_Oimage @ SX2 @ SX4 @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5633]) ).
thf(6007,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5598]) ).
thf(6008,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5691]) ).
thf(6009,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5649]) ).
thf(6010,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX1 ) )
| ( SX2 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5650]) ).
thf(6011,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Orderings_Oord @ SX4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ SX4 ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX4 ) @ ( hAPP @ SX2 @ SX0 ) ) @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5669]) ).
thf(6012,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)],[5858]) ).
thf(6013,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5785]) ).
thf(6014,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5692]) ).
thf(6015,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)],[5807]) ).
thf(6016,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)],[5587]) ).
thf(6017,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX2 ) @ SX1 ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5637]) ).
thf(6018,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Groups_Ouminus @ SX1 )
| ( class_Groups_Ouminus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5882]) ).
thf(6019,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)],[5610]) ).
thf(6020,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SX2 @ SX0 ) ) @ ( c_Wellfounded_Oaccp @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5743]) ).
thf(6021,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)],[5855]) ).
thf(6022,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)],[5852]) ).
thf(6023,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)],[5845]) ).
thf(6024,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Fun_Obij__betw @ SX3 @ SX2 @ SX1 @ SX0 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5868]) ).
thf(6025,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ( SX2 != SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5647]) ).
thf(6026,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)],[5595]) ).
thf(6027,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5600]) ).
thf(6028,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5634]) ).
thf(6029,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5583]) ).
thf(6030,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5750]) ).
thf(6031,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Groups_Ominus @ SX1 )
| ( class_Groups_Ominus @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5883]) ).
thf(6032,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SX1 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5872]) ).
thf(6033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5718]) ).
thf(6034,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)],[5835]) ).
thf(6035,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) @ SX0 ) @ SX5 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5769]) ).
thf(6036,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5781]) ).
thf(6037,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5784]) ).
thf(6038,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Opreorder @ SX1 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5875]) ).
thf(6039,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)],[5830]) ).
thf(6040,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX3 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ~ ( ( SX3 != SX0 )
| ( SX2 != SX1 ) ) )
| ~ ( ~ ( ~ ( ( SX3 != SX1 )
| ( SX2 != SX0 ) )
| ~ ( ( SX3 != SX0 )
| ( SX2 != SX1 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX3 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX4 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5618]) ).
thf(6041,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Obot @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ SX1 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5667]) ).
thf(6042,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5651]) ).
thf(6043,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)],[5859]) ).
thf(6044,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX1 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5817]) ).
thf(6045,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)],[5687]) ).
thf(6046,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)],[5814]) ).
thf(6047,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5585]) ).
thf(6048,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oorder @ SX3 )
| ( SX2 != SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5648]) ).
thf(6049,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5791]) ).
thf(6050,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SX1 )
| ~ ( class_Finite__Set_Ofinite @ SX0 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5876]) ).
thf(6051,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)],[5853]) ).
thf(6052,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)],[5591]) ).
thf(6053,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5832]) ).
thf(6054,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)],[5711]) ).
thf(6055,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX1
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5778]) ).
thf(6056,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX2 ) ) )
| ( SX2 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5602]) ).
thf(6057,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Fun_Obij__betw @ SX3 @ SX2 @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX0 )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5867]) ).
thf(6058,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SX4 @ SX1 @ SX0 ) @ SX3 ) ) @ ( hAPP @ ( c_Set_Oimage @ SX4 @ SX1 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5632]) ).
thf(6059,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Finite__Set_Ofolding__one @ SX3 @ SX2 @ SX1 )
| ( ( hAPP @ SX1 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5685]) ).
thf(6060,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SX3 @ SX2 @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SX3 @ SX2 @ SX1 ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5623]) ).
thf(6061,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX1
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SX2 ) @ SX1 ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5779]) ).
thf(6062,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)],[5586]) ).
thf(6063,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5693]) ).
thf(6064,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ~ ( ( SX1
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ~ ( ( SX1
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5763]) ).
thf(6065,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)],[5740]) ).
thf(6066,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX2 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX3 ) @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5628]) ).
thf(6067,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)],[5857]) ).
thf(6068,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)],[5658]) ).
thf(6069,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)],[5744]) ).
thf(6070,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5604]) ).
thf(6071,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Orderings_Oord @ SX3 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ SX3 ) ) @ SX1 ) @ SX0 ) )
| ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ ( hAPP @ SX1 @ SX4 ) ) @ ( hAPP @ SX0 @ SX4 ) ) ) )
| ~ ( ~ ! [SX4: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX3 ) @ ( hAPP @ SX1 @ SX4 ) ) @ ( hAPP @ SX0 @ SX4 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ SX3 ) ) @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5668]) ).
thf(6072,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX3 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX1 @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) @ SX2 ) @ SX5 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5767]) ).
thf(6073,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)],[5772]) ).
thf(6074,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5787]) ).
thf(6075,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Obot @ SX1 )
| ( class_Orderings_Obot @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5881]) ).
thf(6076,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5614]) ).
thf(6077,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX5 @ SX4 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX4 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX1 @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) @ SX5 ) @ SX2 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5799]) ).
thf(6078,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_OCollect @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SX1 ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5819]) ).
thf(6079,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5580]) ).
thf(6080,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5861]) ).
thf(6081,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5590]) ).
thf(6082,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 )
| ( ( hAPP @ SX0 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5684]) ).
thf(6083,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)],[5719]) ).
thf(6084,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)],[5707]) ).
thf(6085,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Opreorder @ SX2 )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5645]) ).
thf(6086,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX2 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5635]) ).
thf(6087,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX3 ) @ SX1 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5762]) ).
thf(6088,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)],[5738]) ).
thf(6089,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SX2 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SX2 @ SX1 ) ) @ ( c_Predicate_OPowp @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5776]) ).
thf(6090,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Opreorder @ SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX1 ) @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5640]) ).
thf(6091,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)],[5805]) ).
thf(6092,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)],[5834]) ).
thf(6093,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5728]) ).
thf(6094,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)],[5806]) ).
thf(6095,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5620]) ).
thf(6096,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)],[5589]) ).
thf(6097,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)],[5611]) ).
thf(6098,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5909]) ).
thf(6099,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)],[5846]) ).
thf(6100,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)],[5593]) ).
thf(6101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX3 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5613]) ).
thf(6102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5599]) ).
thf(6103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Oorder @ SX1 )
| ( class_Orderings_Oorder @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5878]) ).
thf(6104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( c_Finite__Set_Ofold1 @ SX2 @ SX1 ) )
| ( ( hAPP @ SX3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5714]) ).
thf(6105,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)],[5849]) ).
thf(6106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SX1 @ SX1 ) @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SX1 @ SX1 ) @ tc_HOL_Obool ) ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5733]) ).
thf(6107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( hAPP @ ( c_Set_OPow @ SX1 ) @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SX1 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5773]) ).
thf(6108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Fun_Oinj__on @ SX4 @ SX3 @ SX2 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 ) )
| ( c_Fun_Oinj__on @ SX4 @ SX3 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5701]) ).
thf(6109,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)],[5851]) ).
thf(6110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5780]) ).
thf(6111,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)],[5864]) ).
thf(6112,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5656]) ).
thf(6113,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SX0
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) )
| ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5607]) ).
thf(6114,plain,
( ( ! [SX0: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SX0 @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5803]) ).
thf(6115,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)],[5833]) ).
thf(6116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5786]) ).
thf(6117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Orderings_Oord @ SX1 )
| ( class_Orderings_Oord @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5880]) ).
thf(6118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX1 ) @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5745]) ).
thf(6119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SX4 @ SX3 @ SX2 @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5696]) ).
thf(6120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX2 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5655]) ).
thf(6121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Orderings_Oord @ SX4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ SX4 ) ) @ SX2 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SX4 ) @ ( hAPP @ SX2 @ SX0 ) ) @ ( hAPP @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5670]) ).
thf(6122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5727]) ).
thf(6123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SX2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5621]) ).
thf(6124,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)],[5829]) ).
thf(6125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX0 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
!= SX0 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5758]) ).
thf(6126,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SX1 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5642]) ).
thf(6127,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)],[5865]) ).
thf(6128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2 != SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX0 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5601]) ).
thf(6129,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)],[5739]) ).
thf(6130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Obot @ SX2 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ SX2 ) ) @ SX0 )
= ( c_Orderings_Obot__class_Obot @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5641]) ).
thf(6131,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)],[5828]) ).
thf(6132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5759]) ).
thf(6133,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX2 @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5746]) ).
thf(6134,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX1 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5871]) ).
thf(6135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ SX3 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX1 @ tc_HOL_Obool ) ) @ SX3 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5660]) ).
thf(6136,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5731]) ).
thf(6137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
| ( SX1
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5638]) ).
thf(6138,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)],[5860]) ).
thf(6139,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)],[5741]) ).
thf(6140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5665]) ).
thf(6141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5659]) ).
thf(6142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ SX0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SX3 @ tc_HOL_Obool ) ) @ SX0 ) @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5678]) ).
thf(6143,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)],[5708]) ).
thf(6144,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)],[5674]) ).
thf(6145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX1 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SX2 ) @ SX0 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_HOL_Obool ) ) ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5617]) ).
thf(6146,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SX5 @ ( tc_fun @ SX4 @ tc_HOL_Obool ) ) ) @ SX3 ) @ SX2 ) @ SX1 ) @ SX0 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SX3 @ SX1 ) @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5768]) ).
thf(6147,plain,
! [SV1: $i] :
( ( ! [SY1156: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1156 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1156 @ tc_HOL_Obool ) ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5582]) ).
thf(6148,plain,
! [SV2: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV2 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(6149,plain,
! [SV3: $i] :
( ( ! [SY1157: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1157 ) @ SV3 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1157 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(6150,plain,
! [SV4: $i] :
( ( ! [SY1158: $i,SY1159: $i,SY1160: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1160 ) @ SY1159 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1160 ) @ SY1158 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1160 ) @ SY1158 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1160 ) @ SY1159 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(6151,plain,
! [SV5: $i] :
( ( ! [SY1161: $i,SY1162: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1162 ) @ SY1161 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1162 ) @ SY1161 ) @ SV5 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1162 ) @ SY1161 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(6152,plain,
! [SV6: $i] :
( ( ! [SY1163: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1163 @ tc_HOL_Obool ) ) @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(6153,plain,
! [SV7: $i] :
( ( ! [SY1164: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1164 ) @ SV7 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1164 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(6154,plain,
! [SV8: $i] :
( ( ! [SY1165: $i,SY1166: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1166 ) @ SY1165 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1166 ) @ SY1165 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(6155,plain,
! [SV9: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV9 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV9 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5616]) ).
thf(6156,plain,
! [SV10: $i] :
( ( ! [SY1167: $i,SY1168: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY1168 @ SY1167 @ SV10 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1168 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1167 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5624]) ).
thf(6157,plain,
! [SV11: $i] :
( ( ! [SY1169: $i,SY1170: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1170 @ tc_HOL_Obool ) ) @ SY1169 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1170 ) @ SV11 ) @ SY1169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(6158,plain,
! [SV12: $i] :
( ( ! [SY1171: $i,SY1172: $i,SY1173: $i,SY1174: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY1174 @ SY1173 @ SY1172 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1174 ) @ SY1171 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1173 ) @ ( hAPP @ SY1172 @ SY1171 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1174 @ SY1173 @ SY1172 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(6159,plain,
! [SV13: $i] :
( ( ! [SY1175: $i] :
( ( c_Set_Othe__elem @ SY1175 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1175 ) @ SV13 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1175 @ tc_HOL_Obool ) ) ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(6160,plain,
! [SV14: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5662]) ).
thf(6161,plain,
! [SV15: $i] :
( ( ! [SY1176: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1176 ) @ SV15 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV15 ) @ SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5663]) ).
thf(6162,plain,
! [SV16: $i] :
( ( ! [SY1177: $i,SY1178: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1178 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1178 @ tc_HOL_Obool ) ) @ SY1177 ) @ SV16 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1178 @ tc_HOL_Obool ) ) @ SY1177 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5672]) ).
thf(6163,plain,
! [SV17: $i] :
( ( ! [SY1179: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1179 @ tc_HOL_Obool ) ) @ SV17 ) @ SV17 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1179 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5675]) ).
thf(6164,plain,
! [SV18: $i] :
( ( ! [SY1180: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1180 @ tc_HOL_Obool ) ) @ SV18 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1180 @ tc_HOL_Obool ) ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(6165,plain,
! [SV19: $i] :
( ( ! [SY1181: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1181 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1181 @ tc_HOL_Obool ) ) ) @ SV19 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1181 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5677]) ).
thf(6166,plain,
! [SV20: $i] :
( ( ! [SY1182: $i,SY1183: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1183 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1183 @ tc_HOL_Obool ) ) @ SY1182 ) @ SV20 ) ) @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(6167,plain,
! [SV21: $i] :
( ( ! [SY1184: $i,SY1185: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1185 ) @ SY1184 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1185 @ tc_HOL_Obool ) ) @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1185 ) @ SY1184 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1185 @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1185 ) @ SY1184 ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(6168,plain,
! [SV22: $i] :
( ( ! [SY1186: $i,SY1187: $i,SY1188: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1188 @ tc_HOL_Obool ) ) @ SY1187 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1188 ) @ SY1186 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1188 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1188 @ tc_HOL_Obool ) ) @ SY1187 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1188 ) @ SY1186 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1188 @ tc_HOL_Obool ) ) ) ) ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(6169,plain,
! [SV23: $i] :
( ( ! [SY1189: $i,SY1190: $i,SY1191: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) ) @ SY1190 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1191 ) @ SY1189 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) ) @ SY1190 ) @ SV23 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1191 ) @ SY1189 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1191 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(6170,plain,
! [SV24: $i] :
( ( ! [SY1192: $i,SY1193: $i,SY1194: $i] : ( c_Nitpick_Ofold__graph_H @ SY1194 @ SY1193 @ SY1192 @ SV24 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1194 @ tc_HOL_Obool ) ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(6171,plain,
! [SV25: $i] :
( ( ! [SY1195: $i,SY1196: $i,SY1197: $i] : ( c_Nitpick_Ofold__graph_H @ SY1197 @ SY1196 @ SY1195 @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1197 @ tc_HOL_Obool ) ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(6172,plain,
! [SV26: $i] :
( ( ! [SY1198: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1198 @ tc_HOL_Obool ) ) @ SV26 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1198 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(6173,plain,
! [SV27: $i] :
( ( ! [SY1199: $i,SY1200: $i,SY1201: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY1201 @ SY1200 @ SY1199 @ SV27 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1201 @ tc_HOL_Obool ) ) ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(6174,plain,
! [SV28: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY1204 @ SY1203 @ SY1202 @ SV28 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1204 @ tc_HOL_Obool ) ) ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(6175,plain,
! [SV29: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ SV29 @ ( tc_fun @ SV29 @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(6176,plain,
! [SV30: $i] :
( ( ! [SY1205: $i,SY1206: $i] : ( c_Fun_Oinj__on @ SY1206 @ SY1205 @ SV30 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1206 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(6177,plain,
! [SV31: $i] :
( ( ! [SY1207: $i,SY1208: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY1208 @ SY1207 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1208 @ tc_HOL_Obool ) ) ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(6178,plain,
! [SV32: $i] :
( ( ! [SY1209: $i,SY1210: $i,SY1211: $i] :
( ( c_Fun_Ofun__upd @ SY1211 @ SY1210 @ SY1209 @ SV32 @ ( hAPP @ SY1209 @ SV32 ) )
= SY1209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(6179,plain,
! [SV33: $i] :
( ( ! [SY1212: $i,SY1213: $i,SY1214: $i,SY1215: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY1215 @ SY1214 @ SY1213 @ SY1212 @ SV33 ) @ SY1212 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(6180,plain,
! [SV34: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i,SY1219: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY1219 @ SY1218 @ SY1217 ) @ SY1216 ) @ SV34 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1218 @ tc_HOL_Obool ) ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5712]) ).
thf(6181,plain,
! [SV35: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ SY1221 @ SY1220 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1221 ) @ SV35 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1221 @ tc_HOL_Obool ) ) ) )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(6182,plain,
! [SV36: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV36 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5715]) ).
thf(6183,plain,
! [SV37: $i] :
( ( ! [SY1222: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1222 ) @ SV37 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV37 ) @ SY1222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(6184,plain,
! [SV38: $i] :
( ( ! [SY1223: $i,SY1224: $i,SY1225: $i,SY1226: $i,SY1227: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1227 @ SY1226 @ SY1225 @ SY1224 ) @ SY1223 ) @ SV38 )
= ( hAPP @ SY1224 @ ( hAPP @ SY1223 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5721]) ).
thf(6185,plain,
! [SV39: $i] :
( ( ! [SY1228: $i,SY1229: $i,SY1230: $i,SY1231: $i,SY1232: $i,SY1233: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1233 @ SY1232 @ SY1231 @ SY1230 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY1229 @ SY1233 @ SY1231 @ SY1228 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY1229 @ SY1232 @ SY1231 @ ( hAPP @ ( c_Fun_Ocomp @ SY1233 @ SY1232 @ SY1229 @ SY1230 ) @ SY1228 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5722]) ).
thf(6186,plain,
! [SV40: $i] :
( ( ! [SY1234: $i,SY1235: $i,SY1236: $i,SY1237: $i,SY1238: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1238 @ SY1237 @ SY1236 @ SY1235 ) @ SY1234 ) @ SV40 )
= ( hAPP @ SY1235 @ ( hAPP @ SY1234 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5723]) ).
thf(6187,plain,
! [SV41: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY1241 @ SY1240 @ SY1239 ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1241 @ tc_HOL_Obool ) ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(6188,plain,
! [SV42: $i] :
( ( ! [SY1242: $i] :
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1242 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1242 @ tc_HOL_Obool ) ) @ SV42 ) )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5730]) ).
thf(6189,plain,
! [SV43: $i] :
( ( ! [SY1243: $i,SY1244: $i,SY1245: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1245 @ ( tc_fun @ SY1244 @ tc_HOL_Obool ) ) ) @ SY1243 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5732]) ).
thf(6190,plain,
! [SV44: $i] :
( ( ! [SY1246: $i,SY1247: $i,SY1248: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1248 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SY1247 ) @ SY1246 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1248 ) @ SY1247 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1248 @ tc_HOL_Obool ) ) @ SY1246 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5747]) ).
thf(6191,plain,
! [SV45: $i] :
( ( ! [SY1249: $i,SY1250: $i,SY1251: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1251 @ tc_HOL_Obool ) ) @ SY1250 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1251 ) @ SY1249 ) @ SV45 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1251 ) @ SY1249 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1251 @ tc_HOL_Obool ) ) @ SY1250 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(6192,plain,
! [SV46: $i] :
( ( ! [SY1252: $i,SY1253: $i,SY1254: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1254 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1254 @ tc_HOL_Obool ) ) @ SY1253 ) @ SY1252 ) ) @ SV46 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1254 @ tc_HOL_Obool ) ) @ SY1253 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1254 @ tc_HOL_Obool ) ) @ SY1252 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(6193,plain,
! [SV47: $i] :
( ( ! [SY1255: $i,SY1256: $i,SY1257: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1257 @ tc_HOL_Obool ) ) @ SY1256 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1257 @ tc_HOL_Obool ) ) @ SY1255 ) @ SV47 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1257 @ tc_HOL_Obool ) ) @ SY1255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1257 @ tc_HOL_Obool ) ) @ SY1256 ) @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5752]) ).
thf(6194,plain,
! [SV48: $i] :
( ( ! [SY1258: $i,SY1259: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1259 @ tc_HOL_Obool ) ) @ SY1258 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1259 @ tc_HOL_Obool ) ) @ SY1258 ) @ SV48 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1259 @ tc_HOL_Obool ) ) @ SY1258 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5753]) ).
thf(6195,plain,
! [SV49: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1261 @ tc_HOL_Obool ) ) @ SY1260 ) @ SV49 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1261 @ tc_HOL_Obool ) ) @ SV49 ) @ SY1260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(6196,plain,
! [SV50: $i] :
( ( ! [SY1262: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1262 @ tc_HOL_Obool ) ) @ SV50 ) @ SV50 )
= SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5755]) ).
thf(6197,plain,
! [SV51: $i] :
( ( ! [SY1263: $i,SY1264: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1264 @ tc_HOL_Obool ) ) @ SY1263 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1264 @ tc_HOL_Obool ) ) @ SY1263 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(6198,plain,
! [SV52: $i] :
( ( ! [SY1265: $i,SY1266: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1266 @ tc_HOL_Obool ) ) @ SY1265 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1266 @ tc_HOL_Obool ) ) @ SV52 ) @ SY1265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(6199,plain,
! [SV53: $i] :
( ( ! [SY1267: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1267 @ tc_HOL_Obool ) ) @ SV53 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1267 @ tc_HOL_Obool ) ) )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(6200,plain,
! [SV54: $i] :
( ( ! [SY1268: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1268 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1268 @ tc_HOL_Obool ) ) ) @ SV54 )
= SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5765]) ).
thf(6201,plain,
! [SV55: $i] :
( ( ! [SY1269: $i,SY1270: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1270 ) @ SY1269 ) @ SV55 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1270 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1270 ) @ SY1269 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1270 @ tc_HOL_Obool ) ) ) ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5766]) ).
thf(6202,plain,
! [SV56: $i] :
( ( ( hAPP @ ( c_Set_OPow @ SV56 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV56 @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_fun @ SV56 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV56 @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV56 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(6203,plain,
! [SV57: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ( hAPP @ ( c_Relation_OImage @ SY1272 @ SY1271 @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1272 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1271 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(6204,plain,
! [SV58: $i] :
( ( ! [SY1273: $i] :
( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1273 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1273 @ tc_HOL_Obool ) ) ) @ SV58 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1273 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5777]) ).
thf(6205,plain,
! [SV59: $i] :
( ( ! [SY1274: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1274 @ tc_HOL_Obool ) ) @ SV59 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1274 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1274 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5782]) ).
thf(6206,plain,
! [SV60: $i] :
( ( ! [SY1275: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1275 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1275 @ tc_HOL_Obool ) ) ) @ SV60 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1275 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5783]) ).
thf(6207,plain,
! [SV61: $i] :
( ( ! [SY1276: $i,SY1277: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1277 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1277 @ tc_HOL_Obool ) ) @ SY1276 ) @ SV61 ) ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5788]) ).
thf(6208,plain,
! [SV62: $i] :
( ( ! [SY1278: $i,SY1279: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1279 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1279 @ tc_HOL_Obool ) ) @ SY1278 ) @ SV62 ) ) @ SY1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5789]) ).
thf(6209,plain,
! [SV63: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1282 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1282 @ tc_HOL_Obool ) ) @ SY1281 ) @ SY1280 ) ) @ SV63 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1282 @ tc_HOL_Obool ) ) @ SY1281 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1282 @ tc_HOL_Obool ) ) @ SY1280 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5792]) ).
thf(6210,plain,
! [SV64: $i] :
( ( ! [SY1283: $i,SY1284: $i,SY1285: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1285 @ tc_HOL_Obool ) ) @ SY1284 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1285 @ tc_HOL_Obool ) ) @ SY1283 ) @ SV64 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1285 @ tc_HOL_Obool ) ) @ SY1283 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1285 @ tc_HOL_Obool ) ) @ SY1284 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5793]) ).
thf(6211,plain,
! [SV65: $i] :
( ( ! [SY1286: $i,SY1287: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1287 @ tc_HOL_Obool ) ) @ SY1286 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1287 @ tc_HOL_Obool ) ) @ SY1286 ) @ SV65 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1287 @ tc_HOL_Obool ) ) @ SY1286 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5794]) ).
thf(6212,plain,
! [SV66: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1289 @ tc_HOL_Obool ) ) @ SY1288 ) @ SV66 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1289 @ tc_HOL_Obool ) ) @ SV66 ) @ SY1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5795]) ).
thf(6213,plain,
! [SV67: $i] :
( ( ! [SY1290: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1290 @ tc_HOL_Obool ) ) @ SV67 ) @ SV67 )
= SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5796]) ).
thf(6214,plain,
! [SV68: $i] :
( ( ! [SY1291: $i,SY1292: $i,SY1293: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1293 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1293 ) @ SY1292 ) @ SY1291 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1293 ) @ SY1292 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1293 ) @ SY1292 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1293 @ tc_HOL_Obool ) ) @ SY1291 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(6215,plain,
! [SV69: $i] :
( ( ! [SY1294: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) @ SV69 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY1294 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5802]) ).
thf(6216,plain,
! [SV70: $i] :
( ( ! [SY1295: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY1295 @ tc_HOL_Obool ) ) @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(6217,plain,
! [SV71: $i] :
( ( ! [SY1296: $i,SY1297: $i] :
( ( hAPP @ ( c_Set_Ovimage @ SY1297 @ SY1296 @ SV71 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1296 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1297 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(6218,plain,
! [SV72: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV72 @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV72 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV72 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5816]) ).
thf(6219,plain,
! [SV73: $i] :
( ( ! [SY1298: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY1298 ) @ SV73 )
= SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(6220,plain,
! [SV74: $i] :
( ( ! [SY1299: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY1299 ) @ SV74 )
= SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5821]) ).
thf(6221,plain,
! [SV75: $i] :
( ( ! [SY1300: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY1300 ) @ SV75 )
= SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5822]) ).
thf(6222,plain,
! [SV76: $i] :
( ( ! [SY1301: $i,SY1302: $i,SY1303: $i,SY1304: $i,SY1305: $i,SY1306: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1306 @ SY1305 @ SY1304 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1306 @ SY1303 @ SY1305 ) @ SY1302 ) @ SY1301 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1306 @ SY1303 @ SY1304 ) @ SY1302 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1303 @ SY1305 @ SY1304 ) @ SY1301 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(6223,plain,
! [SV77: $i] :
( ( ! [SY1307: $i,SY1308: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY1308 @ SY1307 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY1307 @ SY1308 ) @ SV77 ) )
= SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5838]) ).
thf(6224,plain,
! [SV78: $i] :
( ( ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( hAPP @ SY1311 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1310 @ SY1310 ) @ SY1309 ) @ SY1311 ) @ SV78 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY1310 @ SY1310 ) @ SY1309 ) @ SY1311 ) @ ( hAPP @ SY1311 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5839]) ).
thf(6225,plain,
! [SV79: $i] :
( ( ! [SY1312: $i] : ( c_Relation_Ototal__on @ SY1312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1312 @ tc_HOL_Obool ) ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5840]) ).
thf(6226,plain,
! [SV80: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i,SY1316: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1316 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1316 @ SY1315 ) @ SY1314 ) @ SY1313 ) ) @ SY1314 ) @ SV80 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1316 @ SY1315 ) @ SY1314 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(6227,plain,
! [SV81: $i] :
( ( ! [SY1317: $i,SY1318: $i,SY1319: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1319 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1319 ) @ SY1318 ) @ SY1317 ) ) @ SV81 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1319 ) @ SY1318 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1319 ) @ SY1317 ) @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5850]) ).
thf(6228,plain,
! [SV82: $i] :
( ( ! [SY1320: $i] :
( ( hAPP @ ( c_List_Orev @ SY1320 ) @ ( hAPP @ ( c_List_Orev @ SY1320 ) @ SV82 ) )
= SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5854]) ).
thf(6229,plain,
! [SV83: $i] :
( ( ! [SY1321: $i] :
( ( hAPP @ ( c_COMBI @ SY1321 ) @ SV83 )
= SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5903]) ).
thf(6230,plain,
! [SV84: $i] :
( ( ! [SY1322: $i,SY1323: $i,SY1324: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY1324 @ SY1323 ) @ SY1322 ) @ SV84 )
= SY1322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(6231,plain,
! [SV85: $i] :
( ( ! [SY1325: $i,SY1326: $i,SY1327: $i,SY1328: $i,SY1329: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY1329 @ SY1328 @ SY1327 ) @ SY1326 ) @ SY1325 ) @ SV85 )
= ( hAPP @ SY1326 @ ( hAPP @ SY1325 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(6232,plain,
! [SV86: $i] :
( ( ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i,SY1334: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY1334 @ SY1333 @ SY1332 ) @ SY1331 ) @ SY1330 ) @ SV86 )
= ( hAPP @ ( hAPP @ SY1331 @ SV86 ) @ SY1330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5906]) ).
thf(6233,plain,
! [SV87: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i,SY1338: $i,SY1339: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY1339 @ SY1338 @ SY1337 ) @ SY1336 ) @ SY1335 ) @ SV87 )
= ( hAPP @ ( hAPP @ SY1336 @ SV87 ) @ ( hAPP @ SY1335 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5907]) ).
thf(6234,plain,
! [SV88: $i] :
( ( ! [SY1340: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY1340 ) @ SV88 ) )
| ( SY1340 = SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5908]) ).
thf(6235,plain,
( ( hBOOL @ c_fFalse )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6236,plain,
! [SV89: $i] :
( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV89 ) )
| ~ ( hBOOL @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5912]) ).
thf(6237,plain,
! [SV90: $i] :
( ( ~ ~ ( hBOOL @ SV90 )
| ( hBOOL @ ( hAPP @ c_fNot @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5913]) ).
thf(6238,plain,
! [SV91: $i] :
( ( ! [SY1341: $i] :
( ~ ( hBOOL @ SY1341 )
| ~ ( hBOOL @ SV91 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1341 ) @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5914]) ).
thf(6239,plain,
! [SV92: $i] :
( ( ! [SY1342: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1342 ) @ SV92 ) )
| ( hBOOL @ SY1342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5915]) ).
thf(6240,plain,
! [SV93: $i] :
( ( ! [SY1343: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SY1343 ) @ SV93 ) )
| ( hBOOL @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5916]) ).
thf(6241,plain,
! [SV94: $i] :
( ( ! [SY1344: $i] :
( ~ ( hBOOL @ SY1344 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY1344 ) @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5917]) ).
thf(6242,plain,
! [SV95: $i] :
( ( ! [SY1345: $i] :
( ~ ( hBOOL @ SY1345 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV95 ) @ SY1345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5918]) ).
thf(6243,plain,
! [SV96: $i] :
( ( ! [SY1346: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SY1346 ) @ SV96 ) )
| ( hBOOL @ SY1346 )
| ( hBOOL @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5919]) ).
thf(6244,plain,
! [SV97: $i] :
( ( ! [SY1347: $i] :
( ( hBOOL @ SY1347 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY1347 ) @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5920]) ).
thf(6245,plain,
! [SV98: $i] :
( ( ! [SY1348: $i] :
( ~ ( hBOOL @ SY1348 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV98 ) @ SY1348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5921]) ).
thf(6246,plain,
! [SV99: $i] :
( ( ! [SY1349: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SY1349 ) @ SV99 ) )
| ~ ( hBOOL @ SY1349 )
| ( hBOOL @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5922]) ).
thf(6247,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ ( hAPP @ v_mgt__call @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) ) ) @ v_G ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(6248,plain,
! [SV100: $i] :
( ( ! [SY1350: $i,SY1351: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1351 @ SY1350 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1350 @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5924]) ).
thf(6249,plain,
! [SV101: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1354 @ SY1353 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1352 @ tc_HOL_Obool ) ) @ SV101 ) @ SY1354 ) @ SY1353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5925]) ).
thf(6250,plain,
! [SV102: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ~ ( class_Orderings_Obot @ SY1356 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1355 @ SY1356 ) ) @ SV102 )
= ( c_Orderings_Obot__class_Obot @ SY1356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(6251,plain,
! [SV103: $i] :
( ( ! [SY1357: $i,SY1358: $i,SY1359: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY1359 @ SY1358 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1359 ) @ SY1357 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1359 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SY1357 = SV103 ) )
| ~ ( ( SY1357 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY1359 @ SY1358 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1359 ) @ SY1357 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1359 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5927]) ).
thf(6252,plain,
! [SV104: $i] :
( ( ! [SY1360: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) @ SV104 ) ) )
| ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1360 @ tc_HOL_Obool ) ) @ SV104 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5928]) ).
thf(6253,plain,
! [SV105: $i] :
( ( ! [SY1361: $i,SY1362: $i,SY1363: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1363 @ tc_HOL_Obool ) ) @ SY1362 ) @ SY1361 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1363 @ tc_HOL_Obool ) ) @ SY1361 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1363 @ tc_HOL_Obool ) ) @ SY1362 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5929]) ).
thf(6254,plain,
! [SV106: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1365 ) @ SY1364 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1364 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1365 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5930]) ).
thf(6255,plain,
! [SV107: $i] :
( ( ! [SY1366: $i,SY1367: $i,SY1368: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1368 @ tc_HOL_Obool ) ) @ SY1367 ) @ SY1366 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1368 @ tc_HOL_Obool ) ) @ SY1367 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1368 ) @ SV107 ) @ SY1366 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5931]) ).
thf(6256,plain,
! [SV108: $i] :
( ( ! [SY1369: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) ) )
| ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1369 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(6257,plain,
! [SV109: $i] :
( ( ! [SY1370: $i,SY1371: $i,SY1372: $i,SY1373: $i,SY1374: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY1374 @ SY1373 @ SY1372 )
| ( ( hAPP @ ( hAPP @ SY1372 @ SY1371 ) @ ( hAPP @ ( hAPP @ SY1372 @ SY1370 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SY1372 @ SY1370 ) @ ( hAPP @ ( hAPP @ SY1372 @ SY1371 ) @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5933]) ).
thf(6258,plain,
! [SV110: $i] :
( ( ! [SY1375: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SY1375 @ SV110 )
| ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
| ~ ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SY1375 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5934]) ).
thf(6259,plain,
! [SV111: $i] :
( ( ! [SY1380: $i] :
( ( SY1380 != SV111 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1380 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5935]) ).
thf(6260,plain,
! [SV112: $i] :
( ( ! [SY1381: $i] :
( ~ ( class_Orderings_Otop @ SY1381 )
| ( class_Orderings_Otop @ ( tc_fun @ SV112 @ SY1381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5936]) ).
thf(6261,plain,
! [SV113: $i] :
( ( ! [SY1382: $i,SY1383: $i,SY1384: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1384 ) @ SY1383 ) @ SY1382 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SY1382 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1384 ) @ SY1383 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SY1382 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SY1382 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1384 @ tc_HOL_Obool ) ) @ SY1382 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1384 ) @ SY1383 ) @ SV113 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5937]) ).
thf(6262,plain,
! [SV114: $i] :
( ( ! [SY1385: $i,SY1386: $i,SY1387: $i,SY1388: $i,SY1389: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1389 @ SY1388 ) @ SY1387 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1386 @ ( tc_fun @ SY1385 @ tc_HOL_Obool ) ) ) @ SY1389 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SY1388 ) @ SY1387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5938]) ).
thf(6263,plain,
! [SV115: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV115 )
!= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5939]) ).
thf(6264,plain,
! [SV116: $i] :
( ( ! [SY1390: $i,SY1391: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SY1390 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) @ SV116 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY1391 @ tc_HOL_Obool ) @ SY1390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5940]) ).
thf(6265,plain,
! [SV117: $i] :
( ( ! [SY1392: $i,SY1393: $i,SY1394: $i,SY1395: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY1395 @ SY1394 @ SY1393 @ SY1392 @ SV117 )
!= SY1393 )
| ( ( hAPP @ SY1393 @ SY1392 )
= SV117 ) )
| ~ ( ( ( hAPP @ SY1393 @ SY1392 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SY1395 @ SY1394 @ SY1393 @ SY1392 @ SV117 )
= SY1393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5941]) ).
thf(6266,plain,
! [SV118: $i] :
( ( ! [SY1396: $i,SY1397: $i,SY1398: $i,SY1399: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1399 ) @ SY1398 ) @ SY1397 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1399 ) @ SY1396 ) @ SV118 ) )
| ~ ( ( SY1398 != SY1396 )
| ( SY1397 != SV118 ) ) )
| ~ ( ~ ~ ( ( SY1398 != SY1396 )
| ( SY1397 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1399 ) @ SY1398 ) @ SY1397 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1399 ) @ SY1396 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5942]) ).
thf(6267,plain,
! [SV119: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( c_Wellfounded_OwfP @ SY1401 @ SY1400 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1401 @ ( tc_fun @ SY1401 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SY1400 ) )
| ( c_Wellfounded_OwfP @ SY1401 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5943]) ).
thf(6268,plain,
! [SV120: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1404 ) @ SY1403 ) @ SY1402 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1404 ) @ SY1403 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1404 ) @ SV120 ) @ SY1402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5944]) ).
thf(6269,plain,
! [SV121: $i] :
( ( ! [SY1405: $i,SY1406: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1406 ) @ SY1405 ) @ SV121 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1406 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5945]) ).
thf(6270,plain,
! [SV122: $i] :
( ( ! [SY1407: $i,SY1408: $i,SY1409: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1409 @ tc_HOL_Obool ) ) @ SY1408 ) @ SY1407 ) @ SV122 ) )
| ( hBOOL @ ( hAPP @ SY1407 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5946]) ).
thf(6271,plain,
! [SV123: $i] :
( ( ! [SY1410: $i,SY1411: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1411 ) @ SY1410 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SY1410 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV123 @ SY1410 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1411 ) @ SY1410 ) @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5947]) ).
thf(6272,plain,
! [SV124: $i] :
( ( ! [SY1412: $i,SY1413: $i,SY1414: $i,SY1415: $i,SY1416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1416 @ ( tc_fun @ SY1415 @ tc_HOL_Obool ) ) ) @ SY1414 ) @ SY1413 ) @ SY1412 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1413 @ SY1412 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6273,plain,
! [SV125: $i] :
( ( ! [SY1417: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1417 ) @ SV125 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SY1417 ) )
| ( SY1417 = SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5949]) ).
thf(6274,plain,
! [SV126: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i] :
( ~ ( class_Orderings_Oorder @ SY1420 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1420 ) @ SY1419 ) @ SY1418 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1420 ) @ SV126 ) @ SY1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1420 ) @ SV126 ) @ SY1418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5950]) ).
thf(6275,plain,
! [SV127: $i] :
( ( ! [SY1421: $i,SY1422: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1422 @ tc_HOL_Obool ) ) @ SY1421 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1422 @ tc_HOL_Obool ) ) @ SY1421 ) @ SV127 ) )
| ~ ( ( SY1421 != SV127 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1422 @ tc_HOL_Obool ) ) @ SY1421 ) @ SV127 ) )
| ~ ( ( SY1421 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1422 @ tc_HOL_Obool ) ) @ SY1421 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5951]) ).
thf(6276,plain,
! [SV128: $i] :
( ( ! [SY1423: $i,SY1424: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1424 @ SX3 ) )
| ! [SY1426: $i,SY1427: $i] : ( hBOOL @ ( hAPP @ SY1424 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1423 @ SV128 ) @ SY1426 ) @ SY1427 ) ) ) )
| ~ ( ~ ! [SY1428: $i,SY1429: $i] : ( hBOOL @ ( hAPP @ SY1424 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1423 @ SV128 ) @ SY1428 ) @ SY1429 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY1424 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5952]) ).
thf(6277,plain,
! [SV129: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY1433 @ SY1432 @ SY1431 )
| ( ( hAPP @ ( hAPP @ SY1432 @ SV129 ) @ SV129 )
= SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5953]) ).
thf(6278,plain,
! [SV130: $i] :
( ( ! [SY1434: $i,SY1435: $i] :
( ~ ( c_Predicate_Oreflp @ SY1435 @ SY1434 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1434 @ SV130 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5954]) ).
thf(6279,plain,
! [SV131: $i] :
( ( ! [SY1436: $i,SY1437: $i,SY1438: $i,SY1439: $i,SY1440: $i,SY1441: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SY1437 ) @ SY1436 ) @ SV131 ) )
| ~ ! [SY1442: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1438 @ SY1436 ) @ SY1442 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1442 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY1443: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1438 @ SY1436 ) @ SY1443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1443 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SY1437 ) @ SY1436 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5955]) ).
thf(6280,plain,
! [SV132: $i] :
( ( ! [SY1444: $i,SY1445: $i,SY1446: $i,SY1447: $i,SY1448: $i,SY1449: $i,SY1450: $i,SY1451: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1451 @ SY1450 @ SY1449 @ SY1448 ) @ SY1447 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1446 @ SY1450 @ SY1449 @ SY1445 ) @ SY1444 ) )
| ( ( hAPP @ SY1448 @ ( hAPP @ SY1447 @ SV132 ) )
= ( hAPP @ SY1445 @ ( hAPP @ SY1444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(6281,plain,
! [SV133: $i] :
( ( ! [SY1452: $i,SY1453: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1453 @ tc_HOL_Obool ) ) @ SY1452 ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1453 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SY1453 ) @ SY1452 ) ) @ ( hAPP @ ( c_Set_OPow @ SY1453 ) @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5957]) ).
thf(6282,plain,
! [SV134: $i] :
( ( ! [SY1454: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1454 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SY1454 ) @ SV134 ) )
| ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
| ~ ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1454 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SY1454 ) @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5958]) ).
thf(6283,plain,
! [SV135: $i] :
( ( ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i,SY1461: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1461 @ ( tc_fun @ SY1460 @ tc_HOL_Obool ) ) ) @ SY1459 ) @ SY1458 ) @ SY1457 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1459 @ SY1457 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5959]) ).
thf(6284,plain,
! [SV136: $i] :
( ( ! [SY1462: $i,SY1463: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1463 @ tc_HOL_Obool ) ) @ SY1462 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1463 @ tc_HOL_Obool ) ) @ SY1462 ) @ SV136 ) )
| ( SY1462 = SV136 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1463 @ tc_HOL_Obool ) ) @ SY1462 ) @ SV136 ) )
| ( SY1462 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1463 @ tc_HOL_Obool ) ) @ SY1462 ) @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(6285,plain,
! [SV137: $i] :
( ( ! [SY1464: $i,SY1465: $i,SY1466: $i] :
( ~ ( c_Predicate_Osymp @ SY1466 @ SY1465 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1465 @ SY1464 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1465 @ SV137 ) @ SY1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5961]) ).
thf(6286,plain,
! [SV138: $i] :
( ( ! [SY1467: $i,SY1468: $i] :
( ~ ( class_Orderings_Olinorder @ SY1468 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1468 ) @ SY1467 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1468 ) @ SV138 ) @ SY1467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5962]) ).
thf(6287,plain,
! [SV139: $i] :
( ( ! [SY1469: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SY1469 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV139 @ SY1469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5963]) ).
thf(6288,plain,
! [SV140: $i] :
( ( ! [SY1470: $i,SY1471: $i] :
( SY1471
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1470 ) @ SV140 ) @ SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5964]) ).
thf(6289,plain,
! [SV141: $i] :
( ( ! [SY1472: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ SY1472 ) @ SV141 ) )
| ( v_P @ SV141 @ SY1472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5965]) ).
thf(6290,plain,
! [SV142: $i] :
( ( ! [SY1473: $i,SY1474: $i,SY1475: $i,SY1476: $i,SY1477: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1477 @ ( tc_fun @ SY1476 @ tc_HOL_Obool ) ) ) @ SY1475 ) @ SY1474 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1475 @ SY1473 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1474 @ SY1473 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5966]) ).
thf(6291,plain,
! [SV143: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1480 @ tc_HOL_Obool ) ) @ SY1479 ) @ SY1478 ) )
| ~ ( hBOOL @ ( hAPP @ SY1479 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SY1478 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5967]) ).
thf(6292,plain,
! [SV144: $i] :
( ( ! [SY1481: $i,SY1482: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1482 @ tc_HOL_Obool ) ) @ SY1481 ) @ SV144 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1482 ) @ SV144 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1482 ) @ SY1481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5968]) ).
thf(6293,plain,
! [SV145: $i] :
( ( ! [SY1483: $i,SY1484: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1484 @ tc_HOL_Obool ) ) @ SY1483 ) @ SV145 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1484 @ tc_HOL_Obool ) ) @ SV145 ) @ SY1483 )
= SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5969]) ).
thf(6294,plain,
! [SV146: $i] :
( ( ! [SY1485: $i,SY1486: $i,SY1487: $i,SY1488: $i,SY1489: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SY1487 ) @ SY1486 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SY1485 ) @ SV146 ) )
| ~ ( ( SY1487 != SY1485 )
| ( SY1486 != SV146 ) ) )
| ~ ( ~ ~ ( ( SY1487 != SY1485 )
| ( SY1486 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SY1487 ) @ SY1486 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1489 @ SY1488 ) @ SY1485 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5970]) ).
thf(6295,plain,
! [SV147: $i] :
( ( ! [SY1490: $i,SY1491: $i,SY1492: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1492 @ tc_HOL_Obool ) ) @ SY1491 ) @ SY1490 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1492 ) @ SV147 ) @ SY1491 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1492 ) @ SV147 ) @ SY1490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5971]) ).
thf(6296,plain,
! [SV148: $i] :
( ( ! [SY1493: $i,SY1494: $i,SY1495: $i,SY1496: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1496 @ SY1495 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1495 @ SY1494 ) @ SY1493 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1495 @ SY1493 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1495 @ SY1494 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5972]) ).
thf(6297,plain,
! [SV149: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
( ~ ( class_Orderings_Oorder @ SY1498 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1498 ) @ SY1497 ) @ SV149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1498 ) @ SV149 ) @ SY1497 ) )
| ( SV149 = SY1497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5973]) ).
thf(6298,plain,
! [SV150: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i,SY1502: $i] :
( ( ( hAPP @ SY1502 @ SY1501 )
!= SY1500 )
| ( ( c_Fun_Ofun__upd @ SY1499 @ SV150 @ SY1502 @ SY1501 @ SY1500 )
= SY1502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5974]) ).
thf(6299,plain,
! [SV151: $i] :
( ( ! [SY1503: $i,SY1504: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1504 @ SY1503 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1503 @ SV151 ) @ SV151 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1503 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY1504 @ SY1503 ) @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5975]) ).
thf(6300,plain,
! [SV152: $i] :
( ( ! [SY1505: $i,SY1506: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY1506 ) @ SY1505 ) @ SV152 )
!= SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5976]) ).
thf(6301,plain,
! [SV153: $i] :
( ( ! [SY1507: $i,SY1508: $i,SY1509: $i,SY1510: $i,SY1511: $i,SY1512: $i,SY1513: $i,SY1514: $i,SY1515: $i,SY1516: $i] :
( ( ( hAPP @ SY1516 @ ( hAPP @ SY1515 @ SY1514 ) )
!= ( hAPP @ SY1513 @ ( hAPP @ SY1512 @ SY1511 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1510 @ SY1509 @ SY1508 @ SY1516 ) @ SY1515 ) @ SY1514 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY1507 @ SY1509 @ SV153 @ SY1513 ) @ SY1512 ) @ SY1511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5977]) ).
thf(6302,plain,
! [SV154: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i,SY1520: $i] :
( ~ ( c_Predicate_Otransp @ SY1520 @ SY1519 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1519 @ SY1518 ) @ SY1517 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1519 @ SY1517 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1519 @ SY1518 ) @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5978]) ).
thf(6303,plain,
! [SV155: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1522 @ SY1521 ) @ SV155 ) )
| ! [SY1523: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1521 @ SY1523 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1522 @ SY1521 ) @ SY1523 ) ) ) )
| ~ ( ~ ! [SY1524: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1521 @ SY1524 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1522 @ SY1521 ) @ SY1524 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1522 @ SY1521 ) @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5979]) ).
thf(6304,plain,
! [SV156: $i] :
( ( ! [SY1525: $i,SY1526: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1526 ) @ SY1525 ) @ SV156 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1526 ) @ SY1525 ) @ SV156 )
= SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5980]) ).
thf(6305,plain,
! [SV157: $i] :
( ( ! [SY1527: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1527 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1527 @ ( c_Hilbert__Choice_OEps @ SV157 @ SY1527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5981]) ).
thf(6306,plain,
! [SV158: $i] :
( ( ! [SY1529: $i,SY1530: $i,SY1531: $i] :
( ~ ( class_Orderings_Opreorder @ SY1531 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1531 ) @ SY1530 ) @ SY1529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1531 ) @ SY1529 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1531 ) @ SY1530 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5982]) ).
thf(6307,plain,
! [SV159: $i] :
( ( ! [SY1532: $i,SY1533: $i,SY1534: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY1534 @ SY1533 @ SY1532 ) @ SV159 ) )
| ( SY1532
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1534 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6308,plain,
! [SV160: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1537 @ tc_HOL_Obool ) ) @ SY1536 ) @ SY1535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1537 @ tc_HOL_Obool ) ) @ SV160 ) @ SY1535 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1537 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1537 @ tc_HOL_Obool ) ) @ SY1536 ) @ SV160 ) ) @ SY1535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5984]) ).
thf(6309,plain,
! [SV161: $i] :
( ( ! [SY1538: $i] :
~ ( ~ ( ~ ~ ! [SY1539: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1538 ) @ SY1539 ) @ SV161 ) )
| ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1538 @ tc_HOL_Obool ) ) ) )
| ~ ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1538 @ tc_HOL_Obool ) ) ) )
| ~ ! [SY1540: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1538 ) @ SY1540 ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5985]) ).
thf(6310,plain,
! [SV162: $i] :
( ( ! [SY1541: $i,SY1542: $i,SY1543: $i] :
( ( SY1543 != SY1542 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1541 ) @ SY1543 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1541 ) @ SY1542 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1541 ) @ SY1542 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1541 ) @ SY1543 ) @ SV162 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5986]) ).
thf(6311,plain,
! [SV163: $i] :
( ( ! [SY1544: $i,SY1545: $i,SY1546: $i,SY1547: $i,SY1548: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1548 @ SY1547 @ SY1546 @ SY1545 @ SY1544 )
| ( ( hAPP @ SY1545 @ ( hAPP @ SY1546 @ SV163 ) )
= SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5987]) ).
thf(6312,plain,
! [SV164: $i] :
( ( ! [SY1549: $i,SY1550: $i,SY1551: $i,SY1552: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1552 @ tc_HOL_Obool ) ) @ SY1551 ) @ SY1550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1549 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SY1549 @ SY1552 @ SV164 ) @ SY1551 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SY1549 @ SY1552 @ SV164 ) @ SY1550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5988]) ).
thf(6313,plain,
! [SV165: $i] :
( ( ! [SY1553: $i,SY1554: $i,SY1555: $i,SY1556: $i,SY1557: $i,SY1558: $i,SY1559: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1559 @ SY1558 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1556 @ SY1557 ) @ SY1555 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY1554 @ SY1553 @ SV165 @ SY1559 @ SY1556 ) @ SY1558 ) @ SY1555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5989]) ).
thf(6314,plain,
! [SV166: $i] :
( ( ! [SY1560: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SY1560 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV166 @ SY1560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5990]) ).
thf(6315,plain,
! [SV167: $i] :
( ( ! [SY1561: $i,SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1562 @ SY1561 ) )
| ( hBOOL @ ( hAPP @ SY1562 @ ( c_Hilbert__Choice_OEps @ SV167 @ SY1562 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5991]) ).
thf(6316,plain,
! [SV168: $i] :
( ( ! [SY1563: $i,SY1564: $i] :
( ~ ( class_Orderings_Oorder @ SY1564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1564 ) @ SY1563 ) @ SV168 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1564 ) @ SV168 ) @ SY1563 ) )
| ( SV168 = SY1563 ) )
| ~ ( ( SV168 != SY1563 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1564 ) @ SV168 ) @ SY1563 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6317,plain,
! [SV169: $i] :
( ( ! [SY1565: $i,SY1566: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1566 ) @ SY1565 )
!= ( hAPP @ ( c_List_Orev @ SY1566 ) @ SV169 ) )
| ( SY1565 = SV169 ) )
| ~ ( ( SY1565 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SY1566 ) @ SY1565 )
= ( hAPP @ ( c_List_Orev @ SY1566 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5993]) ).
thf(6318,plain,
! [SV170: $i] :
( ( ! [SY1567: $i,SY1568: $i,SY1569: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1569 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SY1568 @ SY1569 @ SY1567 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1568 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1568 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1569 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SY1568 @ SY1569 @ SY1567 ) @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5994]) ).
thf(6319,plain,
! [SV171: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ~ ( class_Orderings_Oorder @ SY1571 )
| ~ ( ~ ( ( SY1570 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1571 ) @ SY1570 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1571 ) @ SV171 ) @ SY1570 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1571 ) @ SY1570 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1571 ) @ SV171 ) @ SY1570 ) ) )
| ( SY1570 = SV171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5995]) ).
thf(6320,plain,
! [SV172: $i] :
( ( ! [SY1572: $i] :
( ~ ( class_Lattices_Olattice @ SY1572 )
| ( class_Lattices_Olattice @ ( tc_fun @ SV172 @ SY1572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5996]) ).
thf(6321,plain,
! [SV173: $i] :
( ( ! [SY1573: $i] :
( ~ ~ ( ~ ( class_Enum_Oenum @ SY1573 )
| ~ ( class_Enum_Oenum @ SV173 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SY1573 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5997]) ).
thf(6322,plain,
! [SV174: $i] :
( ( ! [SY1574: $i,SY1575: $i,SY1576: $i,SY1577: $i,SY1578: $i,SY1579: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1579 @ SY1578 @ SY1577 @ SY1576 @ SY1575 )
| ~ ( ~ ( ( ( hAPP @ SY1577 @ SY1574 )
!= ( hAPP @ SY1577 @ SV174 ) )
| ( SY1574 = SV174 ) )
| ~ ( ( SY1574 != SV174 )
| ( ( hAPP @ SY1577 @ SY1574 )
= ( hAPP @ SY1577 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5998]) ).
thf(6323,plain,
! [SV175: $i] :
( ( ! [SY1580: $i,SY1581: $i,SY1582: $i,SY1583: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1583 @ tc_HOL_Obool ) ) @ SY1582 ) @ SY1581 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1583 @ tc_HOL_Obool ) ) @ SY1580 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1583 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1583 @ tc_HOL_Obool ) ) @ SY1582 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1583 @ tc_HOL_Obool ) ) @ SY1581 ) @ SY1580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5999]) ).
thf(6324,plain,
! [SV176: $i] :
( ( ! [SY1584: $i,SY1585: $i,SY1586: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1586 ) @ SY1585 ) @ SY1584 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1586 ) @ SV176 ) @ SY1584 ) )
| ( SY1585 = SV176 ) )
| ~ ( ( SY1585 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1586 ) @ SY1585 ) @ SY1584 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1586 ) @ SV176 ) @ SY1584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6325,plain,
! [SV177: $i] :
( ( ! [SY1587: $i,SY1588: $i,SY1589: $i,SY1590: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1590 @ SY1589 ) @ SY1588 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1587 @ SV177 @ SY1590 ) @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6326,plain,
! [SV178: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1593 ) @ SY1592 ) @ SY1591 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1593 ) @ SY1592 ) @ SV178 ) )
| ( SY1591 = SV178 ) )
| ~ ( ( SY1591 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1593 ) @ SY1592 ) @ SY1591 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1593 ) @ SY1592 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6002]) ).
thf(6327,plain,
! [SV179: $i] :
( ( ! [SY1594: $i,SY1595: $i,SY1596: $i,SY1597: $i,SY1598: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1598 @ ( tc_fun @ SY1597 @ tc_HOL_Obool ) ) ) @ SY1596 ) @ SY1595 ) @ SY1594 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1596 @ SY1594 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1595 @ SY1594 ) @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6003]) ).
thf(6328,plain,
! [SV180: $i] :
( ( ! [SY1599: $i,SY1600: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1600 ) @ SY1599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1600 @ tc_HOL_Obool ) ) @ SV180 ) @ SY1599 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1600 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6004]) ).
thf(6329,plain,
! [SV181: $i] :
( ( ! [SY1601: $i,SY1602: $i,SY1603: $i,SY1604: $i,SY1605: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1605 @ SY1604 ) @ SY1603 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1602 @ ( tc_fun @ SY1601 @ tc_HOL_Obool ) ) ) @ SY1605 ) @ SV181 ) @ SY1604 ) @ SY1603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6330,plain,
! [SV182: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i,SY1609: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1609 @ tc_HOL_Obool ) ) @ SY1608 ) @ ( hAPP @ ( c_Set_Oimage @ SY1607 @ SY1609 @ SY1606 ) @ SV182 ) ) )
| ~ ! [SY1610: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1607 @ tc_HOL_Obool ) ) @ SY1610 ) @ SV182 ) )
| ( SY1608
!= ( hAPP @ ( c_Set_Oimage @ SY1607 @ SY1609 @ SY1606 ) @ SY1610 ) ) ) )
| ~ ( ~ ~ ! [SY1611: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1607 @ tc_HOL_Obool ) ) @ SY1611 ) @ SV182 ) )
| ( SY1608
!= ( hAPP @ ( c_Set_Oimage @ SY1607 @ SY1609 @ SY1606 ) @ SY1611 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1609 @ tc_HOL_Obool ) ) @ SY1608 ) @ ( hAPP @ ( c_Set_Oimage @ SY1607 @ SY1609 @ SY1606 ) @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6331,plain,
! [SV183: $i] :
( ( ! [SY1612: $i,SY1613: $i] :
( ( SY1613 != SY1612 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SY1613 ) @ SY1612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SY1612 ) @ SY1613 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6007]) ).
thf(6332,plain,
! [SV184: $i] :
( ( ! [SY1614: $i,SY1615: $i,SY1616: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1616 @ tc_HOL_Obool ) ) @ SY1615 ) @ SY1614 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1616 @ tc_HOL_Obool ) ) @ SY1614 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1616 @ tc_HOL_Obool ) ) @ SY1615 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6333,plain,
! [SV185: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i] :
( ~ ( class_Orderings_Oord @ SY1619 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1619 ) @ SY1618 ) @ SY1617 ) )
| ( SY1617 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1619 ) @ SY1618 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6009]) ).
thf(6334,plain,
! [SV186: $i] :
( ( ! [SY1620: $i,SY1621: $i,SY1622: $i] :
( ~ ( class_Orderings_Oorder @ SY1622 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1622 ) @ SY1621 ) @ SY1620 ) )
| ( SY1621 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1622 ) @ SV186 ) @ SY1620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6010]) ).
thf(6335,plain,
! [SV187: $i] :
( ( ! [SY1623: $i,SY1624: $i,SY1625: $i,SY1626: $i] :
( ~ ( class_Orderings_Oord @ SY1626 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1625 @ SY1626 ) ) @ SY1624 ) @ SY1623 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1626 ) @ ( hAPP @ SY1624 @ SV187 ) ) @ ( hAPP @ SY1623 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6011]) ).
thf(6336,plain,
! [SV188: $i] :
( ( ! [SY1627: $i,SY1628: $i,SY1629: $i,SY1630: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1630 @ SY1629 ) @ SY1628 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1627 @ SV188 @ SY1630 ) @ SY1628 ) @ SY1629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6012]) ).
thf(6337,plain,
! [SV189: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1633 @ tc_HOL_Obool ) ) @ SY1632 ) @ SY1631 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1633 @ tc_HOL_Obool ) ) @ SY1632 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1633 @ tc_HOL_Obool ) ) @ SY1632 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1633 @ tc_HOL_Obool ) ) @ SY1631 ) @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6338,plain,
! [SV190: $i] :
( ( ! [SY1634: $i,SY1635: $i,SY1636: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1636 @ tc_HOL_Obool ) ) @ SY1635 ) @ SY1634 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1636 @ tc_HOL_Obool ) ) @ SY1634 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1636 @ tc_HOL_Obool ) ) @ SY1635 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6339,plain,
! [SV191: $i] :
( ( ! [SY1637: $i,SY1638: $i,SY1639: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1639 @ SY1638 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1638 @ SY1637 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1638 @ SV191 ) @ SY1637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6340,plain,
! [SV192: $i] :
( ( ! [SY1640: $i,SY1641: $i,SY1642: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1642 ) @ SY1641 ) @ SY1640 ) )
| ( SY1641 = SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1642 ) @ SY1641 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1642 ) @ SV192 ) @ SY1640 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6341,plain,
! [SV193: $i] :
( ( ! [SY1643: $i,SY1644: $i,SY1645: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1645 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1645 ) @ SY1644 ) @ SY1643 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1645 ) @ SY1644 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1645 @ tc_HOL_Obool ) ) @ SY1643 ) @ SV193 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1645 ) @ SY1644 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1645 @ tc_HOL_Obool ) ) @ SY1643 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1645 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1645 ) @ SY1644 ) @ SY1643 ) ) @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6017]) ).
thf(6342,plain,
! [SV194: $i] :
( ( ! [SY1646: $i] :
( ~ ( class_Groups_Ouminus @ SY1646 )
| ( class_Groups_Ouminus @ ( tc_fun @ SV194 @ SY1646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6018]) ).
thf(6343,plain,
! [SV195: $i] :
( ( ! [SY1647: $i,SY1648: $i,SY1649: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1649 ) @ SY1648 ) @ SY1647 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1649 ) @ SY1648 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1649 ) @ SY1648 ) @ SY1647 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1649 ) @ SY1648 ) @ SV195 ) )
| ( SY1647 = SV195 ) )
| ~ ( ( SY1647 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1649 ) @ SY1648 ) @ SY1647 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1649 ) @ SY1648 ) @ SV195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6019]) ).
thf(6344,plain,
! [SV196: $i] :
( ( ! [SY1650: $i,SY1651: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1651 @ ( tc_fun @ SY1651 @ tc_HOL_Obool ) ) ) @ SY1650 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1651 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SY1651 @ SV196 ) ) @ ( c_Wellfounded_Oaccp @ SY1651 @ SY1650 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6020]) ).
thf(6345,plain,
! [SV197: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY1653 ) @ SY1652 )
!= SV197 )
| ( SY1652
= ( hAPP @ ( c_List_Orev @ SY1653 ) @ SV197 ) ) )
| ~ ( ( SY1652
!= ( hAPP @ ( c_List_Orev @ SY1653 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SY1653 ) @ SY1652 )
= SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6021]) ).
thf(6346,plain,
! [SV198: $i] :
( ( ! [SY1654: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1654 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
| ( SY1654 = SV198 ) )
| ~ ( ( SY1654 != SV198 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1654 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6022]) ).
thf(6347,plain,
! [SV199: $i] :
( ( ! [SY1655: $i,SY1656: $i,SY1657: $i,SY1658: $i,SY1659: $i] :
( ~ ( ( SY1659 != SY1658 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1657 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1657 @ SY1656 ) @ SY1659 ) @ SY1655 ) ) @ SY1658 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1657 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY1657 @ SY1656 ) @ SY1658 ) @ SV199 ) ) @ SY1659 ) @ SY1655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6348,plain,
! [SV200: $i] :
( ( ! [SY1660: $i,SY1661: $i,SY1662: $i] :
( ~ ( c_Fun_Obij__betw @ SY1662 @ SY1661 @ SY1660 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1661 @ tc_HOL_Obool ) ) )
| ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1662 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6024]) ).
thf(6349,plain,
! [SV201: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i] :
( ~ ( class_Orderings_Oord @ SY1665 )
| ( SY1664 != SY1663 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1665 ) @ SY1663 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1665 ) @ SY1664 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6025]) ).
thf(6350,plain,
! [SV202: $i] :
( ( ! [SY1666: $i,SY1667: $i,SY1668: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1668 ) @ SY1667 ) @ SY1666 ) @ SV202 ) )
| ( SY1667 = SV202 )
| ( hBOOL @ ( hAPP @ SY1666 @ SV202 ) ) )
| ~ ( ~ ( ( SY1667 = SV202 )
| ( hBOOL @ ( hAPP @ SY1666 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1668 ) @ SY1667 ) @ SY1666 ) @ SV202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6026]) ).
thf(6351,plain,
! [SV203: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ( SY1670 != SY1669 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SY1669 ) @ SY1670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6027]) ).
thf(6352,plain,
! [SV204: $i] :
( ( ! [SY1671: $i,SY1672: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1672 ) @ SY1671 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1672 ) @ SV204 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1672 @ tc_HOL_Obool ) ) ) ) )
| ( SY1671 = SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6028]) ).
thf(6353,plain,
! [SV205: $i] :
( ( ! [SY1673: $i,SY1674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1674 ) @ SY1673 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1674 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1674 ) @ SV205 ) @ SY1673 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6029]) ).
thf(6354,plain,
! [SV206: $i] :
( ( ! [SY1675: $i,SY1676: $i,SY1677: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1677 @ SY1676 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1675 @ tc_HOL_Obool ) ) @ SY1677 ) @ SV206 ) @ SY1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6030]) ).
thf(6355,plain,
! [SV207: $i] :
( ( ! [SY1678: $i] :
( ~ ( class_Groups_Ominus @ SY1678 )
| ( class_Groups_Ominus @ ( tc_fun @ SV207 @ SY1678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6031]) ).
thf(6356,plain,
! [SV208: $i] :
( ( ! [SY1679: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY1679 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV208 @ SY1679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6032]) ).
thf(6357,plain,
! [SV209: $i] :
( ( ! [SY1680: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY1680 ) @ SV209 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SY1680 ) )
| ( SY1680 = SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6033]) ).
thf(6358,plain,
! [SV210: $i] :
( ( ! [SY1681: $i] :
( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1681 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1681 @ ( c_Hilbert__Choice_OEps @ SV210 @ SY1681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6034]) ).
thf(6359,plain,
! [SV211: $i] :
( ( ! [SY1683: $i,SY1684: $i,SY1685: $i,SY1686: $i,SY1687: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1687 @ SY1686 ) @ SY1685 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1684 @ ( tc_fun @ SY1683 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SY1687 ) @ SY1686 ) @ SY1685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6035]) ).
thf(6360,plain,
! [SV212: $i] :
( ( ! [SY1688: $i,SY1689: $i,SY1690: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1690 @ SY1689 ) )
| ~ ( hBOOL @ ( hAPP @ SY1688 @ SY1689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SY1690 ) @ SY1688 ) @ SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6036]) ).
thf(6361,plain,
! [SV213: $i] :
( ( ! [SY1691: $i,SY1692: $i,SY1693: $i,SY1694: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1694 @ tc_HOL_Obool ) ) @ SY1693 ) @ SY1692 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1694 @ tc_HOL_Obool ) ) @ SY1691 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1694 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1694 @ tc_HOL_Obool ) ) @ SY1693 ) @ SY1691 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1694 @ tc_HOL_Obool ) ) @ SY1692 ) @ SV213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6037]) ).
thf(6362,plain,
! [SV214: $i] :
( ( ! [SY1695: $i] :
( ~ ( class_Orderings_Opreorder @ SY1695 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SV214 @ SY1695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6038]) ).
thf(6363,plain,
! [SV215: $i] :
( ( ! [SY1696: $i,SY1697: $i,SY1698: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1698 @ SY1697 @ SY1696 ) @ SV215 ) )
| ~ ! [SY1699: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1696 @ SV215 ) @ SY1699 ) ) )
| ~ ( ~ ~ ! [SY1700: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1696 @ SV215 ) @ SY1700 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1698 @ SY1697 @ SY1696 ) @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6039]) ).
thf(6364,plain,
! [SV216: $i] :
( ( ! [SY1701: $i,SY1702: $i,SY1703: $i,SY1704: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1703 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1702 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1704 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1701 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1704 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SY1703 != SY1701 )
| ( SY1702 != SV216 ) )
| ~ ( ( SY1703 != SV216 )
| ( SY1702 != SY1701 ) ) )
| ~ ( ~ ( ~ ( ( SY1703 != SY1701 )
| ( SY1702 != SV216 ) )
| ~ ( ( SY1703 != SV216 )
| ( SY1702 != SY1701 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1703 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1702 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1704 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SY1701 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1704 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1704 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6365,plain,
! [SV217: $i] :
( ( ! [SY1705: $i] :
( ~ ( class_Orderings_Obot @ SY1705 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1705 ) @ ( c_Orderings_Obot__class_Obot @ SY1705 ) ) @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6041]) ).
thf(6366,plain,
! [SV218: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
( ~ ( class_Orderings_Oorder @ SY1707 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1707 ) @ SY1706 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1707 ) @ SV218 ) @ SY1706 ) )
| ( SY1706 = SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6042]) ).
thf(6367,plain,
! [SV219: $i] :
( ( ! [SY1708: $i,SY1709: $i,SY1710: $i,SY1711: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1711 @ SY1710 @ SY1709 ) @ SY1708 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1709 @ SV219 ) @ SY1708 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1709 @ SV219 ) @ SY1708 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1711 @ SY1710 @ SY1709 ) @ SY1708 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6043]) ).
thf(6368,plain,
! [SV220: $i] :
( ( ! [SY1712: $i,SY1713: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1713 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SY1712 ) @ SV220 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1713 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1713 @ tc_HOL_Obool ) @ SY1712 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY1713 @ tc_HOL_Obool ) @ SV220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6044]) ).
thf(6369,plain,
! [SV221: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i,SY1717: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY1717 @ SY1716 @ SY1715 )
| ( ( hAPP @ ( hAPP @ SY1715 @ SY1714 ) @ ( hAPP @ ( hAPP @ SY1715 @ SY1714 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SY1715 @ SY1714 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6045]) ).
thf(6370,plain,
! [SV222: $i] :
( ( ! [SY1718: $i,SY1719: $i,SY1720: $i,SY1721: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1721 @ SY1720 @ SY1719 ) @ SY1718 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SY1718 @ ( hAPP @ SY1719 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1718 @ ( hAPP @ SY1719 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY1721 @ SY1720 @ SY1719 ) @ SY1718 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6046]) ).
thf(6371,plain,
! [SV223: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1724 @ tc_HOL_Obool ) ) @ SY1723 ) @ SY1722 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1724 ) @ SV223 ) @ SY1723 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1724 ) @ SV223 ) @ SY1722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6047]) ).
thf(6372,plain,
! [SV224: $i] :
( ( ! [SY1725: $i,SY1726: $i,SY1727: $i] :
( ~ ( class_Orderings_Oorder @ SY1727 )
| ( SY1726 != SY1725 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1727 ) @ SV224 ) @ SY1725 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1727 ) @ SV224 ) @ SY1726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6048]) ).
thf(6373,plain,
! [SV225: $i] :
( ( ! [SY1728: $i,SY1729: $i,SY1730: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1730 @ tc_HOL_Obool ) ) @ SY1729 ) @ SY1728 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ SY1729 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6049]) ).
thf(6374,plain,
! [SV226: $i] :
( ( ! [SY1731: $i] :
( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SY1731 )
| ~ ( class_Finite__Set_Ofinite @ SV226 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SY1731 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6050]) ).
thf(6375,plain,
! [SV227: $i] :
( ( ! [SY1732: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1732 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
| ( SY1732 = SV227 ) )
| ~ ( ( SY1732 != SV227 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY1732 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6051]) ).
thf(6376,plain,
! [SV228: $i] :
( ( ! [SY1733: $i,SY1734: $i,SY1735: $i] :
( ( SY1735 != SY1734 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1733 ) @ SY1734 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1733 ) @ SY1735 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6052]) ).
thf(6377,plain,
! [SV229: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1736 ) @ SY1737 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1736 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ SV229 @ SY1737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6053]) ).
thf(6378,plain,
! [SV230: $i] :
( ( ! [SY1738: $i,SY1739: $i,SY1740: $i,SY1741: $i,SY1742: $i] :
~ ( ~ ( ( SY1742 != SY1741 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1740 @ SY1739 @ SY1738 @ SY1741 @ SV230 ) @ SY1742 )
= SV230 ) )
| ~ ( ~ ( ( SY1742 != SY1741 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1740 @ SY1739 @ SY1738 @ SY1741 @ SV230 ) @ SY1742 )
= ( hAPP @ SY1738 @ SY1742 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6054]) ).
thf(6379,plain,
! [SV231: $i] :
( ( ! [SY1743: $i,SY1744: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1744 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1744 ) @ SY1743 ) @ SV231 ) )
| ( SY1743
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1744 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SY1743
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1744 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1744 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1744 ) @ SY1743 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6055]) ).
thf(6380,plain,
! [SV232: $i] :
( ( ! [SY1745: $i,SY1746: $i] :
~ ( ~ ( ( SY1746 != SY1745 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY1746 ) @ SY1745 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY1745 ) @ SY1746 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY1746 ) @ SY1745 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY1745 ) @ SY1746 ) ) )
| ( SY1746 = SY1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6056]) ).
thf(6381,plain,
! [SV233: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i] :
( ~ ( c_Fun_Obij__betw @ SY1749 @ SY1748 @ SY1747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1749 @ tc_HOL_Obool ) ) @ SV233 )
| ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1748 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6057]) ).
thf(6382,plain,
! [SV234: $i] :
( ( ! [SY1750: $i,SY1751: $i,SY1752: $i,SY1753: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1753 @ tc_HOL_Obool ) ) @ SY1752 ) @ SY1751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1750 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1753 @ SY1750 @ SV234 ) @ SY1752 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY1753 @ SY1750 @ SV234 ) @ SY1751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6058]) ).
thf(6383,plain,
! [SV235: $i] :
( ( ! [SY1754: $i,SY1755: $i,SY1756: $i] :
( ~ ( c_Finite__Set_Ofolding__one @ SY1756 @ SY1755 @ SY1754 )
| ( ( hAPP @ SY1754 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1756 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1756 @ tc_HOL_Obool ) ) ) )
= SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6059]) ).
thf(6384,plain,
! [SV236: $i] :
( ( ! [SY1757: $i,SY1758: $i,SY1759: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY1759 @ SY1758 @ SY1757 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1758 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1759 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1759 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SY1759 @ SY1758 @ SY1757 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1758 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6385,plain,
! [SV237: $i] :
( ( ! [SY1760: $i,SY1761: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1761 ) @ SY1760 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1761 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SY1760
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1761 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SY1760
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1761 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY1761 ) @ SY1760 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1761 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6061]) ).
thf(6386,plain,
! [SV238: $i] :
( ( ! [SY1762: $i,SY1763: $i,SY1764: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1764 ) @ SY1763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1764 ) @ SY1762 ) @ SV238 ) ) )
| ~ ( ( SY1763 != SY1762 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1764 ) @ SY1763 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6062]) ).
thf(6387,plain,
! [SV239: $i] :
( ( ! [SY1765: $i,SY1766: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY1766 @ tc_HOL_Obool ) ) @ SY1765 ) @ SV239 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1766 @ tc_HOL_Obool ) ) @ SY1765 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6063]) ).
thf(6388,plain,
! [SV240: $i] :
( ( ! [SY1767: $i,SY1768: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) @ SY1767 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) )
| ~ ( ( SY1767
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ~ ( ( SY1767
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) @ SY1767 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1768 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6064]) ).
thf(6389,plain,
! [SV241: $i] :
( ( ! [SY1769: $i,SY1770: $i,SY1771: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1771 @ SY1770 ) @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1770 @ SV241 ) @ SY1769 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1771 @ SY1770 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6065]) ).
thf(6390,plain,
! [SV242: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1774 @ tc_HOL_Obool ) ) @ SY1773 ) @ SY1772 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1774 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1774 ) @ SV242 ) @ SY1773 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1774 ) @ SV242 ) @ SY1772 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6066]) ).
thf(6391,plain,
! [SV243: $i] :
( ( ! [SY1775: $i,SY1776: $i,SY1777: $i,SY1778: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1778 @ SY1777 @ SY1776 ) @ SY1775 ) @ SV243 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1776 @ SV243 ) @ SY1775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6392,plain,
! [SV244: $i] :
( ( ! [SY1779: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY1779 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
| ( SY1779 = SV244 ) )
| ~ ( ( SY1779 != SV244 )
| ( ( hAPP @ c_Nat_OSuc @ SY1779 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6068]) ).
thf(6393,plain,
! [SV245: $i] :
( ( ! [SY1780: $i,SY1781: $i,SY1782: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1782 @ SY1781 ) @ SY1780 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY1782 @ SY1781 ) @ SV245 ) )
| ( SY1780 = SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6069]) ).
thf(6394,plain,
! [SV246: $i] :
( ( ! [SY1783: $i,SY1784: $i] :
( ( SY1784
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1783 @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1783 ) @ SV246 ) @ SY1784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6070]) ).
thf(6395,plain,
! [SV247: $i] :
( ( ! [SY1785: $i,SY1786: $i,SY1787: $i] :
( ~ ( class_Orderings_Oord @ SY1787 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1786 @ SY1787 ) ) @ SY1785 ) @ SV247 ) )
| ! [SY1788: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1787 ) @ ( hAPP @ SY1785 @ SY1788 ) ) @ ( hAPP @ SV247 @ SY1788 ) ) ) )
| ~ ( ~ ! [SY1789: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1787 ) @ ( hAPP @ SY1785 @ SY1789 ) ) @ ( hAPP @ SV247 @ SY1789 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1786 @ SY1787 ) ) @ SY1785 ) @ SV247 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6071]) ).
thf(6396,plain,
! [SV248: $i] :
( ( ! [SY1790: $i,SY1791: $i,SY1792: $i,SY1793: $i,SY1794: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1794 @ SY1793 ) @ SY1792 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1791 @ SY1793 ) @ SY1792 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1790 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SY1791 ) @ SY1794 ) @ SY1793 ) @ SY1792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6072]) ).
thf(6397,plain,
! [SV249: $i] :
( ( ! [SY1795: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY1795 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
| ( SY1795 = SV249 ) )
| ~ ( ( SY1795 != SV249 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY1795 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6073]) ).
thf(6398,plain,
! [SV250: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1797 @ tc_HOL_Obool ) ) @ SY1796 ) @ SV250 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1797 @ tc_HOL_Obool ) ) @ SY1796 ) @ SV250 )
= SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6074]) ).
thf(6399,plain,
! [SV251: $i] :
( ( ! [SY1798: $i] :
( ~ ( class_Orderings_Obot @ SY1798 )
| ( class_Orderings_Obot @ ( tc_fun @ SV251 @ SY1798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6075]) ).
thf(6400,plain,
! [SV252: $i] :
( ( ! [SY1799: $i,SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1801 ) @ SY1800 ) @ SY1799 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1801 @ tc_HOL_Obool ) ) @ SY1799 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1801 ) @ SY1800 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6076]) ).
thf(6401,plain,
! [SV253: $i] :
( ( ! [SY1802: $i,SY1803: $i,SY1804: $i,SY1805: $i,SY1806: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1806 @ SY1805 ) @ SY1804 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1803 @ SY1805 ) @ SY1804 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1802 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SY1806 ) @ SY1803 ) @ SY1805 ) @ SY1804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6077]) ).
thf(6402,plain,
! [SV254: $i] :
( ( ! [SY1807: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_OCollect @ SY1807 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1807 @ tc_HOL_Obool ) ) )
| ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
| ~ ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SY1807 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1807 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6078]) ).
thf(6403,plain,
! [SV255: $i] :
( ( ! [SY1810: $i] :
( ~ ! [SY1811: $i] :
( ( hAPP @ SY1810 @ SY1811 )
= ( hAPP @ SV255 @ SY1811 ) )
| ( SY1810 = SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6079]) ).
thf(6404,plain,
! [SV256: $i] :
( ( ! [SY1812: $i] :
~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1812 ) @ SY1813 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1812 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SY1813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6080]) ).
thf(6405,plain,
! [SV257: $i] :
( ( ! [SY1814: $i,SY1815: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1815 @ tc_HOL_Obool ) ) @ SY1814 ) @ SV257 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1815 @ tc_HOL_Obool ) ) @ SV257 ) @ SY1814 ) )
| ( SY1814 = SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6081]) ).
thf(6406,plain,
! [SV258: $i] :
( ( ! [SY1816: $i,SY1817: $i,SY1818: $i,SY1819: $i,SY1820: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SY1820 @ SY1819 @ SY1818 @ SY1817 @ SY1816 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1819 @ tc_HOL_Obool ) ) )
= SY1817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6082]) ).
thf(6407,plain,
! [SV259: $i] :
( ( ! [SY1821: $i,SY1822: $i,SY1823: $i,SY1824: $i,SY1825: $i,SY1826: $i,SY1827: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1827 @ SY1826 @ SY1825 @ SY1824 ) @ SY1823 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY1822 @ SY1826 @ SY1825 @ SY1821 ) @ SV259 ) )
| ! [SY1828: $i] :
( ( hAPP @ SY1824 @ ( hAPP @ SY1823 @ SY1828 ) )
= ( hAPP @ SY1821 @ ( hAPP @ SV259 @ SY1828 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6083]) ).
thf(6408,plain,
! [SV260: $i] :
( ( ! [SY1829: $i,SY1830: $i,SY1831: $i,SY1832: $i,SY1833: $i] :
( ~ ( ( SY1833 != SY1832 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1831 @ SY1830 @ SY1829 @ SY1832 @ SV260 ) @ SY1833 )
= ( hAPP @ SY1829 @ SY1833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6084]) ).
thf(6409,plain,
! [SV261: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ~ ( class_Orderings_Opreorder @ SY1835 )
| ( SY1834 != SV261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1835 ) @ SY1834 ) @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6085]) ).
thf(6410,plain,
! [SV262: $i] :
( ( ! [SY1836: $i,SY1837: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1837 ) @ SY1836 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1837 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) ) ) )
| ( SY1836 = SV262 ) )
| ~ ( ( SY1836 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1837 ) @ SY1836 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1837 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1837 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6086]) ).
thf(6411,plain,
! [SV263: $i] :
( ( ! [SY1838: $i,SY1839: $i,SY1840: $i,SY1841: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1841 @ tc_HOL_Obool ) ) @ SY1840 ) @ SY1839 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1841 @ tc_HOL_Obool ) ) @ SY1838 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1841 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1841 @ tc_HOL_Obool ) ) @ SY1840 ) @ SY1838 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1841 @ tc_HOL_Obool ) ) @ SY1839 ) @ SV263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6087]) ).
thf(6412,plain,
! [SV264: $i] :
( ( ! [SY1842: $i,SY1843: $i,SY1844: $i,SY1845: $i,SY1846: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1846 @ SY1845 ) @ SY1844 ) @ SY1843 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY1846 @ SY1845 ) @ SY1842 ) @ SV264 ) )
| ~ ( ( SY1844 != SY1842 )
| ( SY1843 != SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6088]) ).
thf(6413,plain,
! [SV265: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) ) @ SY1847 ) @ SV265 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY1848 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SY1848 @ SY1847 ) ) @ ( c_Predicate_OPowp @ SY1848 @ SV265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6089]) ).
thf(6414,plain,
! [SV266: $i] :
( ( ! [SY1849: $i] :
( ~ ( class_Orderings_Opreorder @ SY1849 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1849 ) @ SV266 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6090]) ).
thf(6415,plain,
! [SV267: $i] :
( ( ! [SY1850: $i,SY1851: $i,SY1852: $i,SY1853: $i,SY1854: $i,SY1855: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1855 @ SY1854 @ SY1853 @ SY1852 ) @ SY1851 )
!= SY1850 )
| ( ( hAPP @ SY1852 @ ( hAPP @ SY1851 @ SV267 ) )
= ( hAPP @ SY1850 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6091]) ).
thf(6416,plain,
! [SV268: $i] :
( ( ! [SY1856: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SY1856 @ ( c_Hilbert__Choice_OEps @ SV268 @ SY1856 ) ) )
| ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1856 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ( hBOOL @ ( hAPP @ SY1856 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SY1856 @ ( c_Hilbert__Choice_OEps @ SV268 @ SY1856 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6092]) ).
thf(6417,plain,
! [SV269: $i] :
( ( ! [SY1859: $i,SY1860: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SY1859 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SV269 ) @ SY1859 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SV269 ) @ SY1859 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SY1859 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1860 @ tc_HOL_Obool ) ) @ SV269 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6093]) ).
thf(6418,plain,
! [SV270: $i] :
( ( ! [SY1861: $i,SY1862: $i,SY1863: $i,SY1864: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY1864 @ SY1863 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1863 @ SY1862 ) @ SY1861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1863 @ SY1861 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1863 @ SY1862 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6094]) ).
thf(6419,plain,
! [SV271: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1866 @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1866 ) @ SY1865 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6095]) ).
thf(6420,plain,
! [SV272: $i] :
( ( ! [SY1867: $i,SY1868: $i,SY1869: $i] :
( ( SY1869 != SY1868 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV272 ) @ SY1869 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV272 ) @ SY1868 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV272 ) @ SY1869 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1867 ) @ SV272 ) @ SY1868 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6096]) ).
thf(6421,plain,
! [SV273: $i] :
( ( ! [SY1870: $i,SY1871: $i,SY1872: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1872 ) @ SY1871 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1872 ) @ SY1870 ) @ SV273 ) ) )
| ( SY1871 = SY1870 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1872 ) @ SY1871 ) @ SV273 ) ) )
| ~ ( ~ ( ( SY1871 = SY1870 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1872 ) @ SY1871 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1872 ) @ SY1871 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1872 ) @ SY1870 ) @ SV273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6097]) ).
thf(6422,plain,
! [SV274: $i] :
( ( ! [SY1873: $i] :
( ( SY1873 != SV274 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SY1873 ) @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6098]) ).
thf(6423,plain,
! [SV275: $i] :
( ( ! [SY1874: $i,SY1875: $i,SY1876: $i,SY1877: $i,SY1878: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1878 ) @ SY1877 ) @ SY1876 )
!= SY1875 )
| ( SY1874
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1878 ) @ SY1876 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1878 ) @ SY1877 ) @ SY1874 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1878 ) @ SY1875 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6099]) ).
thf(6424,plain,
! [SV276: $i] :
( ( ! [SY1879: $i,SY1880: $i,SY1881: $i] :
( ( SY1881 != SY1880 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1879 ) @ SV276 ) @ SY1881 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1879 ) @ SV276 ) @ SY1880 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1879 ) @ SV276 ) @ SY1880 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1879 ) @ SV276 ) @ SY1881 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6100]) ).
thf(6425,plain,
! [SV277: $i] :
( ( ! [SY1882: $i,SY1883: $i,SY1884: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1884 @ tc_HOL_Obool ) ) @ SY1883 ) @ SY1882 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1884 ) @ SV277 ) @ SY1883 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1884 ) @ SV277 ) @ SY1882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6101]) ).
thf(6426,plain,
! [SV278: $i] :
( ( ! [SY1885: $i,SY1886: $i,SY1887: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1887 @ tc_HOL_Obool ) ) @ SY1886 ) @ SY1885 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1887 @ tc_HOL_Obool ) ) @ SY1885 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1887 @ tc_HOL_Obool ) ) @ SY1886 ) @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6102]) ).
thf(6427,plain,
! [SV279: $i] :
( ( ! [SY1888: $i] :
( ~ ( class_Orderings_Oorder @ SY1888 )
| ( class_Orderings_Oorder @ ( tc_fun @ SV279 @ SY1888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6103]) ).
thf(6428,plain,
! [SV280: $i] :
( ( ! [SY1889: $i,SY1890: $i,SY1891: $i] :
( ( SY1891
!= ( c_Finite__Set_Ofold1 @ SY1890 @ SY1889 ) )
| ( ( hAPP @ SY1891 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1890 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1890 @ tc_HOL_Obool ) ) ) )
= SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6104]) ).
thf(6429,plain,
! [SV281: $i] :
( ( ! [SY1892: $i,SY1893: $i,SY1894: $i,SY1895: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1894 ) @ SY1893 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1892 ) @ SV281 ) )
| ~ ! [SY1896: $i] :
~ ( ~ ( ( SY1894
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1892 ) @ SY1896 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1896 ) @ SY1893 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1894 ) @ SY1896 )
!= SY1892 )
| ( SY1893
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1896 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY1897: $i] :
~ ( ~ ( ( SY1894
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1892 ) @ SY1897 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1897 ) @ SY1893 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1894 ) @ SY1897 )
!= SY1892 )
| ( SY1893
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1897 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1894 ) @ SY1893 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY1895 ) @ SY1892 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6105]) ).
thf(6430,plain,
! [SV282: $i] :
( ( ! [SY1898: $i,SY1899: $i] :
( ( SY1899
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY1898 @ SY1898 ) @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SY1898 @ SY1898 ) @ tc_HOL_Obool ) ) @ SY1899 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6106]) ).
thf(6431,plain,
! [SV283: $i] :
( ( ! [SY1900: $i] :
( ( hAPP @ ( c_Set_OPow @ SY1900 ) @ SV283 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY1900 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6107]) ).
thf(6432,plain,
! [SV284: $i] :
( ( ! [SY1901: $i,SY1902: $i,SY1903: $i,SY1904: $i] :
( ~ ( c_Fun_Oinj__on @ SY1904 @ SY1903 @ SY1902 @ SY1901 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1904 @ tc_HOL_Obool ) ) @ SV284 ) @ SY1901 ) )
| ( c_Fun_Oinj__on @ SY1904 @ SY1903 @ SY1902 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6108]) ).
thf(6433,plain,
! [SV285: $i] :
( ( ! [SY1905: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1905 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
| ( SY1905 = SV285 ) )
| ~ ( ( SY1905 != SV285 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY1905 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6109]) ).
thf(6434,plain,
! [SV286: $i] :
( ( ! [SY1906: $i,SY1907: $i,SY1908: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1908 @ tc_HOL_Obool ) ) @ SY1907 ) @ SY1906 ) @ SV286 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY1907 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SY1906 @ SV286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6110]) ).
thf(6435,plain,
! [SV287: $i] :
( ( ! [SY1909: $i] :
~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SY1909 @ SV287 )
| ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SY1909 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6111]) ).
thf(6436,plain,
! [SV288: $i] :
( ( SV288
!= ( hAPP @ c_Nat_OSuc @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6112]) ).
thf(6437,plain,
! [SV289: $i] :
( ( ! [SY1916: $i] :
~ ( ~ ( ~ ! [SY1917: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1916 ) @ SY1917 ) @ SV289 ) )
| ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1916 @ tc_HOL_Obool ) ) )
| ! [SY1918: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1916 ) @ SY1918 ) @ SV289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6113]) ).
thf(6438,plain,
! [SV290: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV290 @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV290 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6114]) ).
thf(6439,plain,
! [SV291: $i] :
( ( ! [SY1919: $i,SY1920: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY1920 @ SX3 ) )
| ( SY1919
!= ( c_Hilbert__Choice_OEps @ SV291 @ SY1920 ) )
| ( hBOOL @ ( hAPP @ SY1920 @ SY1919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6115]) ).
thf(6440,plain,
! [SV292: $i] :
( ( ! [SY1922: $i,SY1923: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1923 @ tc_HOL_Obool ) ) @ SY1922 ) @ SV292 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY1923 @ tc_HOL_Obool ) ) @ SV292 ) @ SY1922 )
= SY1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6116]) ).
thf(6441,plain,
! [SV293: $i] :
( ( ! [SY1924: $i] :
( ~ ( class_Orderings_Oord @ SY1924 )
| ( class_Orderings_Oord @ ( tc_fun @ SV293 @ SY1924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6117]) ).
thf(6442,plain,
! [SV294: $i] :
( ( ! [SY1925: $i,SY1926: $i,SY1927: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY1927 @ SY1926 ) )
| ( hBOOL @ ( hAPP @ SY1925 @ SY1926 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SY1925 ) @ SY1927 ) @ SY1926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6118]) ).
thf(6443,plain,
! [SV295: $i] :
( ( ! [SY1928: $i,SY1929: $i,SY1930: $i,SY1931: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY1931 @ SY1930 @ SY1929 @ SY1928 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1931 @ tc_HOL_Obool ) ) ) @ SV295 ) )
| ( SV295 = SY1928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6119]) ).
thf(6444,plain,
! [SV296: $i] :
( ( ! [SY1932: $i,SY1933: $i] :
( ~ ( class_Orderings_Olinorder @ SY1933 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1933 ) @ SY1932 ) @ SV296 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1933 ) @ SV296 ) @ SY1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6120]) ).
thf(6445,plain,
! [SV297: $i] :
( ( ! [SY1934: $i,SY1935: $i,SY1936: $i,SY1937: $i] :
( ~ ( class_Orderings_Oord @ SY1937 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1936 @ SY1937 ) ) @ SY1935 ) @ SY1934 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY1937 ) @ ( hAPP @ SY1935 @ SV297 ) ) @ ( hAPP @ SY1934 @ SV297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6121]) ).
thf(6446,plain,
! [SV298: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1939 @ tc_HOL_Obool ) ) @ SY1938 ) @ SV298 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1939 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1939 @ tc_HOL_Obool ) ) @ SV298 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1939 @ tc_HOL_Obool ) ) @ SY1938 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6122]) ).
thf(6447,plain,
! [SV299: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1941 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1941 ) @ SY1940 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1941 ) @ SV299 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1941 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY1941 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1941 ) @ SY1940 ) @ SV299 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6123]) ).
thf(6448,plain,
! [SV300: $i] :
( ( ! [SY1942: $i,SY1943: $i,SY1944: $i,SY1945: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1945 @ SY1944 ) @ SY1943 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY1942 @ SV300 @ SY1945 ) @ SY1944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6124]) ).
thf(6449,plain,
! [SV301: $i] :
( ( ! [SY1946: $i,SY1947: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1947 @ tc_HOL_Obool ) ) @ SY1946 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1947 @ tc_HOL_Obool ) ) @ SY1946 ) @ SV301 )
= SV301 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1947 @ tc_HOL_Obool ) ) @ SY1946 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1947 @ tc_HOL_Obool ) ) @ SY1946 ) @ SV301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6125]) ).
thf(6450,plain,
! [SV302: $i] :
( ( ! [SY1948: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1948 @ tc_HOL_Obool ) ) @ SV302 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1948 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1948 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY1948 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1948 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1948 @ tc_HOL_Obool ) ) @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6126]) ).
thf(6451,plain,
! [SV303: $i] :
( ( ! [SY1949: $i,SY1950: $i,SY1951: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY1951 @ SY1950 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1950 @ SY1949 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1950 @ SV303 ) @ SY1949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6127]) ).
thf(6452,plain,
! [SV304: $i] :
( ( ! [SY1952: $i,SY1953: $i] :
( ( SY1953 != SY1952 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV304 @ tc_HOL_Obool ) ) @ SY1953 ) @ SY1952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6128]) ).
thf(6453,plain,
! [SV305: $i] :
( ( ! [SY1954: $i,SY1955: $i,SY1956: $i,SY1957: $i,SY1958: $i] :
( ( SY1958 != SY1957 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1956 @ SY1955 @ SY1954 ) @ SV305 ) @ SY1958 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY1956 @ SY1955 @ SY1954 ) @ SV305 ) @ SY1957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6129]) ).
thf(6454,plain,
! [SV306: $i] :
( ( ! [SY1959: $i,SY1960: $i] :
( ~ ( class_Orderings_Obot @ SY1960 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1959 @ SY1960 ) ) @ SV306 )
= ( c_Orderings_Obot__class_Obot @ SY1960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6130]) ).
thf(6455,plain,
! [SV307: $i] :
( ( ! [SY1961: $i,SY1962: $i,SY1963: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1963 @ SY1962 @ SY1961 ) @ SV307 ) )
| ~ ! [SY1964: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1961 @ SY1964 ) @ SV307 ) ) )
| ~ ( ~ ~ ! [SY1965: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1961 @ SY1965 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY1963 @ SY1962 @ SY1961 ) @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6131]) ).
thf(6456,plain,
! [SV308: $i] :
( ( ! [SY1966: $i,SY1967: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1967 @ tc_HOL_Obool ) ) @ SY1966 ) @ SV308 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1967 @ tc_HOL_Obool ) ) @ SY1966 ) @ SV308 )
= SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6132]) ).
thf(6457,plain,
! [SV309: $i] :
( ( ! [SY1968: $i,SY1969: $i,SY1970: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY1970 @ tc_HOL_Obool ) ) @ SY1969 ) @ SY1968 ) @ SV309 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SY1969 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SY1968 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6133]) ).
thf(6458,plain,
! [SV310: $i] :
( ( ! [SY1971: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SY1971 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV310 @ SY1971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6134]) ).
thf(6459,plain,
! [SV311: $i] :
( ( ! [SY1972: $i,SY1973: $i,SY1974: $i] :
( ~ ( hBOOL @ ( hAPP @ SY1974 @ SY1973 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1972 @ tc_HOL_Obool ) ) @ SY1974 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SY1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6135]) ).
thf(6460,plain,
! [SV312: $i] :
( ( ! [SY1975: $i,SY1976: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1976 @ tc_HOL_Obool ) ) @ SY1975 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1976 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SY1975 = SV312 ) )
| ~ ( ( SY1975 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1976 @ tc_HOL_Obool ) ) @ SY1975 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY1976 @ tc_HOL_Obool ) ) @ SV312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6136]) ).
thf(6461,plain,
! [SV313: $i] :
( ( ! [SY1977: $i,SY1978: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) ) @ SY1977 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1978 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) ) ) ) )
| ( SY1977
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) ) )
| ( SY1977
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY1978 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1978 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6137]) ).
thf(6462,plain,
! [SV314: $i] :
( ( ! [SY1979: $i,SY1980: $i,SY1981: $i,SY1982: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1982 @ SY1981 @ SY1980 ) @ SY1979 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1980 @ SV314 ) @ SY1979 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1980 @ SV314 ) @ SY1979 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY1982 @ SY1981 @ SY1980 ) @ SY1979 ) @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6138]) ).
thf(6463,plain,
! [SV315: $i] :
( ( ! [SY1983: $i,SY1984: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1984 @ SY1983 ) @ SV315 ) )
| ! [SY1985: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1983 @ SY1985 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1984 @ SY1983 ) @ SY1985 ) ) ) )
| ~ ( ~ ! [SY1986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1983 @ SY1986 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1984 @ SY1983 ) @ SY1986 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1984 @ SY1983 ) @ SV315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6139]) ).
thf(6464,plain,
! [SV316: $i] :
( ( ! [SY1987: $i,SY1988: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1988 ) @ SY1987 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1987 ) @ SV316 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY1988 ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6140]) ).
thf(6465,plain,
! [SV317: $i] :
( ( ! [SY1989: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY1989 )
!= ( hAPP @ c_Nat_OSuc @ SV317 ) )
| ( SY1989 = SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6141]) ).
thf(6466,plain,
! [SV318: $i] :
( ( ! [SY1990: $i,SY1991: $i,SY1992: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1992 @ tc_HOL_Obool ) ) @ SY1991 ) @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY1992 @ tc_HOL_Obool ) ) @ SY1990 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1992 @ tc_HOL_Obool ) ) @ SY1990 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY1992 @ tc_HOL_Obool ) ) @ SV318 ) @ SY1991 ) )
= SY1991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6142]) ).
thf(6467,plain,
! [SV319: $i] :
( ( ! [SY1993: $i,SY1994: $i,SY1995: $i,SY1996: $i,SY1997: $i] :
~ ( ~ ( ( SY1997 != SY1996 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1995 @ SY1994 @ SY1993 @ SY1996 @ SV319 ) @ SY1997 )
= SV319 ) )
| ~ ( ~ ( ( SY1997 != SY1996 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY1995 @ SY1994 @ SY1993 @ SY1996 @ SV319 ) @ SY1997 )
= ( hAPP @ SY1993 @ SY1997 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6143]) ).
thf(6468,plain,
! [SV320: $i] :
( ( ! [SY1998: $i,SY1999: $i,SY2000: $i,SY2001: $i,SY2002: $i,SY2003: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2003 @ SY2002 @ SY2001 @ SY2000 @ SY1999 @ SY1998 )
| ( ( hAPP @ ( hAPP @ SY2001 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6144]) ).
thf(6469,plain,
! [SV321: $i] :
( ( ! [SY2004: $i,SY2005: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2005 ) @ SY2004 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2005 @ tc_HOL_Obool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2005 ) @ SV321 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2005 @ tc_HOL_Obool ) ) ) )
| ( SY2004 = SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6145]) ).
thf(6470,plain,
! [SV322: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i,SY2009: $i,SY2010: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2010 @ ( tc_fun @ SY2009 @ tc_HOL_Obool ) ) ) @ SY2008 ) @ SY2007 ) @ SY2006 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2008 @ SY2006 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2007 @ SY2006 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6146]) ).
thf(6471,plain,
! [SV1: $i,SV323: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV323 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV323 @ tc_HOL_Obool ) ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6147]) ).
thf(6472,plain,
! [SV3: $i,SV324: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV3 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV324 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6149]) ).
thf(6473,plain,
! [SV4: $i,SV325: $i] :
( ( ! [SY2011: $i,SY2012: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2012 ) @ SY2011 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2012 ) @ SV325 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2012 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2012 ) @ SY2011 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6150]) ).
thf(6474,plain,
! [SV5: $i,SV326: $i] :
( ( ! [SY2013: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2013 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2013 ) @ SV326 ) @ SV5 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2013 ) @ SV326 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6151]) ).
thf(6475,plain,
! [SV6: $i,SV327: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV327 @ tc_HOL_Obool ) ) @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6152]) ).
thf(6476,plain,
! [SV7: $i,SV328: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV328 ) @ SV7 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV328 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6153]) ).
thf(6477,plain,
! [SV8: $i,SV329: $i] :
( ( ! [SY2014: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2014 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2014 ) @ SV329 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6154]) ).
thf(6478,plain,
! [SV10: $i,SV330: $i] :
( ( ! [SY2015: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY2015 @ SV330 @ SV10 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2015 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV330 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6156]) ).
thf(6479,plain,
! [SV11: $i,SV331: $i] :
( ( ! [SY2016: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2016 @ tc_HOL_Obool ) ) @ SV331 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2016 ) @ SV11 ) @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6157]) ).
thf(6480,plain,
! [SV12: $i,SV332: $i] :
( ( ! [SY2017: $i,SY2018: $i,SY2019: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY2019 @ SY2018 @ SY2017 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2019 ) @ SV332 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2018 ) @ ( hAPP @ SY2017 @ SV332 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2019 @ SY2018 @ SY2017 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6158]) ).
thf(6481,plain,
! [SV13: $i,SV333: $i] :
( ( ( c_Set_Othe__elem @ SV333 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV333 ) @ SV13 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV333 @ tc_HOL_Obool ) ) ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6159]) ).
thf(6482,plain,
! [SV15: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV334 ) @ SV15 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV15 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6161]) ).
thf(6483,plain,
! [SV16: $i,SV335: $i] :
( ( ! [SY2020: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2020 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2020 @ tc_HOL_Obool ) ) @ SV335 ) @ SV16 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2020 @ tc_HOL_Obool ) ) @ SV335 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6162]) ).
thf(6484,plain,
! [SV17: $i,SV336: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV336 @ tc_HOL_Obool ) ) @ SV17 ) @ SV17 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6163]) ).
thf(6485,plain,
! [SV18: $i,SV337: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV337 @ tc_HOL_Obool ) ) @ SV18 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV337 @ tc_HOL_Obool ) ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6164]) ).
thf(6486,plain,
! [SV19: $i,SV338: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV338 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV338 @ tc_HOL_Obool ) ) ) @ SV19 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV338 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6165]) ).
thf(6487,plain,
! [SV20: $i,SV339: $i] :
( ( ! [SY2021: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2021 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2021 @ tc_HOL_Obool ) ) @ SV339 ) @ SV20 ) ) @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6166]) ).
thf(6488,plain,
! [SV21: $i,SV340: $i] :
( ( ! [SY2022: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2022 ) @ SV340 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2022 @ tc_HOL_Obool ) ) @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2022 ) @ SV340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2022 @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2022 ) @ SV340 ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6167]) ).
thf(6489,plain,
! [SV22: $i,SV341: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2024 @ tc_HOL_Obool ) ) @ SY2023 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2024 ) @ SV341 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2024 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2024 @ tc_HOL_Obool ) ) @ SY2023 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2024 ) @ SV341 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2024 @ tc_HOL_Obool ) ) ) ) ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6168]) ).
thf(6490,plain,
! [SV23: $i,SV342: $i] :
( ( ! [SY2025: $i,SY2026: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2026 @ tc_HOL_Obool ) ) @ SY2025 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2026 ) @ SV342 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2026 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2026 @ tc_HOL_Obool ) ) @ SY2025 ) @ SV23 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2026 ) @ SV342 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2026 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6169]) ).
thf(6491,plain,
! [SV24: $i,SV343: $i] :
( ( ! [SY2027: $i,SY2028: $i] : ( c_Nitpick_Ofold__graph_H @ SY2028 @ SY2027 @ SV343 @ SV24 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2028 @ tc_HOL_Obool ) ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6170]) ).
thf(6492,plain,
! [SV25: $i,SV344: $i] :
( ( ! [SY2029: $i,SY2030: $i] : ( c_Nitpick_Ofold__graph_H @ SY2030 @ SY2029 @ SV344 @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2030 @ tc_HOL_Obool ) ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6171]) ).
thf(6493,plain,
! [SV26: $i,SV345: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) @ SV26 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6172]) ).
thf(6494,plain,
! [SV27: $i,SV346: $i] :
( ( ! [SY2031: $i,SY2032: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2032 @ SY2031 @ SV346 @ SV27 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2032 @ tc_HOL_Obool ) ) ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6173]) ).
thf(6495,plain,
! [SV28: $i,SV347: $i] :
( ( ! [SY2033: $i,SY2034: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2034 @ SY2033 @ SV347 @ SV28 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2034 @ tc_HOL_Obool ) ) ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6174]) ).
thf(6496,plain,
! [SV30: $i,SV348: $i] :
( ( ! [SY2035: $i] : ( c_Fun_Oinj__on @ SY2035 @ SV348 @ SV30 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2035 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6176]) ).
thf(6497,plain,
! [SV31: $i,SV349: $i] :
( ( ! [SY2036: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2036 @ SV349 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2036 @ tc_HOL_Obool ) ) ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6177]) ).
thf(6498,plain,
! [SV32: $i,SV350: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ( c_Fun_Ofun__upd @ SY2038 @ SY2037 @ SV350 @ SV32 @ ( hAPP @ SV350 @ SV32 ) )
= SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6178]) ).
thf(6499,plain,
! [SV33: $i,SV351: $i] :
( ( ! [SY2039: $i,SY2040: $i,SY2041: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2041 @ SY2040 @ SY2039 @ SV351 @ SV33 ) @ SV351 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6179]) ).
thf(6500,plain,
! [SV34: $i,SV352: $i] :
( ( ! [SY2042: $i,SY2043: $i,SY2044: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY2044 @ SY2043 @ SY2042 ) @ SV352 ) @ SV34 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2043 @ tc_HOL_Obool ) ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6180]) ).
thf(6501,plain,
! [SV35: $i,SV353: $i] :
( ( ! [SY2045: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ SY2045 @ SV353 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2045 ) @ SV35 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2045 @ tc_HOL_Obool ) ) ) )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6181]) ).
thf(6502,plain,
! [SV37: $i,SV354: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV354 ) @ SV37 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV37 ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6183]) ).
thf(6503,plain,
! [SV38: $i,SV355: $i] :
( ( ! [SY2046: $i,SY2047: $i,SY2048: $i,SY2049: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2049 @ SY2048 @ SY2047 @ SY2046 ) @ SV355 ) @ SV38 )
= ( hAPP @ SY2046 @ ( hAPP @ SV355 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6184]) ).
thf(6504,plain,
! [SV39: $i,SV356: $i] :
( ( ! [SY2050: $i,SY2051: $i,SY2052: $i,SY2053: $i,SY2054: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2054 @ SY2053 @ SY2052 @ SY2051 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY2050 @ SY2054 @ SY2052 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY2050 @ SY2053 @ SY2052 @ ( hAPP @ ( c_Fun_Ocomp @ SY2054 @ SY2053 @ SY2050 @ SY2051 ) @ SV356 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6185]) ).
thf(6505,plain,
! [SV40: $i,SV357: $i] :
( ( ! [SY2055: $i,SY2056: $i,SY2057: $i,SY2058: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2058 @ SY2057 @ SY2056 @ SY2055 ) @ SV357 ) @ SV40 )
= ( hAPP @ SY2055 @ ( hAPP @ SV357 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6186]) ).
thf(6506,plain,
! [SV41: $i,SV358: $i] :
( ( ! [SY2059: $i,SY2060: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY2060 @ SY2059 @ SV358 ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2060 @ tc_HOL_Obool ) ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6187]) ).
thf(6507,plain,
! [SV42: $i,SV359: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV359 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV359 @ tc_HOL_Obool ) ) @ SV42 ) )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6188]) ).
thf(6508,plain,
! [SV43: $i,SV360: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2062 @ ( tc_fun @ SY2061 @ tc_HOL_Obool ) ) ) @ SV360 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6189]) ).
thf(6509,plain,
! [SV44: $i,SV361: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2064 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2064 ) @ SY2063 ) @ SV361 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2064 ) @ SY2063 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2064 @ tc_HOL_Obool ) ) @ SV361 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6190]) ).
thf(6510,plain,
! [SV45: $i,SV362: $i] :
( ( ! [SY2065: $i,SY2066: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2066 @ tc_HOL_Obool ) ) @ SY2065 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2066 ) @ SV362 ) @ SV45 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2066 ) @ SV362 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2066 @ tc_HOL_Obool ) ) @ SY2065 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6191]) ).
thf(6511,plain,
! [SV46: $i,SV363: $i] :
( ( ! [SY2067: $i,SY2068: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2068 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2068 @ tc_HOL_Obool ) ) @ SY2067 ) @ SV363 ) ) @ SV46 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2068 @ tc_HOL_Obool ) ) @ SY2067 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2068 @ tc_HOL_Obool ) ) @ SV363 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6192]) ).
thf(6512,plain,
! [SV47: $i,SV364: $i] :
( ( ! [SY2069: $i,SY2070: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2070 @ tc_HOL_Obool ) ) @ SY2069 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2070 @ tc_HOL_Obool ) ) @ SV364 ) @ SV47 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2070 @ tc_HOL_Obool ) ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2070 @ tc_HOL_Obool ) ) @ SY2069 ) @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6193]) ).
thf(6513,plain,
! [SV48: $i,SV365: $i] :
( ( ! [SY2071: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2071 @ tc_HOL_Obool ) ) @ SV365 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2071 @ tc_HOL_Obool ) ) @ SV365 ) @ SV48 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2071 @ tc_HOL_Obool ) ) @ SV365 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6194]) ).
thf(6514,plain,
! [SV49: $i,SV366: $i] :
( ( ! [SY2072: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2072 @ tc_HOL_Obool ) ) @ SV366 ) @ SV49 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2072 @ tc_HOL_Obool ) ) @ SV49 ) @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6195]) ).
thf(6515,plain,
! [SV50: $i,SV367: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV367 @ tc_HOL_Obool ) ) @ SV50 ) @ SV50 )
= SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6196]) ).
thf(6516,plain,
! [SV51: $i,SV368: $i] :
( ( ! [SY2073: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2073 @ tc_HOL_Obool ) ) @ SV368 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2073 @ tc_HOL_Obool ) ) @ SV368 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6197]) ).
thf(6517,plain,
! [SV52: $i,SV369: $i] :
( ( ! [SY2074: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2074 @ tc_HOL_Obool ) ) @ SV369 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2074 @ tc_HOL_Obool ) ) @ SV52 ) @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6198]) ).
thf(6518,plain,
! [SV53: $i,SV370: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV370 @ tc_HOL_Obool ) ) @ SV53 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV370 @ tc_HOL_Obool ) ) )
= SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6199]) ).
thf(6519,plain,
! [SV54: $i,SV371: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV371 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV371 @ tc_HOL_Obool ) ) ) @ SV54 )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6200]) ).
thf(6520,plain,
! [SV55: $i,SV372: $i] :
( ( ! [SY2075: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2075 ) @ SV372 ) @ SV55 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2075 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2075 ) @ SV372 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2075 @ tc_HOL_Obool ) ) ) ) @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6201]) ).
thf(6521,plain,
! [SV57: $i,SV373: $i] :
( ( ! [SY2076: $i] :
( ( hAPP @ ( c_Relation_OImage @ SY2076 @ SV373 @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2076 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV373 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6203]) ).
thf(6522,plain,
! [SV58: $i,SV374: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV374 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV374 @ tc_HOL_Obool ) ) ) @ SV58 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV374 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6204]) ).
thf(6523,plain,
! [SV59: $i,SV375: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV375 @ tc_HOL_Obool ) ) @ SV59 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV375 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV375 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6205]) ).
thf(6524,plain,
! [SV60: $i,SV376: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV376 @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV376 @ tc_HOL_Obool ) ) ) @ SV60 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV376 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6206]) ).
thf(6525,plain,
! [SV61: $i,SV377: $i] :
( ( ! [SY2077: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2077 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2077 @ tc_HOL_Obool ) ) @ SV377 ) @ SV61 ) ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6207]) ).
thf(6526,plain,
! [SV62: $i,SV378: $i] :
( ( ! [SY2078: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2078 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2078 @ tc_HOL_Obool ) ) @ SV378 ) @ SV62 ) ) @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6208]) ).
thf(6527,plain,
! [SV63: $i,SV379: $i] :
( ( ! [SY2079: $i,SY2080: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2080 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2080 @ tc_HOL_Obool ) ) @ SY2079 ) @ SV379 ) ) @ SV63 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2080 @ tc_HOL_Obool ) ) @ SY2079 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2080 @ tc_HOL_Obool ) ) @ SV379 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6209]) ).
thf(6528,plain,
! [SV64: $i,SV380: $i] :
( ( ! [SY2081: $i,SY2082: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2082 @ tc_HOL_Obool ) ) @ SY2081 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2082 @ tc_HOL_Obool ) ) @ SV380 ) @ SV64 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2082 @ tc_HOL_Obool ) ) @ SV380 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2082 @ tc_HOL_Obool ) ) @ SY2081 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6210]) ).
thf(6529,plain,
! [SV65: $i,SV381: $i] :
( ( ! [SY2083: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2083 @ tc_HOL_Obool ) ) @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2083 @ tc_HOL_Obool ) ) @ SV381 ) @ SV65 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2083 @ tc_HOL_Obool ) ) @ SV381 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6211]) ).
thf(6530,plain,
! [SV66: $i,SV382: $i] :
( ( ! [SY2084: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2084 @ tc_HOL_Obool ) ) @ SV382 ) @ SV66 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2084 @ tc_HOL_Obool ) ) @ SV66 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6212]) ).
thf(6531,plain,
! [SV67: $i,SV383: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV383 @ tc_HOL_Obool ) ) @ SV67 ) @ SV67 )
= SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6213]) ).
thf(6532,plain,
! [SV68: $i,SV384: $i] :
( ( ! [SY2085: $i,SY2086: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2086 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2086 ) @ SY2085 ) @ SV384 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2086 ) @ SY2085 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2086 ) @ SY2085 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2086 @ tc_HOL_Obool ) ) @ SV384 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6214]) ).
thf(6533,plain,
! [SV69: $i,SV385: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) @ SV69 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV385 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6215]) ).
thf(6534,plain,
! [SV70: $i,SV386: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV386 @ tc_HOL_Obool ) ) @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6216]) ).
thf(6535,plain,
! [SV71: $i,SV387: $i] :
( ( ! [SY2087: $i] :
( ( hAPP @ ( c_Set_Ovimage @ SY2087 @ SV387 @ SV71 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2087 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6217]) ).
thf(6536,plain,
! [SV73: $i,SV388: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV388 ) @ SV73 )
= SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6219]) ).
thf(6537,plain,
! [SV74: $i,SV389: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV389 ) @ SV74 )
= SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6220]) ).
thf(6538,plain,
! [SV75: $i,SV390: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV390 ) @ SV75 )
= SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6221]) ).
thf(6539,plain,
! [SV76: $i,SV391: $i] :
( ( ! [SY2088: $i,SY2089: $i,SY2090: $i,SY2091: $i,SY2092: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2092 @ SY2091 @ SY2090 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2092 @ SY2089 @ SY2091 ) @ SY2088 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2092 @ SY2089 @ SY2090 ) @ SY2088 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2089 @ SY2091 @ SY2090 ) @ SV391 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6222]) ).
thf(6540,plain,
! [SV77: $i,SV392: $i] :
( ( ! [SY2093: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY2093 @ SV392 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV392 @ SY2093 ) @ SV77 ) )
= SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6223]) ).
thf(6541,plain,
! [SV78: $i,SV393: $i] :
( ( ! [SY2094: $i,SY2095: $i] :
( ( hAPP @ SY2095 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY2094 @ SY2094 ) @ SV393 ) @ SY2095 ) @ SV78 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY2094 @ SY2094 ) @ SV393 ) @ SY2095 ) @ ( hAPP @ SY2095 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6224]) ).
thf(6542,plain,
! [SV79: $i,SV394: $i] :
( ( c_Relation_Ototal__on @ SV394 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV394 @ tc_HOL_Obool ) ) @ SV79 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6225]) ).
thf(6543,plain,
! [SV80: $i,SV395: $i] :
( ( ! [SY2096: $i,SY2097: $i,SY2098: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2098 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2098 @ SY2097 ) @ SY2096 ) @ SV395 ) ) @ SY2096 ) @ SV80 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2098 @ SY2097 ) @ SY2096 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6226]) ).
thf(6544,plain,
! [SV81: $i,SV396: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2100 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2100 ) @ SY2099 ) @ SV396 ) ) @ SV81 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2100 ) @ SY2099 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2100 ) @ SV396 ) @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6227]) ).
thf(6545,plain,
! [SV82: $i,SV397: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV397 ) @ ( hAPP @ ( c_List_Orev @ SV397 ) @ SV82 ) )
= SV82 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6228]) ).
thf(6546,plain,
! [SV83: $i,SV398: $i] :
( ( ( hAPP @ ( c_COMBI @ SV398 ) @ SV83 )
= SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6229]) ).
thf(6547,plain,
! [SV84: $i,SV399: $i] :
( ( ! [SY2101: $i,SY2102: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY2102 @ SY2101 ) @ SV399 ) @ SV84 )
= SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6230]) ).
thf(6548,plain,
! [SV85: $i,SV400: $i] :
( ( ! [SY2103: $i,SY2104: $i,SY2105: $i,SY2106: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2106 @ SY2105 @ SY2104 ) @ SY2103 ) @ SV400 ) @ SV85 )
= ( hAPP @ SY2103 @ ( hAPP @ SV400 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6231]) ).
thf(6549,plain,
! [SV86: $i,SV401: $i] :
( ( ! [SY2107: $i,SY2108: $i,SY2109: $i,SY2110: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2110 @ SY2109 @ SY2108 ) @ SY2107 ) @ SV401 ) @ SV86 )
= ( hAPP @ ( hAPP @ SY2107 @ SV86 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6232]) ).
thf(6550,plain,
! [SV87: $i,SV402: $i] :
( ( ! [SY2111: $i,SY2112: $i,SY2113: $i,SY2114: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2114 @ SY2113 @ SY2112 ) @ SY2111 ) @ SV402 ) @ SV87 )
= ( hAPP @ ( hAPP @ SY2111 @ SV87 ) @ ( hAPP @ SV402 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6233]) ).
thf(6551,plain,
! [SV88: $i,SV403: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV403 ) @ SV88 ) )
| ( SV403 = SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6234]) ).
thf(6552,plain,
! [SV89: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_fNot @ SV89 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6236]) ).
thf(6553,plain,
! [SV90: $i] :
( ( ( ~ ~ ( hBOOL @ SV90 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6237]) ).
thf(6554,plain,
! [SV91: $i,SV404: $i] :
( ( ~ ( hBOOL @ SV404 )
| ~ ( hBOOL @ SV91 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV404 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6238]) ).
thf(6555,plain,
! [SV92: $i,SV405: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV405 ) @ SV92 ) )
| ( hBOOL @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6239]) ).
thf(6556,plain,
! [SV93: $i,SV406: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV406 ) @ SV93 ) )
| ( hBOOL @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6240]) ).
thf(6557,plain,
! [SV94: $i,SV407: $i] :
( ( ~ ( hBOOL @ SV407 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV407 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6241]) ).
thf(6558,plain,
! [SV95: $i,SV408: $i] :
( ( ~ ( hBOOL @ SV408 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV95 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6242]) ).
thf(6559,plain,
! [SV96: $i,SV409: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV409 ) @ SV96 ) )
| ( hBOOL @ SV409 )
| ( hBOOL @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6243]) ).
thf(6560,plain,
! [SV97: $i,SV410: $i] :
( ( ( hBOOL @ SV410 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV410 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6244]) ).
thf(6561,plain,
! [SV98: $i,SV411: $i] :
( ( ~ ( hBOOL @ SV411 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV98 ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6245]) ).
thf(6562,plain,
! [SV99: $i,SV412: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV412 ) @ SV99 ) )
| ~ ( hBOOL @ SV412 )
| ( hBOOL @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6246]) ).
thf(6563,plain,
! [SV100: $i,SV413: $i] :
( ( ! [SY2115: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2115 @ SV413 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV413 @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6248]) ).
thf(6564,plain,
! [SV101: $i,SV414: $i] :
( ( ! [SY2116: $i,SY2117: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2117 @ SY2116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV414 @ tc_HOL_Obool ) ) @ SV101 ) @ SY2117 ) @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6249]) ).
thf(6565,plain,
! [SV102: $i,SV415: $i] :
( ( ! [SY2118: $i] :
( ~ ( class_Orderings_Obot @ SY2118 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV415 @ SY2118 ) ) @ SV102 )
= ( c_Orderings_Obot__class_Obot @ SY2118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6250]) ).
thf(6566,plain,
! [SV103: $i,SV416: $i] :
( ( ! [SY2119: $i,SY2120: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2120 @ SY2119 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2120 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2120 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) )
| ~ ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2120 @ SY2119 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2120 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2120 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6251]) ).
thf(6567,plain,
! [SV104: $i,SV417: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
| ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6252]) ).
thf(6568,plain,
! [SV105: $i,SV418: $i] :
( ( ! [SY2121: $i,SY2122: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2122 @ tc_HOL_Obool ) ) @ SY2121 ) @ SV418 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2122 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2122 @ tc_HOL_Obool ) ) @ SY2121 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6253]) ).
thf(6569,plain,
! [SV106: $i,SV419: $i] :
( ( ! [SY2123: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY2123 ) @ SV419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SY2123 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6254]) ).
thf(6570,plain,
! [SV107: $i,SV420: $i] :
( ( ! [SY2124: $i,SY2125: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2125 @ tc_HOL_Obool ) ) @ SY2124 ) @ SV420 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2125 @ tc_HOL_Obool ) ) @ SY2124 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2125 ) @ SV107 ) @ SV420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6255]) ).
thf(6571,plain,
! [SV108: $i,SV421: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6256]) ).
thf(6572,plain,
! [SV109: $i,SV422: $i] :
( ( ! [SY2126: $i,SY2127: $i,SY2128: $i,SY2129: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2129 @ SY2128 @ SY2127 )
| ( ( hAPP @ ( hAPP @ SY2127 @ SY2126 ) @ ( hAPP @ ( hAPP @ SY2127 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SY2127 @ SV422 ) @ ( hAPP @ ( hAPP @ SY2127 @ SY2126 ) @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6257]) ).
thf(6573,plain,
! [SV110: $i,SV423: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
| ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
| ~ ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6258]) ).
thf(6574,plain,
! [SV111: $i,SV424: $i] :
( ( ( SV424 != SV111 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV424 ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6259]) ).
thf(6575,plain,
! [SV112: $i,SV425: $i] :
( ( ~ ( class_Orderings_Otop @ SV425 )
| ( class_Orderings_Otop @ ( tc_fun @ SV112 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6260]) ).
thf(6576,plain,
! [SV113: $i,SV426: $i] :
( ( ! [SY2134: $i,SY2135: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2135 ) @ SY2134 ) @ SV426 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2135 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2135 ) @ SY2134 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2135 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2135 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2135 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2135 ) @ SY2134 ) @ SV113 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6261]) ).
thf(6577,plain,
! [SV114: $i,SV427: $i] :
( ( ! [SY2136: $i,SY2137: $i,SY2138: $i,SY2139: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2139 @ SY2138 ) @ SY2137 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2136 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SY2139 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SY2138 ) @ SY2137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6262]) ).
thf(6578,plain,
! [SV115: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV115 )
= SV115 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6263]) ).
thf(6579,plain,
! [SV116: $i,SV428: $i] :
( ( ! [SY2140: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY2140 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV428 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2140 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY2140 @ tc_HOL_Obool ) @ SV116 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SY2140 @ tc_HOL_Obool ) @ SV428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6264]) ).
thf(6580,plain,
! [SV117: $i,SV429: $i] :
( ( ! [SY2141: $i,SY2142: $i,SY2143: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY2143 @ SY2142 @ SY2141 @ SV429 @ SV117 )
!= SY2141 )
| ( ( hAPP @ SY2141 @ SV429 )
= SV117 ) )
| ~ ( ( ( hAPP @ SY2141 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SY2143 @ SY2142 @ SY2141 @ SV429 @ SV117 )
= SY2141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6265]) ).
thf(6581,plain,
! [SV118: $i,SV430: $i] :
( ( ! [SY2144: $i,SY2145: $i,SY2146: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2146 ) @ SY2145 ) @ SY2144 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2146 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SY2145 != SV430 )
| ( SY2144 != SV118 ) ) )
| ~ ( ~ ~ ( ( SY2145 != SV430 )
| ( SY2144 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2146 ) @ SY2145 ) @ SY2144 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2146 ) @ SV430 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6266]) ).
thf(6582,plain,
! [SV119: $i,SV431: $i] :
( ( ! [SY2147: $i] :
( ~ ( c_Wellfounded_OwfP @ SY2147 @ SV431 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2147 @ ( tc_fun @ SY2147 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) )
| ( c_Wellfounded_OwfP @ SY2147 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6267]) ).
thf(6583,plain,
! [SV120: $i,SV432: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2149 ) @ SY2148 ) @ SV432 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2149 ) @ SY2148 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2149 ) @ SV120 ) @ SV432 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6268]) ).
thf(6584,plain,
! [SV121: $i,SV433: $i] :
( ( ! [SY2150: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2150 ) @ SV433 ) @ SV121 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2150 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6269]) ).
thf(6585,plain,
! [SV122: $i,SV434: $i] :
( ( ! [SY2151: $i,SY2152: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2152 @ tc_HOL_Obool ) ) @ SY2151 ) @ SV434 ) @ SV122 ) )
| ( hBOOL @ ( hAPP @ SV434 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6270]) ).
thf(6586,plain,
! [SV123: $i,SV435: $i] :
( ( ! [SY2153: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2153 ) @ SV435 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2153 ) @ SV435 ) @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6271]) ).
thf(6587,plain,
! [SV124: $i,SV436: $i] :
( ( ! [SY2154: $i,SY2155: $i,SY2156: $i,SY2157: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2157 @ ( tc_fun @ SY2156 @ tc_HOL_Obool ) ) ) @ SY2155 ) @ SY2154 ) @ SV436 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2154 @ SV436 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6272]) ).
thf(6588,plain,
! [SV125: $i,SV437: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV437 ) @ SV125 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SV437 ) )
| ( SV437 = SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6273]) ).
thf(6589,plain,
! [SV126: $i,SV438: $i] :
( ( ! [SY2158: $i,SY2159: $i] :
( ~ ( class_Orderings_Oorder @ SY2159 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2159 ) @ SY2158 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2159 ) @ SV126 ) @ SY2158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2159 ) @ SV126 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6274]) ).
thf(6590,plain,
! [SV127: $i,SV439: $i] :
( ( ! [SY2160: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2160 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2160 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2160 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2160 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6275]) ).
thf(6591,plain,
! [SV128: $i,SV440: $i] :
( ( ! [SY2161: $i] :
~ ( ~ ( ~ ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2161 @ SX3 ) )
| ! [SY2163: $i,SY2164: $i] : ( hBOOL @ ( hAPP @ SY2161 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2163 ) @ SY2164 ) ) ) )
| ~ ( ~ ! [SY2165: $i,SY2166: $i] : ( hBOOL @ ( hAPP @ SY2161 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2165 ) @ SY2166 ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ SY2161 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6276]) ).
thf(6592,plain,
! [SV129: $i,SV441: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY2169 @ SY2168 @ SV441 )
| ( ( hAPP @ ( hAPP @ SY2168 @ SV129 ) @ SV129 )
= SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6277]) ).
thf(6593,plain,
! [SV130: $i,SV442: $i] :
( ( ! [SY2170: $i] :
( ~ ( c_Predicate_Oreflp @ SY2170 @ SV442 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV442 @ SV130 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6278]) ).
thf(6594,plain,
! [SV131: $i,SV443: $i] :
( ( ! [SY2171: $i,SY2172: $i,SY2173: $i,SY2174: $i,SY2175: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2175 @ SY2174 @ SY2173 @ SY2172 @ SY2171 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2176: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2172 @ SV443 ) @ SY2176 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2171 @ SY2176 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2177: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2172 @ SV443 ) @ SY2177 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2171 @ SY2177 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2175 @ SY2174 @ SY2173 @ SY2172 @ SY2171 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6279]) ).
thf(6595,plain,
! [SV132: $i,SV444: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i,SY2181: $i,SY2182: $i,SY2183: $i,SY2184: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2184 @ SY2183 @ SY2182 @ SY2181 ) @ SY2180 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY2179 @ SY2183 @ SY2182 @ SY2178 ) @ SV444 ) )
| ( ( hAPP @ SY2181 @ ( hAPP @ SY2180 @ SV132 ) )
= ( hAPP @ SY2178 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6280]) ).
thf(6596,plain,
! [SV133: $i,SV445: $i] :
( ( ! [SY2185: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2185 @ tc_HOL_Obool ) ) @ SV445 ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY2185 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SY2185 ) @ SV445 ) ) @ ( hAPP @ ( c_Set_OPow @ SY2185 ) @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6281]) ).
thf(6597,plain,
! [SV134: $i,SV446: $i] :
( ( ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
| ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
| ~ ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6282]) ).
thf(6598,plain,
! [SV135: $i,SV447: $i] :
( ( ! [SY2188: $i,SY2189: $i,SY2190: $i,SY2191: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2191 @ ( tc_fun @ SY2190 @ tc_HOL_Obool ) ) ) @ SY2189 ) @ SY2188 ) @ SV447 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2189 @ SV447 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6283]) ).
thf(6599,plain,
! [SV136: $i,SV448: $i] :
( ( ! [SY2192: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2192 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2192 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2192 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2192 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6284]) ).
thf(6600,plain,
! [SV137: $i,SV449: $i] :
( ( ! [SY2193: $i,SY2194: $i] :
( ~ ( c_Predicate_Osymp @ SY2194 @ SY2193 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2193 @ SV449 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2193 @ SV137 ) @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6285]) ).
thf(6601,plain,
! [SV138: $i,SV450: $i] :
( ( ! [SY2195: $i] :
( ~ ( class_Orderings_Olinorder @ SY2195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2195 ) @ SV450 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2195 ) @ SV138 ) @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6286]) ).
thf(6602,plain,
! [SV139: $i,SV451: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV451 )
| ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV139 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6287]) ).
thf(6603,plain,
! [SV140: $i,SV452: $i] :
( ( ! [SY2196: $i] :
( SY2196
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV452 ) @ SV140 ) @ SY2196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6288]) ).
thf(6604,plain,
! [SV141: $i,SV453: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ SV453 ) @ SV141 ) )
| ( v_P @ SV141 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6289]) ).
thf(6605,plain,
! [SV142: $i,SV454: $i] :
( ( ! [SY2197: $i,SY2198: $i,SY2199: $i,SY2200: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2200 @ ( tc_fun @ SY2199 @ tc_HOL_Obool ) ) ) @ SY2198 ) @ SY2197 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2198 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2197 @ SV454 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6290]) ).
thf(6606,plain,
! [SV143: $i,SV455: $i] :
( ( ! [SY2201: $i,SY2202: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2202 @ tc_HOL_Obool ) ) @ SY2201 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP @ SY2201 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SV455 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6291]) ).
thf(6607,plain,
! [SV144: $i,SV456: $i] :
( ( ! [SY2203: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2203 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2203 ) @ SV144 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2203 ) @ SV456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6292]) ).
thf(6608,plain,
! [SV145: $i,SV457: $i] :
( ( ! [SY2204: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2204 @ tc_HOL_Obool ) ) @ SV457 ) @ SV145 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2204 @ tc_HOL_Obool ) ) @ SV145 ) @ SV457 )
= SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6293]) ).
thf(6609,plain,
! [SV146: $i,SV458: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i,SY2208: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2208 @ SY2207 ) @ SY2206 ) @ SY2205 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2208 @ SY2207 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SY2206 != SV458 )
| ( SY2205 != SV146 ) ) )
| ~ ( ~ ~ ( ( SY2206 != SV458 )
| ( SY2205 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2208 @ SY2207 ) @ SY2206 ) @ SY2205 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2208 @ SY2207 ) @ SV458 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6294]) ).
thf(6610,plain,
! [SV147: $i,SV459: $i] :
( ( ! [SY2209: $i,SY2210: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2210 @ tc_HOL_Obool ) ) @ SY2209 ) @ SV459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2210 ) @ SV147 ) @ SY2209 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2210 ) @ SV147 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6295]) ).
thf(6611,plain,
! [SV148: $i,SV460: $i] :
( ( ! [SY2211: $i,SY2212: $i,SY2213: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2213 @ SY2212 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SY2211 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2212 @ SY2211 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6296]) ).
thf(6612,plain,
! [SV149: $i,SV461: $i] :
( ( ! [SY2214: $i] :
( ~ ( class_Orderings_Oorder @ SY2214 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2214 ) @ SV461 ) @ SV149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2214 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6297]) ).
thf(6613,plain,
! [SV150: $i,SV462: $i] :
( ( ! [SY2215: $i,SY2216: $i,SY2217: $i] :
( ( ( hAPP @ SY2217 @ SY2216 )
!= SY2215 )
| ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SY2217 @ SY2216 @ SY2215 )
= SY2217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6298]) ).
thf(6614,plain,
! [SV151: $i,SV463: $i] :
( ( ! [SY2218: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY2218 @ SV463 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SY2218 @ SV463 ) @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6299]) ).
thf(6615,plain,
! [SV152: $i,SV464: $i] :
( ( ! [SY2219: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2219 ) @ SV464 ) @ SV152 )
!= SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6300]) ).
thf(6616,plain,
! [SV153: $i,SV465: $i] :
( ( ! [SY2220: $i,SY2221: $i,SY2222: $i,SY2223: $i,SY2224: $i,SY2225: $i,SY2226: $i,SY2227: $i,SY2228: $i] :
( ( ( hAPP @ SY2228 @ ( hAPP @ SY2227 @ SY2226 ) )
!= ( hAPP @ SY2225 @ ( hAPP @ SY2224 @ SY2223 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2222 @ SY2221 @ SY2220 @ SY2228 ) @ SY2227 ) @ SY2226 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SY2221 @ SV153 @ SY2225 ) @ SY2224 ) @ SY2223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6301]) ).
thf(6617,plain,
! [SV154: $i,SV466: $i] :
( ( ! [SY2229: $i,SY2230: $i,SY2231: $i] :
( ~ ( c_Predicate_Otransp @ SY2231 @ SY2230 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2230 @ SY2229 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2230 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2230 @ SY2229 ) @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6302]) ).
thf(6618,plain,
! [SV155: $i,SV467: $i] :
( ( ! [SY2232: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2232 @ SV467 ) @ SV155 ) )
| ! [SY2233: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2233 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2232 @ SV467 ) @ SY2233 ) ) ) )
| ~ ( ~ ! [SY2234: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2234 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2232 @ SV467 ) @ SY2234 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2232 @ SV467 ) @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6303]) ).
thf(6619,plain,
! [SV156: $i,SV468: $i] :
( ( ! [SY2235: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2235 ) @ SV468 ) @ SV156 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2235 ) @ SV468 ) @ SV156 )
= SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6304]) ).
thf(6620,plain,
! [SV157: $i,SV469: $i] :
( ( ~ ~ ! [SY2236: $i] :
~ ( hBOOL @ ( hAPP @ SV469 @ SY2236 ) )
| ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6305]) ).
thf(6621,plain,
! [SV158: $i,SV470: $i] :
( ( ! [SY2237: $i,SY2238: $i] :
( ~ ( class_Orderings_Opreorder @ SY2238 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2238 ) @ SY2237 ) @ SV470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2238 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2238 ) @ SY2237 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6306]) ).
thf(6622,plain,
! [SV159: $i,SV471: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2240 @ SY2239 @ SV471 ) @ SV159 ) )
| ( SV471
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2240 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6307]) ).
thf(6623,plain,
! [SV160: $i,SV472: $i] :
( ( ! [SY2241: $i,SY2242: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2242 @ tc_HOL_Obool ) ) @ SY2241 ) @ SV472 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2242 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2242 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2242 @ tc_HOL_Obool ) ) @ SY2241 ) @ SV160 ) ) @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6308]) ).
thf(6624,plain,
! [SV161: $i,SV473: $i] :
( ( ~ ( ~ ( ~ ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) )
| ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6309]) ).
thf(6625,plain,
! [SV162: $i,SV474: $i] :
( ( ! [SY2245: $i,SY2246: $i] :
( ( SY2246 != SY2245 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2246 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2245 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2245 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2246 ) @ SV162 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6310]) ).
thf(6626,plain,
! [SV163: $i,SV475: $i] :
( ( ! [SY2247: $i,SY2248: $i,SY2249: $i,SY2250: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2250 @ SY2249 @ SY2248 @ SY2247 @ SV475 )
| ( ( hAPP @ SY2247 @ ( hAPP @ SY2248 @ SV163 ) )
= SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6311]) ).
thf(6627,plain,
! [SV164: $i,SV476: $i] :
( ( ! [SY2251: $i,SY2252: $i,SY2253: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2253 @ tc_HOL_Obool ) ) @ SY2252 ) @ SY2251 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2253 @ SV164 ) @ SY2252 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2253 @ SV164 ) @ SY2251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6312]) ).
thf(6628,plain,
! [SV165: $i,SV477: $i] :
( ( ! [SY2254: $i,SY2255: $i,SY2256: $i,SY2257: $i,SY2258: $i,SY2259: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2259 @ SY2258 ) @ SY2257 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2256 @ SY2257 ) @ SY2255 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2254 @ SV477 @ SV165 @ SY2259 @ SY2256 ) @ SY2258 ) @ SY2255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6313]) ).
thf(6629,plain,
! [SV166: $i,SV478: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV478 )
| ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV166 @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6314]) ).
thf(6630,plain,
! [SV167: $i,SV479: $i] :
( ( ! [SY2260: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2260 @ SV479 ) )
| ( hBOOL @ ( hAPP @ SY2260 @ ( c_Hilbert__Choice_OEps @ SV167 @ SY2260 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6315]) ).
thf(6631,plain,
! [SV168: $i,SV480: $i] :
( ( ! [SY2261: $i] :
( ~ ( class_Orderings_Oorder @ SY2261 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2261 ) @ SV480 ) @ SV168 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2261 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2261 ) @ SV168 ) @ SV480 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6316]) ).
thf(6632,plain,
! [SV169: $i,SV481: $i] :
( ( ! [SY2262: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY2262 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SY2262 ) @ SV169 ) )
| ( SV481 = SV169 ) )
| ~ ( ( SV481 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SY2262 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SY2262 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6317]) ).
thf(6633,plain,
! [SV170: $i,SV482: $i] :
( ( ! [SY2263: $i,SY2264: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2264 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SY2263 @ SY2264 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2263 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2263 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2264 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SY2263 @ SY2264 @ SV482 ) @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6318]) ).
thf(6634,plain,
! [SV171: $i,SV483: $i] :
( ( ! [SY2265: $i] :
( ~ ( class_Orderings_Oorder @ SY2265 )
| ~ ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2265 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2265 ) @ SV171 ) @ SV483 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2265 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2265 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6319]) ).
thf(6635,plain,
! [SV172: $i,SV484: $i] :
( ( ~ ( class_Lattices_Olattice @ SV484 )
| ( class_Lattices_Olattice @ ( tc_fun @ SV172 @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6320]) ).
thf(6636,plain,
! [SV173: $i,SV485: $i] :
( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV485 )
| ~ ( class_Enum_Oenum @ SV173 ) )
| ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6321]) ).
thf(6637,plain,
! [SV174: $i,SV486: $i] :
( ( ! [SY2266: $i,SY2267: $i,SY2268: $i,SY2269: $i,SY2270: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2270 @ SY2269 @ SY2268 @ SY2267 @ SY2266 )
| ~ ( ~ ( ( ( hAPP @ SY2268 @ SV486 )
!= ( hAPP @ SY2268 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SY2268 @ SV486 )
= ( hAPP @ SY2268 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6322]) ).
thf(6638,plain,
! [SV175: $i,SV487: $i] :
( ( ! [SY2271: $i,SY2272: $i,SY2273: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2273 @ tc_HOL_Obool ) ) @ SY2272 ) @ SY2271 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2273 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2273 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2273 @ tc_HOL_Obool ) ) @ SY2272 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2273 @ tc_HOL_Obool ) ) @ SY2271 ) @ SV487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6323]) ).
thf(6639,plain,
! [SV176: $i,SV488: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2275 ) @ SY2274 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2275 ) @ SV176 ) @ SV488 ) )
| ( SY2274 = SV176 ) )
| ~ ( ( SY2274 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2275 ) @ SY2274 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2275 ) @ SV176 ) @ SV488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6324]) ).
thf(6640,plain,
! [SV177: $i,SV489: $i] :
( ( ! [SY2276: $i,SY2277: $i,SY2278: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2278 @ SY2277 ) @ SY2276 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SY2278 ) @ SY2276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6325]) ).
thf(6641,plain,
! [SV178: $i,SV490: $i] :
( ( ! [SY2279: $i,SY2280: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2280 ) @ SY2279 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2280 ) @ SY2279 ) @ SV178 ) )
| ( SV490 = SV178 ) )
| ~ ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2280 ) @ SY2279 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2280 ) @ SY2279 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6326]) ).
thf(6642,plain,
! [SV179: $i,SV491: $i] :
( ( ! [SY2281: $i,SY2282: $i,SY2283: $i,SY2284: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2284 @ ( tc_fun @ SY2283 @ tc_HOL_Obool ) ) ) @ SY2282 ) @ SY2281 ) @ SV491 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2282 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2281 @ SV491 ) @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6327]) ).
thf(6643,plain,
! [SV180: $i,SV492: $i] :
( ( ! [SY2285: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2285 ) @ SV492 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2285 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2285 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6328]) ).
thf(6644,plain,
! [SV181: $i,SV493: $i] :
( ( ! [SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2289 @ SY2288 ) @ SY2287 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2286 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SY2289 ) @ SV181 ) @ SY2288 ) @ SY2287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6329]) ).
thf(6645,plain,
! [SV182: $i,SV494: $i] :
( ( ! [SY2290: $i,SY2291: $i,SY2292: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2292 @ tc_HOL_Obool ) ) @ SY2291 ) @ ( hAPP @ ( c_Set_Oimage @ SY2290 @ SY2292 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY2293: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2290 @ tc_HOL_Obool ) ) @ SY2293 ) @ SV182 ) )
| ( SY2291
!= ( hAPP @ ( c_Set_Oimage @ SY2290 @ SY2292 @ SV494 ) @ SY2293 ) ) ) )
| ~ ( ~ ~ ! [SY2294: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2290 @ tc_HOL_Obool ) ) @ SY2294 ) @ SV182 ) )
| ( SY2291
!= ( hAPP @ ( c_Set_Oimage @ SY2290 @ SY2292 @ SV494 ) @ SY2294 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2292 @ tc_HOL_Obool ) ) @ SY2291 ) @ ( hAPP @ ( c_Set_Oimage @ SY2290 @ SY2292 @ SV494 ) @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6330]) ).
thf(6646,plain,
! [SV183: $i,SV495: $i] :
( ( ! [SY2295: $i] :
( ( SY2295 != SV495 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SY2295 ) @ SV495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SY2295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6331]) ).
thf(6647,plain,
! [SV184: $i,SV496: $i] :
( ( ! [SY2296: $i,SY2297: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2297 @ tc_HOL_Obool ) ) @ SY2296 ) @ SV496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2297 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2297 @ tc_HOL_Obool ) ) @ SY2296 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6332]) ).
thf(6648,plain,
! [SV185: $i,SV497: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ~ ( class_Orderings_Oord @ SY2299 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2299 ) @ SY2298 ) @ SV497 ) )
| ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2299 ) @ SY2298 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6333]) ).
thf(6649,plain,
! [SV186: $i,SV498: $i] :
( ( ! [SY2300: $i,SY2301: $i] :
( ~ ( class_Orderings_Oorder @ SY2301 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2301 ) @ SY2300 ) @ SV498 ) )
| ( SY2300 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2301 ) @ SV186 ) @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6334]) ).
thf(6650,plain,
! [SV187: $i,SV499: $i] :
( ( ! [SY2302: $i,SY2303: $i,SY2304: $i] :
( ~ ( class_Orderings_Oord @ SY2304 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2303 @ SY2304 ) ) @ SY2302 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2304 ) @ ( hAPP @ SY2302 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6335]) ).
thf(6651,plain,
! [SV188: $i,SV500: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2307 @ SY2306 ) @ SY2305 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SY2307 ) @ SY2305 ) @ SY2306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6336]) ).
thf(6652,plain,
! [SV189: $i,SV501: $i] :
( ( ! [SY2308: $i,SY2309: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2309 @ tc_HOL_Obool ) ) @ SY2308 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2309 @ tc_HOL_Obool ) ) @ SY2308 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2309 @ tc_HOL_Obool ) ) @ SY2308 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2309 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6337]) ).
thf(6653,plain,
! [SV190: $i,SV502: $i] :
( ( ! [SY2310: $i,SY2311: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2311 @ tc_HOL_Obool ) ) @ SY2310 ) @ SV502 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2311 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2311 @ tc_HOL_Obool ) ) @ SY2310 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6338]) ).
thf(6654,plain,
! [SV191: $i,SV503: $i] :
( ( ! [SY2312: $i,SY2313: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2313 @ SY2312 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2312 @ SV503 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2312 @ SV191 ) @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6339]) ).
thf(6655,plain,
! [SV192: $i,SV504: $i] :
( ( ! [SY2314: $i,SY2315: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2315 ) @ SY2314 ) @ SV504 ) )
| ( SY2314 = SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2315 ) @ SY2314 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2315 ) @ SV192 ) @ SV504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6340]) ).
thf(6656,plain,
! [SV193: $i,SV505: $i] :
( ( ! [SY2316: $i,SY2317: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2317 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2317 ) @ SY2316 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2317 ) @ SY2316 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2317 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2317 ) @ SY2316 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2317 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2317 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2317 ) @ SY2316 ) @ SV505 ) ) @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6341]) ).
thf(6657,plain,
! [SV194: $i,SV506: $i] :
( ( ~ ( class_Groups_Ouminus @ SV506 )
| ( class_Groups_Ouminus @ ( tc_fun @ SV194 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6342]) ).
thf(6658,plain,
! [SV195: $i,SV507: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2319 ) @ SY2318 ) @ SV507 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2319 ) @ SY2318 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2319 ) @ SY2318 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2319 ) @ SY2318 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2319 ) @ SY2318 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2319 ) @ SY2318 ) @ SV195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6343]) ).
thf(6659,plain,
! [SV196: $i,SV508: $i] :
( ( ! [SY2320: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2320 @ ( tc_fun @ SY2320 @ tc_HOL_Obool ) ) ) @ SV508 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2320 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SY2320 @ SV196 ) ) @ ( c_Wellfounded_Oaccp @ SY2320 @ SV508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6344]) ).
thf(6660,plain,
! [SV197: $i,SV509: $i] :
( ( ! [SY2321: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY2321 ) @ SV509 )
!= SV197 )
| ( SV509
= ( hAPP @ ( c_List_Orev @ SY2321 ) @ SV197 ) ) )
| ~ ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SY2321 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SY2321 ) @ SV509 )
= SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6345]) ).
thf(6661,plain,
! [SV198: $i,SV510: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
| ( SV510 = SV198 ) )
| ~ ( ( SV510 != SV198 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6346]) ).
thf(6662,plain,
! [SV199: $i,SV511: $i] :
( ( ! [SY2322: $i,SY2323: $i,SY2324: $i,SY2325: $i] :
( ~ ( ( SY2325 != SY2324 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2323 @ SY2322 ) @ SY2325 ) @ SV511 ) ) @ SY2324 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2323 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2323 @ SY2322 ) @ SY2324 ) @ SV199 ) ) @ SY2325 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6347]) ).
thf(6663,plain,
! [SV200: $i,SV512: $i] :
( ( ! [SY2326: $i,SY2327: $i] :
( ~ ( c_Fun_Obij__betw @ SY2327 @ SY2326 @ SV512 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2326 @ tc_HOL_Obool ) ) )
| ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2327 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6348]) ).
thf(6664,plain,
! [SV201: $i,SV513: $i] :
( ( ! [SY2328: $i,SY2329: $i] :
( ~ ( class_Orderings_Oord @ SY2329 )
| ( SY2328 != SV513 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2329 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2329 ) @ SY2328 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6349]) ).
thf(6665,plain,
! [SV202: $i,SV514: $i] :
( ( ! [SY2330: $i,SY2331: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2331 ) @ SY2330 ) @ SV514 ) @ SV202 ) )
| ( SY2330 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ~ ( ~ ( ( SY2330 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2331 ) @ SY2330 ) @ SV514 ) @ SV202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6350]) ).
thf(6666,plain,
! [SV203: $i,SV515: $i] :
( ( ! [SY2332: $i] :
( ( SY2332 != SV515 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SV515 ) @ SY2332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6351]) ).
thf(6667,plain,
! [SV204: $i,SV516: $i] :
( ( ! [SY2333: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2333 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2333 ) @ SV204 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2333 @ tc_HOL_Obool ) ) ) ) )
| ( SV516 = SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6352]) ).
thf(6668,plain,
! [SV205: $i,SV517: $i] :
( ( ! [SY2334: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2334 ) @ SV517 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2334 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2334 ) @ SV205 ) @ SV517 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6353]) ).
thf(6669,plain,
! [SV206: $i,SV518: $i] :
( ( ! [SY2335: $i,SY2336: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2336 @ SY2335 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV518 @ tc_HOL_Obool ) ) @ SY2336 ) @ SV206 ) @ SY2335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6354]) ).
thf(6670,plain,
! [SV207: $i,SV519: $i] :
( ( ~ ( class_Groups_Ominus @ SV519 )
| ( class_Groups_Ominus @ ( tc_fun @ SV207 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6355]) ).
thf(6671,plain,
! [SV208: $i,SV520: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV520 )
| ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV208 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6356]) ).
thf(6672,plain,
! [SV209: $i,SV521: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV521 ) @ SV209 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SV521 ) )
| ( SV521 = SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6357]) ).
thf(6673,plain,
! [SV210: $i,SV522: $i] :
( ( ~ ~ ! [SY2337: $i] :
~ ( hBOOL @ ( hAPP @ SV522 @ SY2337 ) )
| ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6358]) ).
thf(6674,plain,
! [SV211: $i,SV523: $i] :
( ( ! [SY2338: $i,SY2339: $i,SY2340: $i,SY2341: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2341 @ SY2340 ) @ SY2339 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2338 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SY2341 ) @ SY2340 ) @ SY2339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6359]) ).
thf(6675,plain,
! [SV212: $i,SV524: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2343 @ SY2342 ) )
| ~ ( hBOOL @ ( hAPP @ SV524 @ SY2342 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SY2343 ) @ SV524 ) @ SY2342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6360]) ).
thf(6676,plain,
! [SV213: $i,SV525: $i] :
( ( ! [SY2344: $i,SY2345: $i,SY2346: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2346 @ tc_HOL_Obool ) ) @ SY2345 ) @ SY2344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2346 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2346 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2346 @ tc_HOL_Obool ) ) @ SY2345 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2346 @ tc_HOL_Obool ) ) @ SY2344 ) @ SV213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6361]) ).
thf(6677,plain,
! [SV214: $i,SV526: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV526 )
| ( class_Orderings_Opreorder @ ( tc_fun @ SV214 @ SV526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6362]) ).
thf(6678,plain,
! [SV215: $i,SV527: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2348 @ SY2347 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
| ~ ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2348 @ SY2347 @ SV527 ) @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6363]) ).
thf(6679,plain,
! [SV216: $i,SV528: $i] :
( ( ! [SY2351: $i,SY2352: $i,SY2353: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SY2352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SY2351 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2353 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2353 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SY2352 != SV528 )
| ( SY2351 != SV216 ) )
| ~ ( ( SY2352 != SV216 )
| ( SY2351 != SV528 ) ) )
| ~ ( ~ ( ~ ( ( SY2352 != SV528 )
| ( SY2351 != SV216 ) )
| ~ ( ( SY2352 != SV216 )
| ( SY2351 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SY2352 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SY2351 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2353 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2353 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2353 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6364]) ).
thf(6680,plain,
! [SV217: $i,SV529: $i] :
( ( ~ ( class_Orderings_Obot @ SV529 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV529 ) @ ( c_Orderings_Obot__class_Obot @ SV529 ) ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6365]) ).
thf(6681,plain,
! [SV218: $i,SV530: $i] :
( ( ! [SY2354: $i] :
( ~ ( class_Orderings_Oorder @ SY2354 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2354 ) @ SV530 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2354 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6366]) ).
thf(6682,plain,
! [SV219: $i,SV531: $i] :
( ( ! [SY2355: $i,SY2356: $i,SY2357: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2357 @ SY2356 @ SY2355 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2355 @ SV219 ) @ SV531 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2355 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2357 @ SY2356 @ SY2355 ) @ SV531 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6367]) ).
thf(6683,plain,
! [SV220: $i,SV532: $i] :
( ( ! [SY2358: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY2358 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV532 ) @ SV220 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2358 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY2358 @ tc_HOL_Obool ) @ SV532 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SY2358 @ tc_HOL_Obool ) @ SV220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6368]) ).
thf(6684,plain,
! [SV221: $i,SV533: $i] :
( ( ! [SY2359: $i,SY2360: $i,SY2361: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2361 @ SY2360 @ SY2359 )
| ( ( hAPP @ ( hAPP @ SY2359 @ SV533 ) @ ( hAPP @ ( hAPP @ SY2359 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SY2359 @ SV533 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6369]) ).
thf(6685,plain,
! [SV222: $i,SV534: $i] :
( ( ! [SY2362: $i,SY2363: $i,SY2364: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2364 @ SY2363 @ SY2362 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SY2362 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SY2362 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2364 @ SY2363 @ SY2362 ) @ SV534 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6370]) ).
thf(6686,plain,
! [SV223: $i,SV535: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2366 @ tc_HOL_Obool ) ) @ SY2365 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2366 ) @ SV223 ) @ SY2365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2366 ) @ SV223 ) @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6371]) ).
thf(6687,plain,
! [SV224: $i,SV536: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ~ ( class_Orderings_Oorder @ SY2368 )
| ( SY2367 != SV536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2368 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2368 ) @ SV224 ) @ SY2367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6372]) ).
thf(6688,plain,
! [SV225: $i,SV537: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2370 @ tc_HOL_Obool ) ) @ SY2369 ) @ SV537 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ SY2369 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6373]) ).
thf(6689,plain,
! [SV226: $i,SV538: $i] :
( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV538 )
| ~ ( class_Finite__Set_Ofinite @ SV226 ) )
| ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6374]) ).
thf(6690,plain,
! [SV227: $i,SV539: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
| ( SV539 = SV227 ) )
| ~ ( ( SV539 != SV227 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6375]) ).
thf(6691,plain,
! [SV228: $i,SV540: $i] :
( ( ! [SY2371: $i,SY2372: $i] :
( ( SY2372 != SY2371 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SY2371 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SY2372 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6376]) ).
thf(6692,plain,
! [SV229: $i,SV541: $i] :
( ( ! [SY2373: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV541 ) @ SY2373 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV541 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ SV229 @ SY2373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6377]) ).
thf(6693,plain,
! [SV230: $i,SV542: $i] :
( ( ! [SY2374: $i,SY2375: $i,SY2376: $i,SY2377: $i] :
~ ( ~ ( ( SY2377 != SY2376 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2375 @ SY2374 @ SV542 @ SY2376 @ SV230 ) @ SY2377 )
= SV230 ) )
| ~ ( ~ ( ( SY2377 != SY2376 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2375 @ SY2374 @ SV542 @ SY2376 @ SV230 ) @ SY2377 )
= ( hAPP @ SV542 @ SY2377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6378]) ).
thf(6694,plain,
! [SV231: $i,SV543: $i] :
( ( ! [SY2378: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY2378 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY2378 ) @ SV543 ) @ SV231 ) )
| ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2378 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2378 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY2378 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY2378 ) @ SV543 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6379]) ).
thf(6695,plain,
! [SV232: $i,SV544: $i] :
( ( ! [SY2379: $i] :
~ ( ~ ( ( SY2379 != SV544 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY2379 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SY2379 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SY2379 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SY2379 ) ) )
| ( SY2379 = SV544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6380]) ).
thf(6696,plain,
! [SV233: $i,SV545: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ~ ( c_Fun_Obij__betw @ SY2381 @ SY2380 @ SV545 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2381 @ tc_HOL_Obool ) ) @ SV233 )
| ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2380 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6381]) ).
thf(6697,plain,
! [SV234: $i,SV546: $i] :
( ( ! [SY2382: $i,SY2383: $i,SY2384: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2384 @ tc_HOL_Obool ) ) @ SY2383 ) @ SY2382 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2384 @ SV546 @ SV234 ) @ SY2383 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2384 @ SV546 @ SV234 ) @ SY2382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6382]) ).
thf(6698,plain,
! [SV235: $i,SV547: $i] :
( ( ! [SY2385: $i,SY2386: $i] :
( ~ ( c_Finite__Set_Ofolding__one @ SY2386 @ SY2385 @ SV547 )
| ( ( hAPP @ SV547 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2386 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2386 @ tc_HOL_Obool ) ) ) )
= SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6383]) ).
thf(6699,plain,
! [SV236: $i,SV548: $i] :
( ( ! [SY2387: $i,SY2388: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY2388 @ SY2387 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2387 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SY2388 @ SY2387 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2387 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6384]) ).
thf(6700,plain,
! [SV237: $i,SV549: $i] :
( ( ! [SY2389: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY2389 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY2389 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2389 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2389 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SY2389 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SY2389 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6385]) ).
thf(6701,plain,
! [SV238: $i,SV550: $i] :
( ( ! [SY2390: $i,SY2391: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2391 ) @ SY2390 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2391 ) @ SV550 ) @ SV238 ) ) )
| ~ ( ( SY2390 != SV550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2391 ) @ SY2390 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6386]) ).
thf(6702,plain,
! [SV239: $i,SV551: $i] :
( ( ! [SY2392: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2392 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2392 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6387]) ).
thf(6703,plain,
! [SV240: $i,SV552: $i] :
( ( ! [SY2393: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) )
| ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6388]) ).
thf(6704,plain,
! [SV241: $i,SV553: $i] :
( ( ! [SY2394: $i,SY2395: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2395 @ SY2394 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2394 @ SV241 ) @ SV553 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2395 @ SY2394 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6389]) ).
thf(6705,plain,
! [SV242: $i,SV554: $i] :
( ( ! [SY2396: $i,SY2397: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2397 @ tc_HOL_Obool ) ) @ SY2396 ) @ SV554 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2397 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2397 ) @ SV242 ) @ SY2396 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2397 ) @ SV242 ) @ SV554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6390]) ).
thf(6706,plain,
! [SV243: $i,SV555: $i] :
( ( ! [SY2398: $i,SY2399: $i,SY2400: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2400 @ SY2399 @ SY2398 ) @ SV555 ) @ SV243 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2398 @ SV243 ) @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6391]) ).
thf(6707,plain,
! [SV244: $i,SV556: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
| ( SV556 = SV244 ) )
| ~ ( ( SV556 != SV244 )
| ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6392]) ).
thf(6708,plain,
! [SV245: $i,SV557: $i] :
( ( ! [SY2401: $i,SY2402: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2402 @ SY2401 ) @ SV557 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2402 @ SY2401 ) @ SV245 ) )
| ( SV557 = SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6393]) ).
thf(6709,plain,
! [SV246: $i,SV558: $i] :
( ( ! [SY2403: $i] :
( ( SY2403
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV558 @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV558 ) @ SV246 ) @ SY2403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6394]) ).
thf(6710,plain,
! [SV247: $i,SV559: $i] :
( ( ! [SY2404: $i,SY2405: $i] :
( ~ ( class_Orderings_Oord @ SY2405 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2404 @ SY2405 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2406: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2405 ) @ ( hAPP @ SV559 @ SY2406 ) ) @ ( hAPP @ SV247 @ SY2406 ) ) ) )
| ~ ( ~ ! [SY2407: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2405 ) @ ( hAPP @ SV559 @ SY2407 ) ) @ ( hAPP @ SV247 @ SY2407 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2404 @ SY2405 ) ) @ SV559 ) @ SV247 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6395]) ).
thf(6711,plain,
! [SV248: $i,SV560: $i] :
( ( ! [SY2408: $i,SY2409: $i,SY2410: $i,SY2411: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2411 @ SY2410 ) @ SY2409 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2408 @ SY2410 ) @ SY2409 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SY2408 ) @ SY2411 ) @ SY2410 ) @ SY2409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6396]) ).
thf(6712,plain,
! [SV249: $i,SV561: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
| ( SV561 = SV249 ) )
| ~ ( ( SV561 != SV249 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6397]) ).
thf(6713,plain,
! [SV250: $i,SV562: $i] :
( ( ! [SY2412: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2412 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2412 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 )
= SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6398]) ).
thf(6714,plain,
! [SV251: $i,SV563: $i] :
( ( ~ ( class_Orderings_Obot @ SV563 )
| ( class_Orderings_Obot @ ( tc_fun @ SV251 @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6399]) ).
thf(6715,plain,
! [SV252: $i,SV564: $i] :
( ( ! [SY2413: $i,SY2414: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2414 ) @ SY2413 ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2414 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2414 ) @ SY2413 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6400]) ).
thf(6716,plain,
! [SV253: $i,SV565: $i] :
( ( ! [SY2415: $i,SY2416: $i,SY2417: $i,SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2418 @ SY2417 ) @ SY2416 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2415 @ SY2417 ) @ SY2416 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SY2418 ) @ SY2415 ) @ SY2417 ) @ SY2416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6401]) ).
thf(6717,plain,
! [SV254: $i,SV566: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
| ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
| ~ ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6402]) ).
thf(6718,plain,
! [SV255: $i,SV567: $i] :
( ( ~ ! [SY2421: $i] :
( ( hAPP @ SV567 @ SY2421 )
= ( hAPP @ SV255 @ SY2421 ) )
| ( SV567 = SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6403]) ).
thf(6719,plain,
! [SV256: $i,SV568: $i] :
( ( ~ ~ ! [SY2422: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SY2422 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SY2422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6404]) ).
thf(6720,plain,
! [SV257: $i,SV569: $i] :
( ( ! [SY2423: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2423 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2423 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) )
| ( SV569 = SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6405]) ).
thf(6721,plain,
! [SV258: $i,SV570: $i] :
( ( ! [SY2424: $i,SY2425: $i,SY2426: $i,SY2427: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SY2427 @ SY2426 @ SY2425 @ SY2424 @ SV570 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2426 @ tc_HOL_Obool ) ) )
= SY2424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6406]) ).
thf(6722,plain,
! [SV259: $i,SV571: $i] :
( ( ! [SY2428: $i,SY2429: $i,SY2430: $i,SY2431: $i,SY2432: $i,SY2433: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2433 @ SY2432 @ SY2431 @ SY2430 ) @ SY2429 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY2428 @ SY2432 @ SY2431 @ SV571 ) @ SV259 ) )
| ! [SY2434: $i] :
( ( hAPP @ SY2430 @ ( hAPP @ SY2429 @ SY2434 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY2434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6407]) ).
thf(6723,plain,
! [SV260: $i,SV572: $i] :
( ( ! [SY2435: $i,SY2436: $i,SY2437: $i,SY2438: $i] :
( ~ ( ( SY2438 != SY2437 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2436 @ SY2435 @ SV572 @ SY2437 @ SV260 ) @ SY2438 )
= ( hAPP @ SV572 @ SY2438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6408]) ).
thf(6724,plain,
! [SV261: $i,SV573: $i] :
( ( ! [SY2439: $i] :
( ~ ( class_Orderings_Opreorder @ SY2439 )
| ( SV573 != SV261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2439 ) @ SV573 ) @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6409]) ).
thf(6725,plain,
! [SV262: $i,SV574: $i] :
( ( ! [SY2440: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2440 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2440 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2440 @ tc_HOL_Obool ) ) ) ) )
| ( SV574 = SV262 ) )
| ~ ( ( SV574 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2440 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2440 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2440 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6410]) ).
thf(6726,plain,
! [SV263: $i,SV575: $i] :
( ( ! [SY2441: $i,SY2442: $i,SY2443: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2443 @ tc_HOL_Obool ) ) @ SY2442 ) @ SY2441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2443 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2443 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2443 @ tc_HOL_Obool ) ) @ SY2442 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2443 @ tc_HOL_Obool ) ) @ SY2441 ) @ SV263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6411]) ).
thf(6727,plain,
! [SV264: $i,SV576: $i] :
( ( ! [SY2444: $i,SY2445: $i,SY2446: $i,SY2447: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2447 @ SY2446 ) @ SY2445 ) @ SY2444 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2447 @ SY2446 ) @ SV576 ) @ SV264 ) )
| ~ ( ( SY2445 != SV576 )
| ( SY2444 != SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6412]) ).
thf(6728,plain,
! [SV265: $i,SV577: $i] :
( ( ! [SY2448: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2448 @ tc_HOL_Obool ) ) @ SV577 ) @ SV265 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SY2448 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SY2448 @ SV577 ) ) @ ( c_Predicate_OPowp @ SY2448 @ SV265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6413]) ).
thf(6729,plain,
! [SV266: $i,SV578: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV578 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV578 ) @ SV266 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6414]) ).
thf(6730,plain,
! [SV267: $i,SV579: $i] :
( ( ! [SY2449: $i,SY2450: $i,SY2451: $i,SY2452: $i,SY2453: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2453 @ SY2452 @ SY2451 @ SY2450 ) @ SY2449 )
!= SV579 )
| ( ( hAPP @ SY2450 @ ( hAPP @ SY2449 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6415]) ).
thf(6731,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
| ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
| ~ ( ~ ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) )
| ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6416]) ).
thf(6732,plain,
! [SV269: $i,SV581: $i] :
( ( ! [SY2456: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2456 @ tc_HOL_Obool ) ) @ SV269 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6417]) ).
thf(6733,plain,
! [SV270: $i,SV582: $i] :
( ( ! [SY2457: $i,SY2458: $i,SY2459: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2459 @ SY2458 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2458 @ SY2457 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2458 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2458 @ SY2457 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6418]) ).
thf(6734,plain,
! [SV271: $i,SV583: $i] :
( ( ! [SY2460: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2460 @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2460 ) @ SV583 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6419]) ).
thf(6735,plain,
! [SV272: $i,SV584: $i] :
( ( ! [SY2461: $i,SY2462: $i] :
( ( SY2462 != SY2461 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2461 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2462 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6420]) ).
thf(6736,plain,
! [SV273: $i,SV585: $i] :
( ( ! [SY2463: $i,SY2464: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2464 ) @ SY2463 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2464 ) @ SV585 ) @ SV273 ) ) )
| ( SY2463 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2464 ) @ SY2463 ) @ SV273 ) ) )
| ~ ( ~ ( ( SY2463 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2464 ) @ SY2463 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2464 ) @ SY2463 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2464 ) @ SV585 ) @ SV273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6421]) ).
thf(6737,plain,
! [SV274: $i,SV586: $i] :
( ( ( SV586 != SV274 )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV586 ) @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6422]) ).
thf(6738,plain,
! [SV275: $i,SV587: $i] :
( ( ! [SY2465: $i,SY2466: $i,SY2467: $i,SY2468: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2468 ) @ SY2467 ) @ SY2466 )
!= SY2465 )
| ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2468 ) @ SY2466 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2468 ) @ SY2467 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2468 ) @ SY2465 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6423]) ).
thf(6739,plain,
! [SV276: $i,SV588: $i] :
( ( ! [SY2469: $i,SY2470: $i] :
( ( SY2470 != SY2469 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2470 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2469 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2469 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2470 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6424]) ).
thf(6740,plain,
! [SV277: $i,SV589: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2472 @ tc_HOL_Obool ) ) @ SY2471 ) @ SV589 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2472 ) @ SV277 ) @ SY2471 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2472 ) @ SV277 ) @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6425]) ).
thf(6741,plain,
! [SV278: $i,SV590: $i] :
( ( ! [SY2473: $i,SY2474: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2474 @ tc_HOL_Obool ) ) @ SY2473 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2474 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2474 @ tc_HOL_Obool ) ) @ SY2473 ) @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6426]) ).
thf(6742,plain,
! [SV279: $i,SV591: $i] :
( ( ~ ( class_Orderings_Oorder @ SV591 )
| ( class_Orderings_Oorder @ ( tc_fun @ SV279 @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6427]) ).
thf(6743,plain,
! [SV280: $i,SV592: $i] :
( ( ! [SY2475: $i,SY2476: $i] :
( ( SY2476
!= ( c_Finite__Set_Ofold1 @ SY2475 @ SV592 ) )
| ( ( hAPP @ SY2476 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2475 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2475 @ tc_HOL_Obool ) ) ) )
= SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6428]) ).
thf(6744,plain,
! [SV281: $i,SV593: $i] :
( ( ! [SY2477: $i,SY2478: $i,SY2479: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2478 ) @ SY2477 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY2480: $i] :
~ ( ~ ( ( SY2478
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SV593 ) @ SY2480 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2480 ) @ SY2477 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2478 ) @ SY2480 )
!= SV593 )
| ( SY2477
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2480 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY2481: $i] :
~ ( ~ ( ( SY2478
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SV593 ) @ SY2481 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2481 ) @ SY2477 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2478 ) @ SY2481 )
!= SV593 )
| ( SY2477
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2481 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SY2478 ) @ SY2477 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2479 ) @ SV593 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6429]) ).
thf(6745,plain,
! [SV282: $i,SV594: $i] :
( ( ! [SY2482: $i] :
( ( SY2482
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) @ SY2482 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6430]) ).
thf(6746,plain,
! [SV283: $i,SV595: $i] :
( ( ( hAPP @ ( c_Set_OPow @ SV595 ) @ SV283 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV595 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6431]) ).
thf(6747,plain,
! [SV284: $i,SV596: $i] :
( ( ! [SY2483: $i,SY2484: $i,SY2485: $i] :
( ~ ( c_Fun_Oinj__on @ SY2485 @ SY2484 @ SY2483 @ SV596 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2485 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SY2485 @ SY2484 @ SY2483 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6432]) ).
thf(6748,plain,
! [SV285: $i,SV597: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
| ( SV597 = SV285 ) )
| ~ ( ( SV597 != SV285 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6433]) ).
thf(6749,plain,
! [SV286: $i,SV598: $i] :
( ( ! [SY2486: $i,SY2487: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2487 @ tc_HOL_Obool ) ) @ SY2486 ) @ SV598 ) @ SV286 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SY2486 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6434]) ).
thf(6750,plain,
! [SV287: $i,SV599: $i] :
( ( ~ ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
| ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6435]) ).
thf(6751,plain,
! [SV288: $i] :
( ( SV288
= ( hAPP @ c_Nat_OSuc @ SV288 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6436]) ).
thf(6752,plain,
! [SV289: $i,SV600: $i] :
( ( ~ ( ~ ( ~ ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) )
| ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
| ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6437]) ).
thf(6753,plain,
! [SV290: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV290 @ tc_HOL_Obool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV290 @ tc_HOL_Obool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6438]) ).
thf(6754,plain,
! [SV291: $i,SV601: $i] :
( ( ! [SY2496: $i] :
( ~ ~ ! [SX3: $i] :
~ ( hBOOL @ ( hAPP @ SY2496 @ SX3 ) )
| ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SY2496 ) )
| ( hBOOL @ ( hAPP @ SY2496 @ SV601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6439]) ).
thf(6755,plain,
! [SV292: $i,SV602: $i] :
( ( ! [SY2498: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2498 @ tc_HOL_Obool ) ) @ SV602 ) @ SV292 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2498 @ tc_HOL_Obool ) ) @ SV292 ) @ SV602 )
= SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6440]) ).
thf(6756,plain,
! [SV293: $i,SV603: $i] :
( ( ~ ( class_Orderings_Oord @ SV603 )
| ( class_Orderings_Oord @ ( tc_fun @ SV293 @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6441]) ).
thf(6757,plain,
! [SV294: $i,SV604: $i] :
( ( ! [SY2499: $i,SY2500: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY2500 @ SY2499 ) )
| ( hBOOL @ ( hAPP @ SV604 @ SY2499 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SY2500 ) @ SY2499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6442]) ).
thf(6758,plain,
! [SV295: $i,SV605: $i] :
( ( ! [SY2501: $i,SY2502: $i,SY2503: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2503 @ SY2502 @ SY2501 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2503 @ tc_HOL_Obool ) ) ) @ SV295 ) )
| ( SV295 = SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6443]) ).
thf(6759,plain,
! [SV296: $i,SV606: $i] :
( ( ! [SY2504: $i] :
( ~ ( class_Orderings_Olinorder @ SY2504 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2504 ) @ SV606 ) @ SV296 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2504 ) @ SV296 ) @ SV606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6444]) ).
thf(6760,plain,
! [SV297: $i,SV607: $i] :
( ( ! [SY2505: $i,SY2506: $i,SY2507: $i] :
( ~ ( class_Orderings_Oord @ SY2507 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2506 @ SY2507 ) ) @ SY2505 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2507 ) @ ( hAPP @ SY2505 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6445]) ).
thf(6761,plain,
! [SV298: $i,SV608: $i] :
( ( ! [SY2508: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2508 @ tc_HOL_Obool ) ) @ SV608 ) @ SV298 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2508 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2508 @ tc_HOL_Obool ) ) @ SV298 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2508 @ tc_HOL_Obool ) ) @ SV608 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6446]) ).
thf(6762,plain,
! [SV299: $i,SV609: $i] :
( ( ! [SY2509: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2509 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2509 ) @ SV609 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2509 ) @ SV299 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2509 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SY2509 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2509 ) @ SV609 ) @ SV299 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6447]) ).
thf(6763,plain,
! [SV300: $i,SV610: $i] :
( ( ! [SY2510: $i,SY2511: $i,SY2512: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2512 @ SY2511 ) @ SY2510 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SY2512 ) @ SY2511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6448]) ).
thf(6764,plain,
! [SV301: $i,SV611: $i] :
( ( ! [SY2513: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2513 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2513 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2513 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2513 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6449]) ).
thf(6765,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6450]) ).
thf(6766,plain,
! [SV303: $i,SV613: $i] :
( ( ! [SY2514: $i,SY2515: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2515 @ SY2514 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2514 @ SV613 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2514 @ SV303 ) @ SV613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6451]) ).
thf(6767,plain,
! [SV304: $i,SV614: $i] :
( ( ! [SY2516: $i] :
( ( SY2516 != SV614 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV304 @ tc_HOL_Obool ) ) @ SY2516 ) @ SV614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6452]) ).
thf(6768,plain,
! [SV305: $i,SV615: $i] :
( ( ! [SY2517: $i,SY2518: $i,SY2519: $i,SY2520: $i] :
( ( SY2520 != SY2519 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2518 @ SY2517 @ SV615 ) @ SV305 ) @ SY2520 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2518 @ SY2517 @ SV615 ) @ SV305 ) @ SY2519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6453]) ).
thf(6769,plain,
! [SV306: $i,SV616: $i] :
( ( ! [SY2521: $i] :
( ~ ( class_Orderings_Obot @ SY2521 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ SY2521 ) ) @ SV306 )
= ( c_Orderings_Obot__class_Obot @ SY2521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6454]) ).
thf(6770,plain,
! [SV307: $i,SV617: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2523 @ SY2522 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
| ~ ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2523 @ SY2522 @ SV617 ) @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6455]) ).
thf(6771,plain,
! [SV308: $i,SV618: $i] :
( ( ! [SY2526: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2526 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2526 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 )
= SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6456]) ).
thf(6772,plain,
! [SV309: $i,SV619: $i] :
( ( ! [SY2527: $i,SY2528: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2528 @ tc_HOL_Obool ) ) @ SY2527 ) @ SV619 ) @ SV309 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SY2527 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SV619 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6457]) ).
thf(6773,plain,
! [SV310: $i,SV620: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV620 )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV310 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6458]) ).
thf(6774,plain,
! [SV311: $i,SV621: $i] :
( ( ! [SY2529: $i,SY2530: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2530 @ SY2529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SY2530 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SY2529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6459]) ).
thf(6775,plain,
! [SV312: $i,SV622: $i] :
( ( ! [SY2531: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2531 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2531 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SV622 = SV312 ) )
| ~ ( ( SV622 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2531 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SY2531 @ tc_HOL_Obool ) ) @ SV312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6460]) ).
thf(6776,plain,
! [SV313: $i,SV623: $i] :
( ( ! [SY2532: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2532 @ tc_HOL_Obool ) ) @ SV623 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2532 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2532 @ tc_HOL_Obool ) ) ) ) )
| ( SV623
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2532 @ tc_HOL_Obool ) ) )
| ( SV623
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2532 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2532 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6461]) ).
thf(6777,plain,
! [SV314: $i,SV624: $i] :
( ( ! [SY2533: $i,SY2534: $i,SY2535: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2535 @ SY2534 @ SY2533 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2533 @ SV314 ) @ SV624 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2533 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2535 @ SY2534 @ SY2533 ) @ SV624 ) @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6462]) ).
thf(6778,plain,
! [SV315: $i,SV625: $i] :
( ( ! [SY2536: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2536 @ SV625 ) @ SV315 ) )
| ! [SY2537: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2537 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2536 @ SV625 ) @ SY2537 ) ) ) )
| ~ ( ~ ! [SY2538: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2538 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2536 @ SV625 ) @ SY2538 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2536 @ SV625 ) @ SV315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6463]) ).
thf(6779,plain,
! [SV316: $i,SV626: $i] :
( ( ! [SY2539: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY2539 ) @ SV626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SY2539 ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6464]) ).
thf(6780,plain,
! [SV317: $i,SV627: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV627 )
!= ( hAPP @ c_Nat_OSuc @ SV317 ) )
| ( SV627 = SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6465]) ).
thf(6781,plain,
! [SV318: $i,SV628: $i] :
( ( ! [SY2540: $i,SY2541: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2541 @ tc_HOL_Obool ) ) @ SY2540 ) @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2541 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2541 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2541 @ tc_HOL_Obool ) ) @ SV318 ) @ SY2540 ) )
= SY2540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6466]) ).
thf(6782,plain,
! [SV319: $i,SV629: $i] :
( ( ! [SY2542: $i,SY2543: $i,SY2544: $i,SY2545: $i] :
~ ( ~ ( ( SY2545 != SY2544 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2543 @ SY2542 @ SV629 @ SY2544 @ SV319 ) @ SY2545 )
= SV319 ) )
| ~ ( ~ ( ( SY2545 != SY2544 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2543 @ SY2542 @ SV629 @ SY2544 @ SV319 ) @ SY2545 )
= ( hAPP @ SV629 @ SY2545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6467]) ).
thf(6783,plain,
! [SV320: $i,SV630: $i] :
( ( ! [SY2546: $i,SY2547: $i,SY2548: $i,SY2549: $i,SY2550: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2550 @ SY2549 @ SY2548 @ SY2547 @ SY2546 @ SV630 )
| ( ( hAPP @ ( hAPP @ SY2548 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6468]) ).
thf(6784,plain,
! [SV321: $i,SV631: $i] :
( ( ! [SY2551: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2551 ) @ SV631 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2551 @ tc_HOL_Obool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2551 ) @ SV321 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2551 @ tc_HOL_Obool ) ) ) )
| ( SV631 = SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6469]) ).
thf(6785,plain,
! [SV322: $i,SV632: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i,SY2555: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2555 @ ( tc_fun @ SY2554 @ tc_HOL_Obool ) ) ) @ SY2553 ) @ SY2552 ) @ SV632 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2553 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2552 @ SV632 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6470]) ).
thf(6786,plain,
! [SV3: $i,SV324: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV324 ) @ SV3 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV324 @ tc_HOL_Obool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6787,plain,
! [SV4: $i,SV325: $i,SV633: $i] :
( ( ! [SY2556: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2556 ) @ SV633 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2556 ) @ SV325 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2556 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2556 ) @ SV633 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6473]) ).
thf(6788,plain,
! [SV5: $i,SV326: $i,SV634: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV634 ) @ SV326 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV634 ) @ SV326 ) @ SV5 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV634 ) @ SV326 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6474]) ).
thf(6789,plain,
! [SV7: $i,SV328: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV328 ) @ SV7 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV328 @ tc_HOL_Obool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6476]) ).
thf(6790,plain,
! [SV8: $i,SV329: $i,SV635: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV635 ) @ SV329 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV635 ) @ SV329 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6477]) ).
thf(6791,plain,
! [SV10: $i,SV330: $i,SV636: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ SV636 @ SV330 @ SV10 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV636 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV330 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6478]) ).
thf(6792,plain,
! [SV11: $i,SV331: $i,SV637: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV637 @ tc_HOL_Obool ) ) @ SV331 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV637 ) @ SV11 ) @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6479]) ).
thf(6793,plain,
! [SV12: $i,SV332: $i,SV638: $i] :
( ( ! [SY2557: $i,SY2558: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY2558 @ SY2557 @ SV638 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2558 ) @ SV332 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2557 ) @ ( hAPP @ SV638 @ SV332 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2558 @ SY2557 @ SV638 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6480]) ).
thf(6794,plain,
! [SV15: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV334 ) @ SV15 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV15 ) @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6482]) ).
thf(6795,plain,
! [SV16: $i,SV335: $i,SV639: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV639 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV639 @ tc_HOL_Obool ) ) @ SV335 ) @ SV16 ) ) @ SV16 )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV639 @ tc_HOL_Obool ) ) @ SV335 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6483]) ).
thf(6796,plain,
! [SV20: $i,SV339: $i,SV640: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV640 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV640 @ tc_HOL_Obool ) ) @ SV339 ) @ SV20 ) ) @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6487]) ).
thf(6797,plain,
! [SV21: $i,SV340: $i,SV641: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV641 ) @ SV340 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV641 @ tc_HOL_Obool ) ) @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV641 ) @ SV340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV641 @ tc_HOL_Obool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV641 ) @ SV340 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6488]) ).
thf(6798,plain,
! [SV22: $i,SV341: $i,SV642: $i] :
( ( ! [SY2559: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2559 @ tc_HOL_Obool ) ) @ SV642 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2559 ) @ SV341 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2559 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2559 @ tc_HOL_Obool ) ) @ SV642 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2559 ) @ SV341 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2559 @ tc_HOL_Obool ) ) ) ) ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6489]) ).
thf(6799,plain,
! [SV23: $i,SV342: $i,SV643: $i] :
( ( ! [SY2560: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2560 @ tc_HOL_Obool ) ) @ SV643 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2560 ) @ SV342 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2560 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2560 @ tc_HOL_Obool ) ) @ SV643 ) @ SV23 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2560 ) @ SV342 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2560 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6490]) ).
thf(6800,plain,
! [SV24: $i,SV343: $i,SV644: $i] :
( ( ! [SY2561: $i] : ( c_Nitpick_Ofold__graph_H @ SY2561 @ SV644 @ SV343 @ SV24 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2561 @ tc_HOL_Obool ) ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6491]) ).
thf(6801,plain,
! [SV25: $i,SV344: $i,SV645: $i] :
( ( ! [SY2562: $i] : ( c_Nitpick_Ofold__graph_H @ SY2562 @ SV645 @ SV344 @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2562 @ tc_HOL_Obool ) ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6492]) ).
thf(6802,plain,
! [SV26: $i,SV345: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) @ SV26 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV345 @ tc_HOL_Obool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(6803,plain,
! [SV27: $i,SV346: $i,SV646: $i] :
( ( ! [SY2563: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2563 @ SV646 @ SV346 @ SV27 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2563 @ tc_HOL_Obool ) ) ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6494]) ).
thf(6804,plain,
! [SV28: $i,SV347: $i,SV647: $i] :
( ( ! [SY2564: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2564 @ SV647 @ SV347 @ SV28 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2564 @ tc_HOL_Obool ) ) ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6495]) ).
thf(6805,plain,
! [SV30: $i,SV348: $i,SV648: $i] :
( ( c_Fun_Oinj__on @ SV648 @ SV348 @ SV30 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV648 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6496]) ).
thf(6806,plain,
! [SV31: $i,SV349: $i,SV649: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV649 @ SV349 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV649 @ tc_HOL_Obool ) ) ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6497]) ).
thf(6807,plain,
! [SV32: $i,SV350: $i,SV650: $i] :
( ( ! [SY2565: $i] :
( ( c_Fun_Ofun__upd @ SY2565 @ SV650 @ SV350 @ SV32 @ ( hAPP @ SV350 @ SV32 ) )
= SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6498]) ).
thf(6808,plain,
! [SV33: $i,SV351: $i,SV651: $i] :
( ( ! [SY2566: $i,SY2567: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2567 @ SY2566 @ SV651 @ SV351 @ SV33 ) @ SV351 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6499]) ).
thf(6809,plain,
! [SV34: $i,SV352: $i,SV652: $i] :
( ( ! [SY2568: $i,SY2569: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY2569 @ SY2568 @ SV652 ) @ SV352 ) @ SV34 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2568 @ tc_HOL_Obool ) ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6500]) ).
thf(6810,plain,
! [SV35: $i,SV353: $i,SV653: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ SV653 @ SV353 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV653 ) @ SV35 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV653 @ tc_HOL_Obool ) ) ) )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6501]) ).
thf(6811,plain,
! [SV37: $i,SV354: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV354 ) @ SV37 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV37 ) @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6502]) ).
thf(6812,plain,
! [SV38: $i,SV355: $i,SV654: $i] :
( ( ! [SY2570: $i,SY2571: $i,SY2572: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2572 @ SY2571 @ SY2570 @ SV654 ) @ SV355 ) @ SV38 )
= ( hAPP @ SV654 @ ( hAPP @ SV355 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6503]) ).
thf(6813,plain,
! [SV39: $i,SV356: $i,SV655: $i] :
( ( ! [SY2573: $i,SY2574: $i,SY2575: $i,SY2576: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2576 @ SY2575 @ SY2574 @ SY2573 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2576 @ SY2574 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2575 @ SY2574 @ ( hAPP @ ( c_Fun_Ocomp @ SY2576 @ SY2575 @ SV655 @ SY2573 ) @ SV356 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6504]) ).
thf(6814,plain,
! [SV40: $i,SV357: $i,SV656: $i] :
( ( ! [SY2577: $i,SY2578: $i,SY2579: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2579 @ SY2578 @ SY2577 @ SV656 ) @ SV357 ) @ SV40 )
= ( hAPP @ SV656 @ ( hAPP @ SV357 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6505]) ).
thf(6815,plain,
! [SV41: $i,SV358: $i,SV657: $i] :
( ( ! [SY2580: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SY2580 @ SV657 @ SV358 ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2580 @ tc_HOL_Obool ) ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6506]) ).
thf(6816,plain,
! [SV43: $i,SV360: $i,SV658: $i] :
( ( ! [SY2581: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2581 @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) ) @ SV360 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6508]) ).
thf(6817,plain,
! [SV44: $i,SV361: $i,SV659: $i] :
( ( ! [SY2582: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2582 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2582 ) @ SV659 ) @ SV361 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2582 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2582 @ tc_HOL_Obool ) ) @ SV361 ) @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6509]) ).
thf(6818,plain,
! [SV45: $i,SV362: $i,SV660: $i] :
( ( ! [SY2583: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2583 @ tc_HOL_Obool ) ) @ SV660 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2583 ) @ SV362 ) @ SV45 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2583 ) @ SV362 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2583 @ tc_HOL_Obool ) ) @ SV660 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6510]) ).
thf(6819,plain,
! [SV46: $i,SV363: $i,SV661: $i] :
( ( ! [SY2584: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2584 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2584 @ tc_HOL_Obool ) ) @ SV661 ) @ SV363 ) ) @ SV46 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2584 @ tc_HOL_Obool ) ) @ SV661 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2584 @ tc_HOL_Obool ) ) @ SV363 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6511]) ).
thf(6820,plain,
! [SV47: $i,SV364: $i,SV662: $i] :
( ( ! [SY2585: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2585 @ tc_HOL_Obool ) ) @ SV662 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2585 @ tc_HOL_Obool ) ) @ SV364 ) @ SV47 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2585 @ tc_HOL_Obool ) ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2585 @ tc_HOL_Obool ) ) @ SV662 ) @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6512]) ).
thf(6821,plain,
! [SV48: $i,SV365: $i,SV663: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV365 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV365 ) @ SV48 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV663 @ tc_HOL_Obool ) ) @ SV365 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6513]) ).
thf(6822,plain,
! [SV49: $i,SV366: $i,SV664: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ SV366 ) @ SV49 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV664 @ tc_HOL_Obool ) ) @ SV49 ) @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6514]) ).
thf(6823,plain,
! [SV51: $i,SV368: $i,SV665: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV665 @ tc_HOL_Obool ) ) @ SV368 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV665 @ tc_HOL_Obool ) ) @ SV368 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6516]) ).
thf(6824,plain,
! [SV52: $i,SV369: $i,SV666: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV666 @ tc_HOL_Obool ) ) @ SV369 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV666 @ tc_HOL_Obool ) ) @ SV52 ) @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6517]) ).
thf(6825,plain,
! [SV55: $i,SV372: $i,SV667: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV667 ) @ SV372 ) @ SV55 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV667 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV667 ) @ SV372 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV667 @ tc_HOL_Obool ) ) ) ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6520]) ).
thf(6826,plain,
! [SV57: $i,SV373: $i,SV668: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ SV668 @ SV373 @ SV57 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV668 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV373 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6521]) ).
thf(6827,plain,
! [SV61: $i,SV377: $i,SV669: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV669 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV669 @ tc_HOL_Obool ) ) @ SV377 ) @ SV61 ) ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6525]) ).
thf(6828,plain,
! [SV62: $i,SV378: $i,SV670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV670 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV670 @ tc_HOL_Obool ) ) @ SV378 ) @ SV62 ) ) @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6526]) ).
thf(6829,plain,
! [SV63: $i,SV379: $i,SV671: $i] :
( ( ! [SY2586: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2586 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2586 @ tc_HOL_Obool ) ) @ SV671 ) @ SV379 ) ) @ SV63 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2586 @ tc_HOL_Obool ) ) @ SV671 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2586 @ tc_HOL_Obool ) ) @ SV379 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6527]) ).
thf(6830,plain,
! [SV64: $i,SV380: $i,SV672: $i] :
( ( ! [SY2587: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2587 @ tc_HOL_Obool ) ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2587 @ tc_HOL_Obool ) ) @ SV380 ) @ SV64 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2587 @ tc_HOL_Obool ) ) @ SV380 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2587 @ tc_HOL_Obool ) ) @ SV672 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6528]) ).
thf(6831,plain,
! [SV65: $i,SV381: $i,SV673: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV673 @ tc_HOL_Obool ) ) @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV673 @ tc_HOL_Obool ) ) @ SV381 ) @ SV65 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV673 @ tc_HOL_Obool ) ) @ SV381 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6529]) ).
thf(6832,plain,
! [SV66: $i,SV382: $i,SV674: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV674 @ tc_HOL_Obool ) ) @ SV382 ) @ SV66 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV674 @ tc_HOL_Obool ) ) @ SV66 ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6530]) ).
thf(6833,plain,
! [SV68: $i,SV384: $i,SV675: $i] :
( ( ! [SY2588: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2588 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2588 ) @ SV675 ) @ SV384 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2588 ) @ SV675 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2588 ) @ SV675 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2588 @ tc_HOL_Obool ) ) @ SV384 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6532]) ).
thf(6834,plain,
! [SV71: $i,SV387: $i,SV676: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ SV676 @ SV387 @ SV71 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV676 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6535]) ).
thf(6835,plain,
! [SV76: $i,SV391: $i,SV677: $i] :
( ( ! [SY2589: $i,SY2590: $i,SY2591: $i,SY2592: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2592 @ SY2591 @ SY2590 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2592 @ SY2589 @ SY2591 ) @ SV677 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2592 @ SY2589 @ SY2590 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2589 @ SY2591 @ SY2590 ) @ SV391 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6539]) ).
thf(6836,plain,
! [SV77: $i,SV392: $i,SV678: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV678 @ SV392 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV392 @ SV678 ) @ SV77 ) )
= SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6540]) ).
thf(6837,plain,
! [SV78: $i,SV393: $i,SV679: $i] :
( ( ! [SY2593: $i] :
( ( hAPP @ SY2593 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV679 @ SV679 ) @ SV393 ) @ SY2593 ) @ SV78 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV679 @ SV679 ) @ SV393 ) @ SY2593 ) @ ( hAPP @ SY2593 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6541]) ).
thf(6838,plain,
! [SV80: $i,SV395: $i,SV680: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2595 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2595 @ SY2594 ) @ SV680 ) @ SV395 ) ) @ SV680 ) @ SV80 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2595 @ SY2594 ) @ SV680 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6543]) ).
thf(6839,plain,
! [SV81: $i,SV396: $i,SV681: $i] :
( ( ! [SY2596: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2596 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2596 ) @ SV681 ) @ SV396 ) ) @ SV81 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2596 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2596 ) @ SV396 ) @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6544]) ).
thf(6840,plain,
! [SV84: $i,SV399: $i,SV682: $i] :
( ( ! [SY2597: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY2597 @ SV682 ) @ SV399 ) @ SV84 )
= SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6547]) ).
thf(6841,plain,
! [SV85: $i,SV400: $i,SV683: $i] :
( ( ! [SY2598: $i,SY2599: $i,SY2600: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2600 @ SY2599 @ SY2598 ) @ SV683 ) @ SV400 ) @ SV85 )
= ( hAPP @ SV683 @ ( hAPP @ SV400 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6548]) ).
thf(6842,plain,
! [SV86: $i,SV401: $i,SV684: $i] :
( ( ! [SY2601: $i,SY2602: $i,SY2603: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2603 @ SY2602 @ SY2601 ) @ SV684 ) @ SV401 ) @ SV86 )
= ( hAPP @ ( hAPP @ SV684 @ SV86 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6549]) ).
thf(6843,plain,
! [SV87: $i,SV402: $i,SV685: $i] :
( ( ! [SY2604: $i,SY2605: $i,SY2606: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2606 @ SY2605 @ SY2604 ) @ SV685 ) @ SV402 ) @ SV87 )
= ( hAPP @ ( hAPP @ SV685 @ SV87 ) @ ( hAPP @ SV402 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6550]) ).
thf(6844,plain,
! [SV88: $i,SV403: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV403 ) @ SV88 ) ) )
= $true )
| ( ( SV403 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6551]) ).
thf(6845,plain,
! [SV89: $i] :
( ( ( hBOOL @ ( hAPP @ c_fNot @ SV89 ) )
= $false )
| ( ( ~ ( hBOOL @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6552]) ).
thf(6846,plain,
! [SV90: $i] :
( ( ( ~ ( hBOOL @ SV90 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6553]) ).
thf(6847,plain,
! [SV91: $i,SV404: $i] :
( ( ( ~ ( hBOOL @ SV404 )
| ~ ( hBOOL @ SV91 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV404 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6554]) ).
thf(6848,plain,
! [SV92: $i,SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV405 ) @ SV92 ) ) )
= $true )
| ( ( hBOOL @ SV405 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6555]) ).
thf(6849,plain,
! [SV93: $i,SV406: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV406 ) @ SV93 ) ) )
= $true )
| ( ( hBOOL @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6556]) ).
thf(6850,plain,
! [SV94: $i,SV407: $i] :
( ( ( ~ ( hBOOL @ SV407 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV407 ) @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6557]) ).
thf(6851,plain,
! [SV95: $i,SV408: $i] :
( ( ( ~ ( hBOOL @ SV408 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV95 ) @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6852,plain,
! [SV96: $i,SV409: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV409 ) @ SV96 ) )
| ( hBOOL @ SV409 ) )
= $true )
| ( ( hBOOL @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6559]) ).
thf(6853,plain,
! [SV97: $i,SV410: $i] :
( ( ( hBOOL @ SV410 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV410 ) @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6560]) ).
thf(6854,plain,
! [SV98: $i,SV411: $i] :
( ( ( ~ ( hBOOL @ SV411 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV98 ) @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6561]) ).
thf(6855,plain,
! [SV99: $i,SV412: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV412 ) @ SV99 ) )
| ~ ( hBOOL @ SV412 ) )
= $true )
| ( ( hBOOL @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6562]) ).
thf(6856,plain,
! [SV100: $i,SV413: $i,SV686: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV686 @ SV413 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV413 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6563]) ).
thf(6857,plain,
! [SV101: $i,SV414: $i,SV687: $i] :
( ( ! [SY2607: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2607 @ SV687 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV414 @ tc_HOL_Obool ) ) @ SV101 ) @ SY2607 ) @ SV687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6564]) ).
thf(6858,plain,
! [SV102: $i,SV415: $i,SV688: $i] :
( ( ~ ( class_Orderings_Obot @ SV688 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV415 @ SV688 ) ) @ SV102 )
= ( c_Orderings_Obot__class_Obot @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6565]) ).
thf(6859,plain,
! [SV103: $i,SV416: $i,SV689: $i] :
( ( ! [SY2608: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2608 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2608 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2608 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) )
| ~ ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2608 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2608 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2608 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6566]) ).
thf(6860,plain,
! [SV104: $i,SV417: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
| ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6567]) ).
thf(6861,plain,
! [SV105: $i,SV418: $i,SV690: $i] :
( ( ! [SY2609: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2609 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2609 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2609 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6568]) ).
thf(6862,plain,
! [SV106: $i,SV419: $i,SV691: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6569]) ).
thf(6863,plain,
! [SV107: $i,SV420: $i,SV692: $i] :
( ( ! [SY2610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2610 @ tc_HOL_Obool ) ) @ SV692 ) @ SV420 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2610 @ tc_HOL_Obool ) ) @ SV692 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2610 ) @ SV107 ) @ SV420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6570]) ).
thf(6864,plain,
! [SV108: $i,SV421: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6571]) ).
thf(6865,plain,
! [SV109: $i,SV422: $i,SV693: $i] :
( ( ! [SY2611: $i,SY2612: $i,SY2613: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2613 @ SY2612 @ SY2611 )
| ( ( hAPP @ ( hAPP @ SY2611 @ SV693 ) @ ( hAPP @ ( hAPP @ SY2611 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SY2611 @ SV422 ) @ ( hAPP @ ( hAPP @ SY2611 @ SV693 ) @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6572]) ).
thf(6866,plain,
! [SV110: $i,SV423: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
| ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
| ~ ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6573]) ).
thf(6867,plain,
! [SV111: $i,SV424: $i] :
( ( ( SV424 != SV111 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV424 ) @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6574]) ).
thf(6868,plain,
! [SV112: $i,SV425: $i] :
( ( ( ~ ( class_Orderings_Otop @ SV425 ) )
= $true )
| ( ( class_Orderings_Otop @ ( tc_fun @ SV112 @ SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6575]) ).
thf(6869,plain,
! [SV113: $i,SV426: $i,SV694: $i] :
( ( ! [SY2614: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2614 ) @ SV694 ) @ SV426 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2614 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2614 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2614 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2614 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2614 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2614 ) @ SV694 ) @ SV113 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6576]) ).
thf(6870,plain,
! [SV114: $i,SV427: $i,SV695: $i] :
( ( ! [SY2615: $i,SY2616: $i,SY2617: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2617 @ SY2616 ) @ SY2615 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SY2617 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SY2616 ) @ SY2615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6577]) ).
thf(6871,plain,
! [SV116: $i,SV428: $i,SV696: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV428 ) @ SV116 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV696 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV116 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6579]) ).
thf(6872,plain,
! [SV117: $i,SV429: $i,SV697: $i] :
( ( ! [SY2618: $i,SY2619: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY2619 @ SY2618 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) )
| ~ ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SY2619 @ SY2618 @ SV697 @ SV429 @ SV117 )
= SV697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6580]) ).
thf(6873,plain,
! [SV118: $i,SV430: $i,SV698: $i] :
( ( ! [SY2620: $i,SY2621: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2621 ) @ SY2620 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2621 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SY2620 != SV430 )
| ( SV698 != SV118 ) ) )
| ~ ( ~ ~ ( ( SY2620 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2621 ) @ SY2620 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2621 ) @ SV430 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6581]) ).
thf(6874,plain,
! [SV119: $i,SV431: $i,SV699: $i] :
( ( ~ ( c_Wellfounded_OwfP @ SV699 @ SV431 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV699 @ ( tc_fun @ SV699 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) )
| ( c_Wellfounded_OwfP @ SV699 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6582]) ).
thf(6875,plain,
! [SV120: $i,SV432: $i,SV700: $i] :
( ( ! [SY2622: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2622 ) @ SV700 ) @ SV432 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2622 ) @ SV700 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2622 ) @ SV120 ) @ SV432 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6583]) ).
thf(6876,plain,
! [SV121: $i,SV433: $i,SV701: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV701 ) @ SV433 ) @ SV121 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV701 @ tc_HOL_Obool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6584]) ).
thf(6877,plain,
! [SV122: $i,SV434: $i,SV702: $i] :
( ( ! [SY2623: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2623 @ tc_HOL_Obool ) ) @ SV702 ) @ SV434 ) @ SV122 ) )
| ( hBOOL @ ( hAPP @ SV434 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6585]) ).
thf(6878,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6586]) ).
thf(6879,plain,
! [SV124: $i,SV436: $i,SV704: $i] :
( ( ! [SY2624: $i,SY2625: $i,SY2626: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2626 @ ( tc_fun @ SY2625 @ tc_HOL_Obool ) ) ) @ SY2624 ) @ SV704 ) @ SV436 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6587]) ).
thf(6880,plain,
! [SV125: $i,SV437: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV437 ) @ SV125 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SV437 ) )
| ( SV437 = SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6588]) ).
thf(6881,plain,
! [SV126: $i,SV438: $i,SV705: $i] :
( ( ! [SY2627: $i] :
( ~ ( class_Orderings_Oorder @ SY2627 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2627 ) @ SV705 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2627 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2627 ) @ SV126 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6589]) ).
thf(6882,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6590]) ).
thf(6883,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ( ~ ( ~ ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) )
| ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
| ~ ( ~ ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) )
| ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6591]) ).
thf(6884,plain,
! [SV129: $i,SV441: $i,SV708: $i] :
( ( ! [SY2634: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY2634 @ SV708 @ SV441 )
| ( ( hAPP @ ( hAPP @ SV708 @ SV129 ) @ SV129 )
= SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6592]) ).
thf(6885,plain,
! [SV130: $i,SV442: $i,SV709: $i] :
( ( ~ ( c_Predicate_Oreflp @ SV709 @ SV442 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV442 @ SV130 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6593]) ).
thf(6886,plain,
! [SV131: $i,SV443: $i,SV710: $i] :
( ( ! [SY2635: $i,SY2636: $i,SY2637: $i,SY2638: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2638 @ SY2637 @ SY2636 @ SY2635 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2639: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2635 @ SV443 ) @ SY2639 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2639 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2640: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2635 @ SV443 ) @ SY2640 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2640 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2638 @ SY2637 @ SY2636 @ SY2635 @ SV710 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6594]) ).
thf(6887,plain,
! [SV132: $i,SV444: $i,SV711: $i] :
( ( ! [SY2641: $i,SY2642: $i,SY2643: $i,SY2644: $i,SY2645: $i,SY2646: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2646 @ SY2645 @ SY2644 @ SY2643 ) @ SY2642 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY2641 @ SY2645 @ SY2644 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SY2643 @ ( hAPP @ SY2642 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6595]) ).
thf(6888,plain,
! [SV133: $i,SV445: $i,SV712: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV712 @ tc_HOL_Obool ) ) @ SV445 ) @ SV133 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV712 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV445 ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6596]) ).
thf(6889,plain,
! [SV134: $i,SV446: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
| ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
| ~ ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6597]) ).
thf(6890,plain,
! [SV135: $i,SV447: $i,SV713: $i] :
( ( ! [SY2647: $i,SY2648: $i,SY2649: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2649 @ ( tc_fun @ SY2648 @ tc_HOL_Obool ) ) ) @ SY2647 ) @ SV713 ) @ SV447 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2647 @ SV447 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6598]) ).
thf(6891,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6599]) ).
thf(6892,plain,
! [SV137: $i,SV449: $i,SV715: $i] :
( ( ! [SY2650: $i] :
( ~ ( c_Predicate_Osymp @ SY2650 @ SV715 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6600]) ).
thf(6893,plain,
! [SV138: $i,SV450: $i,SV716: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV716 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV450 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV138 ) @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6601]) ).
thf(6894,plain,
! [SV139: $i,SV451: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV451 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV139 @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6602]) ).
thf(6895,plain,
! [SV140: $i,SV452: $i,SV717: $i] :
( ( SV717
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV452 ) @ SV140 ) @ SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6603]) ).
thf(6896,plain,
! [SV141: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ SV453 ) @ SV141 ) ) )
= $true )
| ( ( v_P @ SV141 @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6604]) ).
thf(6897,plain,
! [SV142: $i,SV454: $i,SV718: $i] :
( ( ! [SY2651: $i,SY2652: $i,SY2653: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2653 @ ( tc_fun @ SY2652 @ tc_HOL_Obool ) ) ) @ SY2651 ) @ SV718 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2651 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6605]) ).
thf(6898,plain,
! [SV143: $i,SV455: $i,SV719: $i] :
( ( ! [SY2654: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2654 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP @ SV719 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SV455 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6606]) ).
thf(6899,plain,
! [SV144: $i,SV456: $i,SV720: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV720 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV144 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6607]) ).
thf(6900,plain,
! [SV145: $i,SV457: $i,SV721: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV457 ) @ SV145 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV145 ) @ SV457 )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6608]) ).
thf(6901,plain,
! [SV146: $i,SV458: $i,SV722: $i] :
( ( ! [SY2655: $i,SY2656: $i,SY2657: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2657 @ SY2656 ) @ SY2655 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2657 @ SY2656 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SY2655 != SV458 )
| ( SV722 != SV146 ) ) )
| ~ ( ~ ~ ( ( SY2655 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2657 @ SY2656 ) @ SY2655 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2657 @ SY2656 ) @ SV458 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6609]) ).
thf(6902,plain,
! [SV147: $i,SV459: $i,SV723: $i] :
( ( ! [SY2658: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2658 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2658 ) @ SV147 ) @ SV723 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2658 ) @ SV147 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6610]) ).
thf(6903,plain,
! [SV148: $i,SV460: $i,SV724: $i] :
( ( ! [SY2659: $i,SY2660: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2660 @ SY2659 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2659 @ SV724 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2659 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2659 @ SV724 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6611]) ).
thf(6904,plain,
! [SV149: $i,SV461: $i,SV725: $i] :
( ( ~ ( class_Orderings_Oorder @ SV725 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6612]) ).
thf(6905,plain,
! [SV150: $i,SV462: $i,SV726: $i] :
( ( ! [SY2661: $i,SY2662: $i] :
( ( ( hAPP @ SY2662 @ SY2661 )
!= SV726 )
| ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SY2662 @ SY2661 @ SV726 )
= SY2662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6613]) ).
thf(6906,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6614]) ).
thf(6907,plain,
! [SV152: $i,SV464: $i,SV728: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV728 ) @ SV464 ) @ SV152 )
!= SV152 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6615]) ).
thf(6908,plain,
! [SV153: $i,SV465: $i,SV729: $i] :
( ( ! [SY2663: $i,SY2664: $i,SY2665: $i,SY2666: $i,SY2667: $i,SY2668: $i,SY2669: $i,SY2670: $i] :
( ( ( hAPP @ SY2670 @ ( hAPP @ SY2669 @ SY2668 ) )
!= ( hAPP @ SY2667 @ ( hAPP @ SY2666 @ SY2665 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2664 @ SY2663 @ SV729 @ SY2670 ) @ SY2669 ) @ SY2668 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SY2663 @ SV153 @ SY2667 ) @ SY2666 ) @ SY2665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6616]) ).
thf(6909,plain,
! [SV154: $i,SV466: $i,SV730: $i] :
( ( ! [SY2671: $i,SY2672: $i] :
( ~ ( c_Predicate_Otransp @ SY2672 @ SY2671 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2671 @ SV730 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2671 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2671 @ SV730 ) @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6617]) ).
thf(6910,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
| ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) )
| ~ ( ~ ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6618]) ).
thf(6911,plain,
! [SV156: $i,SV468: $i,SV732: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV732 ) @ SV468 ) @ SV156 ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV732 ) @ SV468 ) @ SV156 )
= SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6619]) ).
thf(6912,plain,
! [SV157: $i,SV469: $i] :
( ( ( ~ ~ ! [SY2236: $i] :
~ ( hBOOL @ ( hAPP @ SV469 @ SY2236 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6620]) ).
thf(6913,plain,
! [SV158: $i,SV470: $i,SV733: $i] :
( ( ! [SY2675: $i] :
( ~ ( class_Orderings_Opreorder @ SY2675 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2675 ) @ SV733 ) @ SV470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2675 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2675 ) @ SV733 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6621]) ).
thf(6914,plain,
! [SV159: $i,SV471: $i,SV734: $i] :
( ( ! [SY2676: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2676 @ SV734 @ SV471 ) @ SV159 ) )
| ( SV471
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2676 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6622]) ).
thf(6915,plain,
! [SV160: $i,SV472: $i,SV735: $i] :
( ( ! [SY2677: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2677 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2677 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2677 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2677 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6623]) ).
thf(6916,plain,
! [SV161: $i,SV473: $i] :
( ( ~ ( ~ ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) )
| ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6624]) ).
thf(6917,plain,
! [SV162: $i,SV474: $i,SV736: $i] :
( ( ! [SY2678: $i] :
( ( SY2678 != SV736 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2678 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SY2678 ) @ SV162 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6625]) ).
thf(6918,plain,
! [SV163: $i,SV475: $i,SV737: $i] :
( ( ! [SY2679: $i,SY2680: $i,SY2681: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2681 @ SY2680 @ SY2679 @ SV737 @ SV475 )
| ( ( hAPP @ SV737 @ ( hAPP @ SY2679 @ SV163 ) )
= SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6626]) ).
thf(6919,plain,
! [SV164: $i,SV476: $i,SV738: $i] :
( ( ! [SY2682: $i,SY2683: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2683 @ tc_HOL_Obool ) ) @ SY2682 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2683 @ SV164 ) @ SY2682 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2683 @ SV164 ) @ SV738 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6627]) ).
thf(6920,plain,
! [SV165: $i,SV477: $i,SV739: $i] :
( ( ! [SY2684: $i,SY2685: $i,SY2686: $i,SY2687: $i,SY2688: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2688 @ SY2687 ) @ SY2686 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2685 @ SY2686 ) @ SY2684 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SY2688 @ SY2685 ) @ SY2687 ) @ SY2684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6628]) ).
thf(6921,plain,
! [SV166: $i,SV478: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV478 ) )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV166 @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6629]) ).
thf(6922,plain,
! [SV167: $i,SV479: $i,SV740: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV740 @ SV479 ) )
| ( hBOOL @ ( hAPP @ SV740 @ ( c_Hilbert__Choice_OEps @ SV167 @ SV740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6630]) ).
thf(6923,plain,
! [SV168: $i,SV480: $i,SV741: $i] :
( ( ~ ( class_Orderings_Oorder @ SV741 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6631]) ).
thf(6924,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
| ( SV481 = SV169 ) )
| ~ ( ( SV481 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6632]) ).
thf(6925,plain,
! [SV170: $i,SV482: $i,SV743: $i] :
( ( ! [SY2689: $i] :
~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2689 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SY2689 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2689 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SY2689 @ SV482 ) @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6633]) ).
thf(6926,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ~ ( class_Orderings_Oorder @ SV744 )
| ~ ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6634]) ).
thf(6927,plain,
! [SV172: $i,SV484: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV484 ) )
= $true )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV172 @ SV484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6635]) ).
thf(6928,plain,
! [SV173: $i,SV485: $i] :
( ( ( ~ ~ ( ~ ( class_Enum_Oenum @ SV485 )
| ~ ( class_Enum_Oenum @ SV173 ) ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6636]) ).
thf(6929,plain,
! [SV174: $i,SV486: $i,SV745: $i] :
( ( ! [SY2690: $i,SY2691: $i,SY2692: $i,SY2693: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2693 @ SY2692 @ SY2691 @ SY2690 @ SV745 )
| ~ ( ~ ( ( ( hAPP @ SY2691 @ SV486 )
!= ( hAPP @ SY2691 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SY2691 @ SV486 )
= ( hAPP @ SY2691 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6637]) ).
thf(6930,plain,
! [SV175: $i,SV487: $i,SV746: $i] :
( ( ! [SY2694: $i,SY2695: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2695 @ tc_HOL_Obool ) ) @ SY2694 ) @ SV746 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2695 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2695 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2695 @ tc_HOL_Obool ) ) @ SY2694 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2695 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6638]) ).
thf(6931,plain,
! [SV176: $i,SV488: $i,SV747: $i] :
( ( ! [SY2696: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2696 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2696 ) @ SV176 ) @ SV488 ) )
| ( SV747 = SV176 ) )
| ~ ( ( SV747 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2696 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2696 ) @ SV176 ) @ SV488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6639]) ).
thf(6932,plain,
! [SV177: $i,SV489: $i,SV748: $i] :
( ( ! [SY2697: $i,SY2698: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2698 @ SY2697 ) @ SV748 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SY2698 ) @ SV748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6640]) ).
thf(6933,plain,
! [SV178: $i,SV490: $i,SV749: $i] :
( ( ! [SY2699: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2699 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2699 ) @ SV749 ) @ SV178 ) )
| ( SV490 = SV178 ) )
| ~ ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2699 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2699 ) @ SV749 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6641]) ).
thf(6934,plain,
! [SV179: $i,SV491: $i,SV750: $i] :
( ( ! [SY2700: $i,SY2701: $i,SY2702: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2702 @ ( tc_fun @ SY2701 @ tc_HOL_Obool ) ) ) @ SY2700 ) @ SV750 ) @ SV491 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2700 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6642]) ).
thf(6935,plain,
! [SV180: $i,SV492: $i,SV751: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV492 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV751 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6643]) ).
thf(6936,plain,
! [SV181: $i,SV493: $i,SV752: $i] :
( ( ! [SY2703: $i,SY2704: $i,SY2705: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2705 @ SY2704 ) @ SY2703 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SY2705 ) @ SV181 ) @ SY2704 ) @ SY2703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6644]) ).
thf(6937,plain,
! [SV182: $i,SV494: $i,SV753: $i] :
( ( ! [SY2706: $i,SY2707: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2707 @ tc_HOL_Obool ) ) @ SY2706 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2707 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY2708: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY2708 ) @ SV182 ) )
| ( SY2706
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2707 @ SV494 ) @ SY2708 ) ) ) )
| ~ ( ~ ~ ! [SY2709: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY2709 ) @ SV182 ) )
| ( SY2706
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2707 @ SV494 ) @ SY2709 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2707 @ tc_HOL_Obool ) ) @ SY2706 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2707 @ SV494 ) @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6645]) ).
thf(6938,plain,
! [SV183: $i,SV495: $i,SV754: $i] :
( ( ( SV754 != SV495 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6646]) ).
thf(6939,plain,
! [SV184: $i,SV496: $i,SV755: $i] :
( ( ! [SY2710: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2710 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2710 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2710 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6647]) ).
thf(6940,plain,
! [SV185: $i,SV497: $i,SV756: $i] :
( ( ! [SY2711: $i] :
( ~ ( class_Orderings_Oord @ SY2711 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2711 ) @ SV756 ) @ SV497 ) )
| ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2711 ) @ SV756 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6648]) ).
thf(6941,plain,
! [SV186: $i,SV498: $i,SV757: $i] :
( ( ! [SY2712: $i] :
( ~ ( class_Orderings_Oorder @ SY2712 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2712 ) @ SV757 ) @ SV498 ) )
| ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2712 ) @ SV186 ) @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6649]) ).
thf(6942,plain,
! [SV187: $i,SV499: $i,SV758: $i] :
( ( ! [SY2713: $i,SY2714: $i] :
( ~ ( class_Orderings_Oord @ SY2714 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2713 @ SY2714 ) ) @ SV758 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2714 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6650]) ).
thf(6943,plain,
! [SV188: $i,SV500: $i,SV759: $i] :
( ( ! [SY2715: $i,SY2716: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2716 @ SY2715 ) @ SV759 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SY2716 ) @ SV759 ) @ SY2715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6651]) ).
thf(6944,plain,
! [SV189: $i,SV501: $i,SV760: $i] :
( ( ! [SY2717: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2717 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2717 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2717 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2717 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6652]) ).
thf(6945,plain,
! [SV190: $i,SV502: $i,SV761: $i] :
( ( ! [SY2718: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2718 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2718 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SY2718 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6653]) ).
thf(6946,plain,
! [SV191: $i,SV503: $i,SV762: $i] :
( ( ! [SY2719: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2719 @ SV762 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6654]) ).
thf(6947,plain,
! [SV192: $i,SV504: $i,SV763: $i] :
( ( ! [SY2720: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2720 ) @ SV763 ) @ SV504 ) )
| ( SV763 = SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2720 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2720 ) @ SV192 ) @ SV504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6655]) ).
thf(6948,plain,
! [SV193: $i,SV505: $i,SV764: $i] :
( ( ! [SY2721: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2721 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2721 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2721 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2721 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2721 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2721 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2721 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2721 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6656]) ).
thf(6949,plain,
! [SV194: $i,SV506: $i] :
( ( ( ~ ( class_Groups_Ouminus @ SV506 ) )
= $true )
| ( ( class_Groups_Ouminus @ ( tc_fun @ SV194 @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6657]) ).
thf(6950,plain,
! [SV195: $i,SV507: $i,SV765: $i] :
( ( ! [SY2722: $i] :
( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2722 ) @ SV765 ) @ SV507 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2722 ) @ SV765 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2722 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2722 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2722 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2722 ) @ SV765 ) @ SV195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6658]) ).
thf(6951,plain,
! [SV196: $i,SV508: $i,SV766: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) ) @ SV508 ) @ SV196 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV196 ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6659]) ).
thf(6952,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
!= SV197 )
| ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) ) )
| ~ ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6660]) ).
thf(6953,plain,
! [SV198: $i,SV510: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
| ( SV510 = SV198 ) )
| ~ ( ( SV510 != SV198 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6661]) ).
thf(6954,plain,
! [SV199: $i,SV511: $i,SV768: $i] :
( ( ! [SY2723: $i,SY2724: $i,SY2725: $i] :
( ~ ( ( SY2725 != SY2724 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2723 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2723 @ SV768 ) @ SY2725 ) @ SV511 ) ) @ SY2724 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2723 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2723 @ SV768 ) @ SY2724 ) @ SV199 ) ) @ SY2725 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6662]) ).
thf(6955,plain,
! [SV200: $i,SV512: $i,SV769: $i] :
( ( ! [SY2726: $i] :
( ~ ( c_Fun_Obij__betw @ SY2726 @ SV769 @ SV512 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV769 @ tc_HOL_Obool ) ) )
| ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2726 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6663]) ).
thf(6956,plain,
! [SV201: $i,SV513: $i,SV770: $i] :
( ( ! [SY2727: $i] :
( ~ ( class_Orderings_Oord @ SY2727 )
| ( SV770 != SV513 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2727 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2727 ) @ SV770 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6664]) ).
thf(6957,plain,
! [SV202: $i,SV514: $i,SV771: $i] :
( ( ! [SY2728: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2728 ) @ SV771 ) @ SV514 ) @ SV202 ) )
| ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ~ ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2728 ) @ SV771 ) @ SV514 ) @ SV202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6665]) ).
thf(6958,plain,
! [SV203: $i,SV515: $i,SV772: $i] :
( ( ( SV772 != SV515 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SV515 ) @ SV772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6666]) ).
thf(6959,plain,
! [SV204: $i,SV516: $i,SV773: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV773 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV773 ) @ SV204 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV773 @ tc_HOL_Obool ) ) ) ) )
| ( SV516 = SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6667]) ).
thf(6960,plain,
! [SV205: $i,SV517: $i,SV774: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ SV517 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV774 ) @ SV205 ) @ SV517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6668]) ).
thf(6961,plain,
! [SV206: $i,SV518: $i,SV775: $i] :
( ( ! [SY2729: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2729 @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV518 @ tc_HOL_Obool ) ) @ SY2729 ) @ SV206 ) @ SV775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6669]) ).
thf(6962,plain,
! [SV207: $i,SV519: $i] :
( ( ( ~ ( class_Groups_Ominus @ SV519 ) )
= $true )
| ( ( class_Groups_Ominus @ ( tc_fun @ SV207 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6670]) ).
thf(6963,plain,
! [SV208: $i,SV520: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV520 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV208 @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6671]) ).
thf(6964,plain,
! [SV209: $i,SV521: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV521 ) @ SV209 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SV521 ) )
| ( SV521 = SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6672]) ).
thf(6965,plain,
! [SV210: $i,SV522: $i] :
( ( ( ~ ~ ! [SY2337: $i] :
~ ( hBOOL @ ( hAPP @ SV522 @ SY2337 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6673]) ).
thf(6966,plain,
! [SV211: $i,SV523: $i,SV776: $i] :
( ( ! [SY2730: $i,SY2731: $i,SY2732: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2732 @ SY2731 ) @ SY2730 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SY2732 ) @ SY2731 ) @ SY2730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6674]) ).
thf(6967,plain,
! [SV212: $i,SV524: $i,SV777: $i] :
( ( ! [SY2733: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2733 @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ SV524 @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SY2733 ) @ SV524 ) @ SV777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6675]) ).
thf(6968,plain,
! [SV213: $i,SV525: $i,SV778: $i] :
( ( ! [SY2734: $i,SY2735: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2735 @ tc_HOL_Obool ) ) @ SY2734 ) @ SV778 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2735 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2735 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2735 @ tc_HOL_Obool ) ) @ SY2734 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2735 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6676]) ).
thf(6969,plain,
! [SV214: $i,SV526: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV526 ) )
= $true )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV214 @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6677]) ).
thf(6970,plain,
! [SV215: $i,SV527: $i,SV779: $i] :
( ( ! [SY2736: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2736 @ SV779 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
| ~ ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SY2736 @ SV779 @ SV527 ) @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6678]) ).
thf(6971,plain,
! [SV216: $i,SV528: $i,SV780: $i] :
( ( ! [SY2739: $i,SY2740: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SY2739 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2740 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2740 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SY2739 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SY2739 != SV216 )
| ( SV780 != SV528 ) ) )
| ~ ( ~ ( ~ ( ( SY2739 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SY2739 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SY2739 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2740 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2740 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2740 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6679]) ).
thf(6972,plain,
! [SV217: $i,SV529: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV529 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV529 ) @ ( c_Orderings_Obot__class_Obot @ SV529 ) ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6680]) ).
thf(6973,plain,
! [SV218: $i,SV530: $i,SV781: $i] :
( ( ~ ( class_Orderings_Oorder @ SV781 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6681]) ).
thf(6974,plain,
! [SV219: $i,SV531: $i,SV782: $i] :
( ( ! [SY2741: $i,SY2742: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2742 @ SY2741 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2742 @ SY2741 @ SV782 ) @ SV531 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6682]) ).
thf(6975,plain,
! [SV220: $i,SV532: $i,SV783: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV532 ) @ SV220 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV783 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV532 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6683]) ).
thf(6976,plain,
! [SV221: $i,SV533: $i,SV784: $i] :
( ( ! [SY2743: $i,SY2744: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2744 @ SY2743 @ SV784 )
| ( ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6684]) ).
thf(6977,plain,
! [SV222: $i,SV534: $i,SV785: $i] :
( ( ! [SY2745: $i,SY2746: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2746 @ SY2745 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2746 @ SY2745 @ SV785 ) @ SV534 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6685]) ).
thf(6978,plain,
! [SV223: $i,SV535: $i,SV786: $i] :
( ( ! [SY2747: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2747 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2747 ) @ SV223 ) @ SV786 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2747 ) @ SV223 ) @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6686]) ).
thf(6979,plain,
! [SV224: $i,SV536: $i,SV787: $i] :
( ( ! [SY2748: $i] :
( ~ ( class_Orderings_Oorder @ SY2748 )
| ( SV787 != SV536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2748 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2748 ) @ SV224 ) @ SV787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6687]) ).
thf(6980,plain,
! [SV225: $i,SV537: $i,SV788: $i] :
( ( ! [SY2749: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2749 @ tc_HOL_Obool ) ) @ SV788 ) @ SV537 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ SV788 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6688]) ).
thf(6981,plain,
! [SV226: $i,SV538: $i] :
( ( ( ~ ~ ( ~ ( class_Finite__Set_Ofinite @ SV538 )
| ~ ( class_Finite__Set_Ofinite @ SV226 ) ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6689]) ).
thf(6982,plain,
! [SV227: $i,SV539: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
| ( SV539 = SV227 ) )
| ~ ( ( SV539 != SV227 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6690]) ).
thf(6983,plain,
! [SV228: $i,SV540: $i,SV789: $i] :
( ( ! [SY2750: $i] :
( ( SY2750 != SV789 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SY2750 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6691]) ).
thf(6984,plain,
! [SV229: $i,SV790: $i,SV541: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV541 ) @ SV790 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV541 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ SV229 @ SV790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6692]) ).
thf(6985,plain,
! [SV230: $i,SV542: $i,SV791: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i] :
~ ( ~ ( ( SY2753 != SY2752 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2751 @ SV791 @ SV542 @ SY2752 @ SV230 ) @ SY2753 )
= SV230 ) )
| ~ ( ~ ( ( SY2753 != SY2752 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2751 @ SV791 @ SV542 @ SY2752 @ SV230 ) @ SY2753 )
= ( hAPP @ SV542 @ SY2753 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(6986,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
| ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6694]) ).
thf(6987,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ~ ( ~ ( ( SV793 != SV544 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
| ( SV793 = SV544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6695]) ).
thf(6988,plain,
! [SV233: $i,SV545: $i,SV794: $i] :
( ( ! [SY2754: $i] :
( ~ ( c_Fun_Obij__betw @ SY2754 @ SV794 @ SV545 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2754 @ tc_HOL_Obool ) ) @ SV233 )
| ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6696]) ).
thf(6989,plain,
! [SV234: $i,SV546: $i,SV795: $i] :
( ( ! [SY2755: $i,SY2756: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2756 @ tc_HOL_Obool ) ) @ SY2755 ) @ SV795 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2756 @ SV546 @ SV234 ) @ SY2755 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2756 @ SV546 @ SV234 ) @ SV795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6697]) ).
thf(6990,plain,
! [SV235: $i,SV547: $i,SV796: $i] :
( ( ! [SY2757: $i] :
( ~ ( c_Finite__Set_Ofolding__one @ SY2757 @ SV796 @ SV547 )
| ( ( hAPP @ SV547 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2757 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2757 @ tc_HOL_Obool ) ) ) )
= SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6698]) ).
thf(6991,plain,
! [SV236: $i,SV548: $i,SV797: $i] :
( ( ! [SY2758: $i] :
~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SY2758 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2758 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2758 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SY2758 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6699]) ).
thf(6992,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6700]) ).
thf(6993,plain,
! [SV238: $i,SV550: $i,SV799: $i] :
( ( ! [SY2759: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2759 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2759 ) @ SV550 ) @ SV238 ) ) )
| ~ ( ( SV799 != SV550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2759 ) @ SV799 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6701]) ).
thf(6994,plain,
! [SV239: $i,SV551: $i,SV800: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6702]) ).
thf(6995,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6703]) ).
thf(6996,plain,
! [SV241: $i,SV553: $i,SV802: $i] :
( ( ! [SY2760: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2760 @ SV802 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY2760 @ SV802 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6704]) ).
thf(6997,plain,
! [SV242: $i,SV554: $i,SV803: $i] :
( ( ! [SY2761: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2761 @ tc_HOL_Obool ) ) @ SV803 ) @ SV554 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2761 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2761 ) @ SV242 ) @ SV803 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2761 ) @ SV242 ) @ SV554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6705]) ).
thf(6998,plain,
! [SV243: $i,SV555: $i,SV804: $i] :
( ( ! [SY2762: $i,SY2763: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2763 @ SY2762 @ SV804 ) @ SV555 ) @ SV243 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV804 @ SV243 ) @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6706]) ).
thf(6999,plain,
! [SV244: $i,SV556: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
| ( SV556 = SV244 ) )
| ~ ( ( SV556 != SV244 )
| ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6707]) ).
thf(7000,plain,
! [SV245: $i,SV557: $i,SV805: $i] :
( ( ! [SY2764: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2764 @ SV805 ) @ SV557 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SY2764 @ SV805 ) @ SV245 ) )
| ( SV557 = SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6708]) ).
thf(7001,plain,
! [SV246: $i,SV558: $i,SV806: $i] :
( ( ( SV806
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV558 @ tc_HOL_Obool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV558 ) @ SV246 ) @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6709]) ).
thf(7002,plain,
! [SV247: $i,SV559: $i,SV807: $i] :
( ( ! [SY2765: $i] :
( ~ ( class_Orderings_Oord @ SY2765 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SY2765 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2406: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2765 ) @ ( hAPP @ SV559 @ SY2406 ) ) @ ( hAPP @ SV247 @ SY2406 ) ) ) )
| ~ ( ~ ! [SY2407: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2765 ) @ ( hAPP @ SV559 @ SY2407 ) ) @ ( hAPP @ SV247 @ SY2407 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SY2765 ) ) @ SV559 ) @ SV247 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6710]) ).
thf(7003,plain,
! [SV248: $i,SV560: $i,SV808: $i] :
( ( ! [SY2768: $i,SY2769: $i,SY2770: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2770 @ SY2769 ) @ SY2768 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SY2769 ) @ SY2768 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SY2770 ) @ SY2769 ) @ SY2768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6711]) ).
thf(7004,plain,
! [SV249: $i,SV561: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
| ( SV561 = SV249 ) )
| ~ ( ( SV561 != SV249 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6712]) ).
thf(7005,plain,
! [SV250: $i,SV562: $i,SV809: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 )
= SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6713]) ).
thf(7006,plain,
! [SV251: $i,SV563: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV563 ) )
= $true )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV251 @ SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6714]) ).
thf(7007,plain,
! [SV252: $i,SV564: $i,SV810: $i] :
( ( ! [SY2771: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2771 ) @ SV810 ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2771 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2771 ) @ SV810 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6715]) ).
thf(7008,plain,
! [SV253: $i,SV565: $i,SV811: $i] :
( ( ! [SY2772: $i,SY2773: $i,SY2774: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2774 @ SY2773 ) @ SY2772 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SY2773 ) @ SY2772 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SY2774 ) @ SV811 ) @ SY2773 ) @ SY2772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6716]) ).
thf(7009,plain,
! [SV254: $i,SV566: $i] :
( ( ~ ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
| ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
| ~ ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6717]) ).
thf(7010,plain,
! [SV255: $i,SV567: $i] :
( ( ( ~ ! [SY2421: $i] :
( ( hAPP @ SV567 @ SY2421 )
= ( hAPP @ SV255 @ SY2421 ) ) )
= $true )
| ( ( SV567 = SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6718]) ).
thf(7011,plain,
! [SV256: $i,SV568: $i] :
( ( ~ ! [SY2422: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SY2422 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SY2422 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6719]) ).
thf(7012,plain,
! [SV257: $i,SV569: $i,SV812: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) )
| ( SV569 = SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6720]) ).
thf(7013,plain,
! [SV258: $i,SV570: $i,SV813: $i] :
( ( ! [SY2775: $i,SY2776: $i,SY2777: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SY2777 @ SY2776 @ SY2775 @ SV813 @ SV570 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2776 @ tc_HOL_Obool ) ) )
= SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6721]) ).
thf(7014,plain,
! [SV259: $i,SV571: $i,SV814: $i] :
( ( ! [SY2778: $i,SY2779: $i,SY2780: $i,SY2781: $i,SY2782: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2782 @ SY2781 @ SY2780 @ SY2779 ) @ SY2778 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SY2781 @ SY2780 @ SV571 ) @ SV259 ) )
| ! [SY2434: $i] :
( ( hAPP @ SY2779 @ ( hAPP @ SY2778 @ SY2434 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY2434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6722]) ).
thf(7015,plain,
! [SV260: $i,SV572: $i,SV815: $i] :
( ( ! [SY2784: $i,SY2785: $i,SY2786: $i] :
( ~ ( ( SY2786 != SY2785 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2784 @ SV815 @ SV572 @ SY2785 @ SV260 ) @ SY2786 )
= ( hAPP @ SV572 @ SY2786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6723]) ).
thf(7016,plain,
! [SV261: $i,SV573: $i,SV816: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV816 )
| ( SV573 != SV261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV816 ) @ SV573 ) @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6724]) ).
thf(7017,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
| ( SV574 = SV262 ) )
| ~ ( ( SV574 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6725]) ).
thf(7018,plain,
! [SV263: $i,SV575: $i,SV818: $i] :
( ( ! [SY2787: $i,SY2788: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2788 @ tc_HOL_Obool ) ) @ SY2787 ) @ SV818 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2788 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2788 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2788 @ tc_HOL_Obool ) ) @ SY2787 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2788 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6726]) ).
thf(7019,plain,
! [SV264: $i,SV576: $i,SV819: $i] :
( ( ! [SY2789: $i,SY2790: $i,SY2791: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2791 @ SY2790 ) @ SY2789 ) @ SV819 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2791 @ SY2790 ) @ SV576 ) @ SV264 ) )
| ~ ( ( SY2789 != SV576 )
| ( SV819 != SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6727]) ).
thf(7020,plain,
! [SV265: $i,SV577: $i,SV820: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV577 ) @ SV265 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV820 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV820 @ SV577 ) ) @ ( c_Predicate_OPowp @ SV820 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6728]) ).
thf(7021,plain,
! [SV266: $i,SV578: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV578 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV578 ) @ SV266 ) @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6729]) ).
thf(7022,plain,
! [SV267: $i,SV579: $i,SV821: $i] :
( ( ! [SY2792: $i,SY2793: $i,SY2794: $i,SY2795: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2795 @ SY2794 @ SY2793 @ SY2792 ) @ SV821 )
!= SV579 )
| ( ( hAPP @ SY2792 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6730]) ).
thf(7023,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
| ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
| ~ ( ~ ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) )
| ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6731]) ).
thf(7024,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6732]) ).
thf(7025,plain,
! [SV270: $i,SV582: $i,SV823: $i] :
( ( ! [SY2796: $i,SY2797: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2797 @ SY2796 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2796 @ SV823 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2796 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2796 @ SV823 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6733]) ).
thf(7026,plain,
! [SV271: $i,SV583: $i,SV824: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV824 @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV824 ) @ SV583 ) @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6734]) ).
thf(7027,plain,
! [SV272: $i,SV584: $i,SV825: $i] :
( ( ! [SY2798: $i] :
( ( SY2798 != SV825 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2798 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SY2798 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6735]) ).
thf(7028,plain,
! [SV273: $i,SV585: $i,SV826: $i] :
( ( ! [SY2799: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2799 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2799 ) @ SV585 ) @ SV273 ) ) )
| ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2799 ) @ SV826 ) @ SV273 ) ) )
| ~ ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2799 ) @ SV826 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2799 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2799 ) @ SV585 ) @ SV273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6736]) ).
thf(7029,plain,
! [SV274: $i,SV586: $i] :
( ( ( SV586 != SV274 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV586 ) @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6737]) ).
thf(7030,plain,
! [SV275: $i,SV587: $i,SV827: $i] :
( ( ! [SY2800: $i,SY2801: $i,SY2802: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2802 ) @ SY2801 ) @ SY2800 )
!= SV827 )
| ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2802 ) @ SY2800 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2802 ) @ SY2801 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2802 ) @ SV827 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6738]) ).
thf(7031,plain,
! [SV276: $i,SV588: $i,SV828: $i] :
( ( ! [SY2803: $i] :
( ( SY2803 != SV828 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2803 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SY2803 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6739]) ).
thf(7032,plain,
! [SV277: $i,SV589: $i,SV829: $i] :
( ( ! [SY2804: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2804 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2804 ) @ SV277 ) @ SV829 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SY2804 ) @ SV277 ) @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6740]) ).
thf(7033,plain,
! [SV278: $i,SV590: $i,SV830: $i] :
( ( ! [SY2805: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2805 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2805 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2805 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6741]) ).
thf(7034,plain,
! [SV279: $i,SV591: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV591 ) )
= $true )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV279 @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6742]) ).
thf(7035,plain,
! [SV280: $i,SV592: $i,SV831: $i] :
( ( ! [SY2806: $i] :
( ( SY2806
!= ( c_Finite__Set_Ofold1 @ SV831 @ SV592 ) )
| ( ( hAPP @ SY2806 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV831 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV831 @ tc_HOL_Obool ) ) ) )
= SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6743]) ).
thf(7036,plain,
! [SV281: $i,SV593: $i,SV832: $i] :
( ( ! [SY2807: $i,SY2808: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2807 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY2809: $i] :
~ ( ~ ( ( SY2807
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SV593 ) @ SY2809 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2809 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2807 ) @ SY2809 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2809 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY2810: $i] :
~ ( ~ ( ( SY2807
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SV593 ) @ SY2810 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2810 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2807 ) @ SY2810 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2810 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SY2807 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2808 ) @ SV593 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6744]) ).
thf(7037,plain,
! [SV282: $i,SV594: $i,SV833: $i] :
( ( ( SV833
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) @ SV833 ) @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6745]) ).
thf(7038,plain,
! [SV283: $i,SV595: $i] :
( ( ( hAPP @ ( c_Set_OPow @ SV595 ) @ SV283 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV595 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6746]) ).
thf(7039,plain,
! [SV284: $i,SV596: $i,SV834: $i] :
( ( ! [SY2811: $i,SY2812: $i] :
( ~ ( c_Fun_Oinj__on @ SY2812 @ SY2811 @ SV834 @ SV596 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2812 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SY2812 @ SY2811 @ SV834 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6747]) ).
thf(7040,plain,
! [SV285: $i,SV597: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
| ( SV597 = SV285 ) )
| ~ ( ( SV597 != SV285 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6748]) ).
thf(7041,plain,
! [SV286: $i,SV598: $i,SV835: $i] :
( ( ! [SY2813: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2813 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6749]) ).
thf(7042,plain,
! [SV287: $i,SV599: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
| ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6750]) ).
thf(7043,plain,
! [SV289: $i,SV600: $i] :
( ( ~ ( ~ ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) )
| ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
| ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6752]) ).
thf(7044,plain,
! [SV291: $i,SV601: $i,SV836: $i] :
( ( ~ ~ ! [SY2814: $i] :
~ ( hBOOL @ ( hAPP @ SV836 @ SY2814 ) )
| ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6754]) ).
thf(7045,plain,
! [SV292: $i,SV602: $i,SV837: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV602 ) @ SV292 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV292 ) @ SV602 )
= SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6755]) ).
thf(7046,plain,
! [SV293: $i,SV603: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV603 ) )
= $true )
| ( ( class_Orderings_Oord @ ( tc_fun @ SV293 @ SV603 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6756]) ).
thf(7047,plain,
! [SV294: $i,SV604: $i,SV838: $i] :
( ( ! [SY2815: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SY2815 @ SV838 ) )
| ( hBOOL @ ( hAPP @ SV604 @ SV838 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SY2815 ) @ SV838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6757]) ).
thf(7048,plain,
! [SV295: $i,SV605: $i,SV839: $i] :
( ( ! [SY2816: $i,SY2817: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2817 @ SY2816 @ SV839 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2817 @ tc_HOL_Obool ) ) ) @ SV295 ) )
| ( SV295 = SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6758]) ).
thf(7049,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV840 )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6759]) ).
thf(7050,plain,
! [SV297: $i,SV607: $i,SV841: $i] :
( ( ! [SY2818: $i,SY2819: $i] :
( ~ ( class_Orderings_Oord @ SY2819 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2818 @ SY2819 ) ) @ SV841 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2819 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6760]) ).
thf(7051,plain,
! [SV298: $i,SV608: $i,SV842: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) @ SV298 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV298 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6761]) ).
thf(7052,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6762]) ).
thf(7053,plain,
! [SV300: $i,SV610: $i,SV844: $i] :
( ( ! [SY2820: $i,SY2821: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2821 @ SY2820 ) @ SV844 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SY2821 ) @ SY2820 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6763]) ).
thf(7054,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6764]) ).
thf(7055,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6765]) ).
thf(7056,plain,
! [SV303: $i,SV613: $i,SV846: $i] :
( ( ! [SY2822: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2822 @ SV846 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6766]) ).
thf(7057,plain,
! [SV304: $i,SV614: $i,SV847: $i] :
( ( ( SV847 != SV614 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV304 @ tc_HOL_Obool ) ) @ SV847 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6767]) ).
thf(7058,plain,
! [SV305: $i,SV615: $i,SV848: $i] :
( ( ! [SY2823: $i,SY2824: $i,SY2825: $i] :
( ( SY2825 != SY2824 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2823 @ SV848 @ SV615 ) @ SV305 ) @ SY2825 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY2823 @ SV848 @ SV615 ) @ SV305 ) @ SY2824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6768]) ).
thf(7059,plain,
! [SV306: $i,SV616: $i,SV849: $i] :
( ( ~ ( class_Orderings_Obot @ SV849 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ SV849 ) ) @ SV306 )
= ( c_Orderings_Obot__class_Obot @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6769]) ).
thf(7060,plain,
! [SV307: $i,SV617: $i,SV850: $i] :
( ( ! [SY2826: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2826 @ SV850 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
| ~ ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SY2826 @ SV850 @ SV617 ) @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6770]) ).
thf(7061,plain,
! [SV308: $i,SV618: $i,SV851: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 )
= SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6771]) ).
thf(7062,plain,
! [SV309: $i,SV619: $i,SV852: $i] :
( ( ! [SY2829: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2829 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SV619 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6772]) ).
thf(7063,plain,
! [SV310: $i,SV620: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV620 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV310 @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6773]) ).
thf(7064,plain,
! [SV311: $i,SV621: $i,SV853: $i] :
( ( ! [SY2830: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2830 @ SV853 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SY2830 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SV853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6774]) ).
thf(7065,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SV622 = SV312 ) )
| ~ ( ( SV622 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6775]) ).
thf(7066,plain,
! [SV313: $i,SV623: $i,SV855: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) @ SV623 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
| ( SV623
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) )
| ( SV623
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6776]) ).
thf(7067,plain,
! [SV314: $i,SV624: $i,SV856: $i] :
( ( ! [SY2831: $i,SY2832: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2832 @ SY2831 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2832 @ SY2831 @ SV856 ) @ SV624 ) @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6777]) ).
thf(7068,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
| ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) )
| ~ ( ~ ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6778]) ).
thf(7069,plain,
! [SV316: $i,SV626: $i,SV858: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6779]) ).
thf(7070,plain,
! [SV317: $i,SV627: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV627 )
!= ( hAPP @ c_Nat_OSuc @ SV317 ) )
= $true )
| ( ( SV627 = SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6780]) ).
thf(7071,plain,
! [SV318: $i,SV628: $i,SV859: $i] :
( ( ! [SY2835: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2835 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2835 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2835 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2835 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6781]) ).
thf(7072,plain,
! [SV319: $i,SV629: $i,SV860: $i] :
( ( ! [SY2836: $i,SY2837: $i,SY2838: $i] :
~ ( ~ ( ( SY2838 != SY2837 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2836 @ SV860 @ SV629 @ SY2837 @ SV319 ) @ SY2838 )
= SV319 ) )
| ~ ( ~ ( ( SY2838 != SY2837 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY2836 @ SV860 @ SV629 @ SY2837 @ SV319 ) @ SY2838 )
= ( hAPP @ SV629 @ SY2838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6782]) ).
thf(7073,plain,
! [SV320: $i,SV630: $i,SV861: $i] :
( ( ! [SY2839: $i,SY2840: $i,SY2841: $i,SY2842: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2842 @ SY2841 @ SY2840 @ SY2839 @ SV861 @ SV630 )
| ( ( hAPP @ ( hAPP @ SY2840 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6783]) ).
thf(7074,plain,
! [SV321: $i,SV631: $i,SV862: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV631 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV321 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) ) )
| ( SV631 = SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6784]) ).
thf(7075,plain,
! [SV322: $i,SV632: $i,SV863: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2845 @ ( tc_fun @ SY2844 @ tc_HOL_Obool ) ) ) @ SY2843 ) @ SV863 ) @ SV632 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2843 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6785]) ).
thf(7076,plain,
! [SV4: $i,SV325: $i,SV633: $i,SV864: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV864 ) @ SV633 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV864 ) @ SV325 ) @ SV4 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV864 ) @ SV325 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV864 ) @ SV633 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6787]) ).
thf(7077,plain,
! [SV12: $i,SV332: $i,SV638: $i,SV865: $i] :
( ( ! [SY2846: $i] :
( ( hAPP @ ( c_Set_Oimage @ SY2846 @ SV865 @ SV638 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2846 ) @ SV332 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV865 ) @ ( hAPP @ SV638 @ SV332 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2846 @ SV865 @ SV638 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6793]) ).
thf(7078,plain,
! [SV22: $i,SV341: $i,SV642: $i,SV866: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV866 @ tc_HOL_Obool ) ) @ SV642 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV866 ) @ SV341 ) @ SV22 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV866 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV866 @ tc_HOL_Obool ) ) @ SV642 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV866 ) @ SV341 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV866 @ tc_HOL_Obool ) ) ) ) ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6798]) ).
thf(7079,plain,
! [SV23: $i,SV342: $i,SV643: $i,SV867: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV867 @ tc_HOL_Obool ) ) @ SV643 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV867 ) @ SV342 ) @ SV23 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV867 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV867 @ tc_HOL_Obool ) ) @ SV643 ) @ SV23 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV867 ) @ SV342 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV867 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6799]) ).
thf(7080,plain,
! [SV24: $i,SV343: $i,SV644: $i,SV868: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV868 @ SV644 @ SV343 @ SV24 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV868 @ tc_HOL_Obool ) ) @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6800]) ).
thf(7081,plain,
! [SV25: $i,SV344: $i,SV645: $i,SV869: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV869 @ SV645 @ SV344 @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV869 @ tc_HOL_Obool ) ) @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6801]) ).
thf(7082,plain,
! [SV27: $i,SV346: $i,SV646: $i,SV870: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SV870 @ SV646 @ SV346 @ SV27 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV870 @ tc_HOL_Obool ) ) ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6803]) ).
thf(7083,plain,
! [SV28: $i,SV347: $i,SV647: $i,SV871: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SV871 @ SV647 @ SV347 @ SV28 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV871 @ tc_HOL_Obool ) ) ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6804]) ).
thf(7084,plain,
! [SV31: $i,SV349: $i,SV649: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV649 @ SV349 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV649 @ tc_HOL_Obool ) ) ) @ SV31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6806]) ).
thf(7085,plain,
! [SV32: $i,SV350: $i,SV650: $i,SV872: $i] :
( ( ( c_Fun_Ofun__upd @ SV872 @ SV650 @ SV350 @ SV32 @ ( hAPP @ SV350 @ SV32 ) )
= SV350 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6807]) ).
thf(7086,plain,
! [SV33: $i,SV351: $i,SV651: $i,SV873: $i] :
( ( ! [SY2847: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2847 @ SV873 @ SV651 @ SV351 @ SV33 ) @ SV351 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6808]) ).
thf(7087,plain,
! [SV34: $i,SV352: $i,SV652: $i,SV874: $i] :
( ( ! [SY2848: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SY2848 @ SV874 @ SV652 ) @ SV352 ) @ SV34 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_HOL_Obool ) ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6809]) ).
thf(7088,plain,
! [SV38: $i,SV355: $i,SV654: $i,SV875: $i] :
( ( ! [SY2849: $i,SY2850: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2850 @ SY2849 @ SV875 @ SV654 ) @ SV355 ) @ SV38 )
= ( hAPP @ SV654 @ ( hAPP @ SV355 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6812]) ).
thf(7089,plain,
! [SV39: $i,SV356: $i,SV655: $i,SV876: $i] :
( ( ! [SY2851: $i,SY2852: $i,SY2853: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2853 @ SY2852 @ SY2851 @ SV876 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2853 @ SY2851 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2852 @ SY2851 @ ( hAPP @ ( c_Fun_Ocomp @ SY2853 @ SY2852 @ SV655 @ SV876 ) @ SV356 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6813]) ).
thf(7090,plain,
! [SV40: $i,SV357: $i,SV656: $i,SV877: $i] :
( ( ! [SY2854: $i,SY2855: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2855 @ SY2854 @ SV877 @ SV656 ) @ SV357 ) @ SV40 )
= ( hAPP @ SV656 @ ( hAPP @ SV357 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6814]) ).
thf(7091,plain,
! [SV41: $i,SV358: $i,SV657: $i,SV878: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ SV878 @ SV657 @ SV358 ) @ SV41 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV878 @ tc_HOL_Obool ) ) )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6815]) ).
thf(7092,plain,
! [SV43: $i,SV360: $i,SV658: $i,SV879: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV879 @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) ) @ SV360 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6816]) ).
thf(7093,plain,
! [SV44: $i,SV361: $i,SV659: $i,SV880: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV880 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV880 ) @ SV659 ) @ SV361 ) ) @ SV44 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV880 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV880 @ tc_HOL_Obool ) ) @ SV361 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6817]) ).
thf(7094,plain,
! [SV45: $i,SV362: $i,SV660: $i,SV881: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV881 @ tc_HOL_Obool ) ) @ SV660 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV881 ) @ SV362 ) @ SV45 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV881 ) @ SV362 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV881 @ tc_HOL_Obool ) ) @ SV660 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6818]) ).
thf(7095,plain,
! [SV46: $i,SV363: $i,SV661: $i,SV882: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV882 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV882 @ tc_HOL_Obool ) ) @ SV661 ) @ SV363 ) ) @ SV46 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV882 @ tc_HOL_Obool ) ) @ SV661 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV882 @ tc_HOL_Obool ) ) @ SV363 ) @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6819]) ).
thf(7096,plain,
! [SV47: $i,SV364: $i,SV662: $i,SV883: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV883 @ tc_HOL_Obool ) ) @ SV662 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV883 @ tc_HOL_Obool ) ) @ SV364 ) @ SV47 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV883 @ tc_HOL_Obool ) ) @ SV364 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV883 @ tc_HOL_Obool ) ) @ SV662 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6820]) ).
thf(7097,plain,
! [SV63: $i,SV379: $i,SV671: $i,SV884: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV884 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV884 @ tc_HOL_Obool ) ) @ SV671 ) @ SV379 ) ) @ SV63 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV884 @ tc_HOL_Obool ) ) @ SV671 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV884 @ tc_HOL_Obool ) ) @ SV379 ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6829]) ).
thf(7098,plain,
! [SV64: $i,SV380: $i,SV672: $i,SV885: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV885 @ tc_HOL_Obool ) ) @ SV672 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV885 @ tc_HOL_Obool ) ) @ SV380 ) @ SV64 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV885 @ tc_HOL_Obool ) ) @ SV380 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV885 @ tc_HOL_Obool ) ) @ SV672 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6830]) ).
thf(7099,plain,
! [SV68: $i,SV384: $i,SV675: $i,SV886: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV886 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV886 ) @ SV675 ) @ SV384 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV886 ) @ SV675 ) @ SV68 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV886 ) @ SV675 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV886 @ tc_HOL_Obool ) ) @ SV384 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6833]) ).
thf(7100,plain,
! [SV76: $i,SV391: $i,SV677: $i,SV887: $i] :
( ( ! [SY2856: $i,SY2857: $i,SY2858: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2858 @ SY2857 @ SY2856 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2858 @ SV887 @ SY2857 ) @ SV677 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2858 @ SV887 @ SY2856 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV887 @ SY2857 @ SY2856 ) @ SV391 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6835]) ).
thf(7101,plain,
! [SV78: $i,SV393: $i,SV679: $i,SV888: $i] :
( ( ( hAPP @ SV888 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV679 @ SV679 ) @ SV393 ) @ SV888 ) @ SV78 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV679 @ SV679 ) @ SV393 ) @ SV888 ) @ ( hAPP @ SV888 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6837]) ).
thf(7102,plain,
! [SV80: $i,SV395: $i,SV680: $i,SV889: $i] :
( ( ! [SY2859: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2859 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2859 @ SV889 ) @ SV680 ) @ SV395 ) ) @ SV680 ) @ SV80 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY2859 @ SV889 ) @ SV680 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6838]) ).
thf(7103,plain,
! [SV81: $i,SV396: $i,SV681: $i,SV890: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV890 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV890 ) @ SV681 ) @ SV396 ) ) @ SV81 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV890 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV890 ) @ SV396 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6839]) ).
thf(7104,plain,
! [SV84: $i,SV399: $i,SV682: $i,SV891: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV891 @ SV682 ) @ SV399 ) @ SV84 )
= SV399 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6840]) ).
thf(7105,plain,
! [SV85: $i,SV400: $i,SV683: $i,SV892: $i] :
( ( ! [SY2860: $i,SY2861: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2861 @ SY2860 @ SV892 ) @ SV683 ) @ SV400 ) @ SV85 )
= ( hAPP @ SV683 @ ( hAPP @ SV400 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6841]) ).
thf(7106,plain,
! [SV86: $i,SV401: $i,SV684: $i,SV893: $i] :
( ( ! [SY2862: $i,SY2863: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2863 @ SY2862 @ SV893 ) @ SV684 ) @ SV401 ) @ SV86 )
= ( hAPP @ ( hAPP @ SV684 @ SV86 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6842]) ).
thf(7107,plain,
! [SV87: $i,SV402: $i,SV685: $i,SV894: $i] :
( ( ! [SY2864: $i,SY2865: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2865 @ SY2864 @ SV894 ) @ SV685 ) @ SV402 ) @ SV87 )
= ( hAPP @ ( hAPP @ SV685 @ SV87 ) @ ( hAPP @ SV402 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6843]) ).
thf(7108,plain,
! [SV88: $i,SV403: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV403 ) @ SV88 ) )
= $false )
| ( ( SV403 = SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(7109,plain,
! [SV89: $i] :
( ( ( hBOOL @ SV89 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(7110,plain,
! [SV90: $i] :
( ( ( hBOOL @ SV90 )
= $true )
| ( ( hBOOL @ ( hAPP @ c_fNot @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[6846]) ).
thf(7111,plain,
! [SV91: $i,SV404: $i] :
( ( ( ~ ( hBOOL @ SV404 ) )
= $true )
| ( ( ~ ( hBOOL @ SV91 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV404 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6847]) ).
thf(7112,plain,
! [SV92: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV405 ) @ SV92 ) )
= $false )
| ( ( hBOOL @ SV405 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6848]) ).
thf(7113,plain,
! [SV93: $i,SV406: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV406 ) @ SV93 ) )
= $false )
| ( ( hBOOL @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6849]) ).
thf(7114,plain,
! [SV94: $i,SV407: $i] :
( ( ( hBOOL @ SV407 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV407 ) @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6850]) ).
thf(7115,plain,
! [SV95: $i,SV408: $i] :
( ( ( hBOOL @ SV408 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV95 ) @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(7116,plain,
! [SV96: $i,SV409: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV409 ) @ SV96 ) ) )
= $true )
| ( ( hBOOL @ SV409 )
= $true )
| ( ( hBOOL @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6852]) ).
thf(7117,plain,
! [SV98: $i,SV411: $i] :
( ( ( hBOOL @ SV411 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV98 ) @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6854]) ).
thf(7118,plain,
! [SV99: $i,SV412: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV412 ) @ SV99 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV412 ) )
= $true )
| ( ( hBOOL @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6855]) ).
thf(7119,plain,
! [SV100: $i,SV413: $i,SV686: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV686 @ SV413 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV413 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6856]) ).
thf(7120,plain,
! [SV101: $i,SV414: $i,SV687: $i,SV895: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV895 @ SV687 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV414 @ tc_HOL_Obool ) ) @ SV101 ) @ SV895 ) @ SV687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6857]) ).
thf(7121,plain,
! [SV102: $i,SV415: $i,SV688: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV688 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV415 @ SV688 ) ) @ SV102 )
= ( c_Orderings_Obot__class_Obot @ SV688 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6858]) ).
thf(7122,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) )
| ~ ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6859]) ).
thf(7123,plain,
! [SV104: $i,SV417: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
| ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6860]) ).
thf(7124,plain,
! [SV417: $i,SV104: $i] :
( ( ~ ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6860]) ).
thf(7125,plain,
! [SV105: $i,SV418: $i,SV690: $i,SV897: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6861]) ).
thf(7126,plain,
! [SV106: $i,SV419: $i,SV691: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV419 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6862]) ).
thf(7127,plain,
! [SV107: $i,SV420: $i,SV692: $i,SV898: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ SV420 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV898 ) @ SV107 ) @ SV420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6863]) ).
thf(7128,plain,
! [SV108: $i,SV421: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6864]) ).
thf(7129,plain,
! [SV421: $i,SV108: $i] :
( ( ~ ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6864]) ).
thf(7130,plain,
! [SV109: $i,SV422: $i,SV693: $i,SV899: $i] :
( ( ! [SY2866: $i,SY2867: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2867 @ SY2866 @ SV899 )
| ( ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6865]) ).
thf(7131,plain,
! [SV110: $i,SV423: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
| ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6866]) ).
thf(7132,plain,
! [SV423: $i,SV110: $i] :
( ( ~ ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6866]) ).
thf(7133,plain,
! [SV111: $i,SV424: $i] :
( ( ( SV424 = SV111 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV424 ) @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6867]) ).
thf(7134,plain,
! [SV112: $i,SV425: $i] :
( ( ( class_Orderings_Otop @ SV425 )
= $false )
| ( ( class_Orderings_Otop @ ( tc_fun @ SV112 @ SV425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6868]) ).
thf(7135,plain,
! [SV113: $i,SV426: $i,SV694: $i,SV900: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6869]) ).
thf(7136,plain,
! [SV114: $i,SV427: $i,SV695: $i,SV901: $i] :
( ( ! [SY2868: $i,SY2869: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2869 @ SY2868 ) @ SV901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SY2869 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SY2868 ) @ SV901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6870]) ).
thf(7137,plain,
! [SV116: $i,SV428: $i,SV696: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV428 ) @ SV116 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV696 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV116 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV428 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6871]) ).
thf(7138,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i] :
( ( ! [SY2870: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY2870 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) )
| ~ ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SY2870 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6872]) ).
thf(7139,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i] :
( ( ! [SY2871: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2871 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2871 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
| ~ ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2871 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY2871 ) @ SV430 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6873]) ).
thf(7140,plain,
! [SV119: $i,SV431: $i,SV699: $i] :
( ( ( ~ ( c_Wellfounded_OwfP @ SV699 @ SV431 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV699 @ ( tc_fun @ SV699 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) )
| ( c_Wellfounded_OwfP @ SV699 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6874]) ).
thf(7141,plain,
! [SV120: $i,SV432: $i,SV700: $i,SV904: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ SV432 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV904 ) @ SV120 ) @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6875]) ).
thf(7142,plain,
! [SV121: $i,SV433: $i,SV701: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV701 ) @ SV433 ) @ SV121 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV701 @ tc_HOL_Obool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6876]) ).
thf(7143,plain,
! [SV122: $i,SV434: $i,SV702: $i,SV905: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV905 @ tc_HOL_Obool ) ) @ SV702 ) @ SV434 ) @ SV122 ) )
| ( hBOOL @ ( hAPP @ SV434 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6877]) ).
thf(7144,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6878]) ).
thf(7145,plain,
! [SV124: $i,SV436: $i,SV704: $i,SV906: $i] :
( ( ! [SY2872: $i,SY2873: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2873 @ ( tc_fun @ SY2872 @ tc_HOL_Obool ) ) ) @ SV906 ) @ SV704 ) @ SV436 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6879]) ).
thf(7146,plain,
! [SV125: $i,SV437: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV437 ) @ SV125 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SV437 ) )
| ( SV437 = SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(7147,plain,
! [SV126: $i,SV438: $i,SV705: $i,SV907: $i] :
( ( ~ ( class_Orderings_Oorder @ SV907 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6881]) ).
thf(7148,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6882]) ).
thf(7149,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ( ~ ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) )
| ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
| ~ ( ~ ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) )
| ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6883]) ).
thf(7150,plain,
! [SV129: $i,SV441: $i,SV708: $i,SV908: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV908 @ SV708 @ SV441 )
| ( ( hAPP @ ( hAPP @ SV708 @ SV129 ) @ SV129 )
= SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6884]) ).
thf(7151,plain,
! [SV130: $i,SV442: $i,SV709: $i] :
( ( ( ~ ( c_Predicate_Oreflp @ SV709 @ SV442 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV442 @ SV130 ) @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6885]) ).
thf(7152,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i] :
( ( ! [SY2874: $i,SY2875: $i,SY2876: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2876 @ SY2875 @ SY2874 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2876 @ SY2875 @ SY2874 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6886]) ).
thf(7153,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i] :
( ( ! [SY2879: $i,SY2880: $i,SY2881: $i,SY2882: $i,SY2883: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2883 @ SY2882 @ SY2881 @ SY2880 ) @ SY2879 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SY2882 @ SY2881 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SY2880 @ ( hAPP @ SY2879 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6887]) ).
thf(7154,plain,
! [SV133: $i,SV445: $i,SV712: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV712 @ tc_HOL_Obool ) ) @ SV445 ) @ SV133 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV712 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV445 ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6888]) ).
thf(7155,plain,
! [SV134: $i,SV446: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
| ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6889]) ).
thf(7156,plain,
! [SV446: $i,SV134: $i] :
( ( ~ ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6889]) ).
thf(7157,plain,
! [SV135: $i,SV447: $i,SV713: $i,SV911: $i] :
( ( ! [SY2884: $i,SY2885: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2885 @ ( tc_fun @ SY2884 @ tc_HOL_Obool ) ) ) @ SV911 ) @ SV713 ) @ SV447 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV911 @ SV447 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6890]) ).
thf(7158,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6891]) ).
thf(7159,plain,
! [SV137: $i,SV449: $i,SV715: $i,SV912: $i] :
( ( ~ ( c_Predicate_Osymp @ SV912 @ SV715 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6892]) ).
thf(7160,plain,
! [SV138: $i,SV450: $i,SV716: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV716 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV450 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV138 ) @ SV450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6893]) ).
thf(7161,plain,
! [SV139: $i,SV451: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV451 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV139 @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6894]) ).
thf(7162,plain,
! [SV140: $i,SV452: $i,SV717: $i] :
( ( SV717
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV452 ) @ SV140 ) @ SV717 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6895]) ).
thf(7163,plain,
! [SV141: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ t_a @ tc_HOL_Obool ) ) @ SV453 ) @ SV141 ) )
= $false )
| ( ( v_P @ SV141 @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6896]) ).
thf(7164,plain,
! [SV142: $i,SV454: $i,SV718: $i,SV913: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2887 @ ( tc_fun @ SY2886 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6897]) ).
thf(7165,plain,
! [SV143: $i,SV455: $i,SV719: $i,SV914: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV914 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP @ SV719 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SV455 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6898]) ).
thf(7166,plain,
! [SV144: $i,SV456: $i,SV720: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV720 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV144 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6899]) ).
thf(7167,plain,
! [SV145: $i,SV457: $i,SV721: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV457 ) @ SV145 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV145 ) @ SV457 )
= SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6900]) ).
thf(7168,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i] :
( ( ! [SY2888: $i,SY2889: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2889 @ SY2888 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2889 @ SY2888 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
| ~ ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2889 @ SY2888 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2889 @ SY2888 ) @ SV458 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6901]) ).
thf(7169,plain,
! [SV147: $i,SV459: $i,SV723: $i,SV916: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV916 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV723 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6902]) ).
thf(7170,plain,
! [SV148: $i,SV460: $i,SV724: $i,SV917: $i] :
( ( ! [SY2890: $i] :
( ~ ( c_Equiv__Relations_Opart__equivp @ SY2890 @ SV917 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6903]) ).
thf(7171,plain,
! [SV149: $i,SV461: $i,SV725: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV725 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6904]) ).
thf(7172,plain,
! [SV150: $i,SV462: $i,SV726: $i,SV918: $i] :
( ( ! [SY2891: $i] :
( ( ( hAPP @ SY2891 @ SV918 )
!= SV726 )
| ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SY2891 @ SV918 @ SV726 )
= SY2891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6905]) ).
thf(7173,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6906]) ).
thf(7174,plain,
! [SV152: $i,SV464: $i,SV728: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV728 ) @ SV464 ) @ SV152 )
= SV152 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6907]) ).
thf(7175,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i] :
( ( ! [SY2892: $i,SY2893: $i,SY2894: $i,SY2895: $i,SY2896: $i,SY2897: $i,SY2898: $i] :
( ( ( hAPP @ SY2898 @ ( hAPP @ SY2897 @ SY2896 ) )
!= ( hAPP @ SY2895 @ ( hAPP @ SY2894 @ SY2893 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2892 @ SV919 @ SV729 @ SY2898 ) @ SY2897 ) @ SY2896 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SY2895 ) @ SY2894 ) @ SY2893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6908]) ).
thf(7176,plain,
! [SV154: $i,SV466: $i,SV730: $i,SV920: $i] :
( ( ! [SY2899: $i] :
( ~ ( c_Predicate_Otransp @ SY2899 @ SV920 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6909]) ).
thf(7177,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
| ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) )
| ~ ( ~ ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6910]) ).
thf(7178,plain,
! [SV156: $i,SV468: $i,SV732: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV732 ) @ SV468 ) @ SV156 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV732 ) @ SV468 ) @ SV156 )
= SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6911]) ).
thf(7179,plain,
! [SV157: $i,SV469: $i] :
( ( ( ~ ! [SY2236: $i] :
~ ( hBOOL @ ( hAPP @ SV469 @ SY2236 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6912]) ).
thf(7180,plain,
! [SV158: $i,SV470: $i,SV733: $i,SV921: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV921 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6913]) ).
thf(7181,plain,
! [SV159: $i,SV471: $i,SV734: $i,SV922: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV922 @ SV734 @ SV471 ) @ SV159 ) )
| ( SV471
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV922 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6914]) ).
thf(7182,plain,
! [SV160: $i,SV472: $i,SV735: $i,SV923: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6915]) ).
thf(7183,plain,
! [SV161: $i,SV473: $i] :
( ( ~ ( ~ ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) )
| ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6916]) ).
thf(7184,plain,
! [SV473: $i,SV161: $i] :
( ( ~ ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6916]) ).
thf(7185,plain,
! [SV162: $i,SV474: $i,SV736: $i,SV924: $i] :
( ( ( SV924 != SV736 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6917]) ).
thf(7186,plain,
! [SV163: $i,SV475: $i,SV737: $i,SV925: $i] :
( ( ! [SY2900: $i,SY2901: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2901 @ SY2900 @ SV925 @ SV737 @ SV475 )
| ( ( hAPP @ SV737 @ ( hAPP @ SV925 @ SV163 ) )
= SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6918]) ).
thf(7187,plain,
! [SV164: $i,SV476: $i,SV738: $i,SV926: $i] :
( ( ! [SY2902: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2902 @ tc_HOL_Obool ) ) @ SV926 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2902 @ SV164 ) @ SV926 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SY2902 @ SV164 ) @ SV738 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6919]) ).
thf(7188,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i] :
( ( ! [SY2903: $i,SY2904: $i,SY2905: $i,SY2906: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2906 @ SY2905 ) @ SY2904 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2903 @ SY2904 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SY2906 @ SY2903 ) @ SY2905 ) @ SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6920]) ).
thf(7189,plain,
! [SV166: $i,SV478: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV478 )
= $false )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV166 @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6921]) ).
thf(7190,plain,
! [SV167: $i,SV479: $i,SV740: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV740 @ SV479 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV740 @ ( c_Hilbert__Choice_OEps @ SV167 @ SV740 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6922]) ).
thf(7191,plain,
! [SV168: $i,SV480: $i,SV741: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV741 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6923]) ).
thf(7192,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
| ( SV481 = SV169 ) )
| ~ ( ( SV481 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6924]) ).
thf(7193,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ~ ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6925]) ).
thf(7194,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV744 ) )
= $true )
| ( ( ~ ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6926]) ).
thf(7195,plain,
! [SV172: $i,SV484: $i] :
( ( ( class_Lattices_Olattice @ SV484 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV172 @ SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6927]) ).
thf(7196,plain,
! [SV173: $i,SV485: $i] :
( ( ( ~ ( ~ ( class_Enum_Oenum @ SV485 )
| ~ ( class_Enum_Oenum @ SV173 ) ) )
= $false )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6928]) ).
thf(7197,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i] :
( ( ! [SY2907: $i,SY2908: $i,SY2909: $i] :
( ~ ( c_Typedef_Otype__definition @ SY2909 @ SY2908 @ SY2907 @ SV929 @ SV745 )
| ~ ( ~ ( ( ( hAPP @ SY2907 @ SV486 )
!= ( hAPP @ SY2907 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SY2907 @ SV486 )
= ( hAPP @ SY2907 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6929]) ).
thf(7198,plain,
! [SV175: $i,SV487: $i,SV746: $i,SV930: $i] :
( ( ! [SY2910: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2910 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2910 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2910 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2910 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SY2910 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6930]) ).
thf(7199,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
| ( SV747 = SV176 ) )
| ~ ( ( SV747 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6931]) ).
thf(7200,plain,
! [SV177: $i,SV489: $i,SV748: $i,SV932: $i] :
( ( ! [SY2911: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2911 @ SV932 ) @ SV748 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SY2911 ) @ SV748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6932]) ).
thf(7201,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
| ( SV490 = SV178 ) )
| ~ ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6933]) ).
thf(7202,plain,
! [SV179: $i,SV491: $i,SV750: $i,SV934: $i] :
( ( ! [SY2912: $i,SY2913: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2913 @ ( tc_fun @ SY2912 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6934]) ).
thf(7203,plain,
! [SV180: $i,SV492: $i,SV751: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV492 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV751 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6935]) ).
thf(7204,plain,
! [SV181: $i,SV493: $i,SV752: $i,SV935: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2915 @ SY2914 ) @ SV935 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SY2915 ) @ SV181 ) @ SY2914 ) @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6936]) ).
thf(7205,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i] :
( ( ! [SY2916: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2916 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2916 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY2917: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY2917 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2916 @ SV494 ) @ SY2917 ) ) ) )
| ~ ( ~ ~ ! [SY2918: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY2918 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2916 @ SV494 ) @ SY2918 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2916 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SY2916 @ SV494 ) @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6937]) ).
thf(7206,plain,
! [SV183: $i,SV495: $i,SV754: $i] :
( ( ( SV754 != SV495 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6938]) ).
thf(7207,plain,
! [SV184: $i,SV496: $i,SV755: $i,SV937: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6939]) ).
thf(7208,plain,
! [SV185: $i,SV497: $i,SV756: $i,SV938: $i] :
( ( ~ ( class_Orderings_Oord @ SV938 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
| ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6940]) ).
thf(7209,plain,
! [SV186: $i,SV498: $i,SV757: $i,SV939: $i] :
( ( ~ ( class_Orderings_Oorder @ SV939 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
| ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6941]) ).
thf(7210,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV940: $i] :
( ( ! [SY2919: $i] :
( ~ ( class_Orderings_Oord @ SY2919 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SY2919 ) ) @ SV758 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2919 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6942]) ).
thf(7211,plain,
! [SV188: $i,SV500: $i,SV759: $i,SV941: $i] :
( ( ! [SY2920: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2920 @ SV941 ) @ SV759 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SY2920 ) @ SV759 ) @ SV941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6943]) ).
thf(7212,plain,
! [SV189: $i,SV501: $i,SV760: $i,SV942: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6944]) ).
thf(7213,plain,
! [SV190: $i,SV502: $i,SV761: $i,SV943: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6945]) ).
thf(7214,plain,
! [SV191: $i,SV503: $i,SV762: $i,SV944: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV944 @ SV762 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6946]) ).
thf(7215,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) )
| ( SV763 = SV192 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6947]) ).
thf(7216,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6948]) ).
thf(7217,plain,
! [SV194: $i,SV506: $i] :
( ( ( class_Groups_Ouminus @ SV506 )
= $false )
| ( ( class_Groups_Ouminus @ ( tc_fun @ SV194 @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6949]) ).
thf(7218,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6950]) ).
thf(7219,plain,
! [SV196: $i,SV508: $i,SV766: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) ) @ SV508 ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV196 ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV508 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6951]) ).
thf(7220,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
!= SV197 )
| ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) ) )
| ~ ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6952]) ).
thf(7221,plain,
! [SV198: $i,SV510: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
| ( SV510 = SV198 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6953]) ).
thf(7222,plain,
! [SV198: $i,SV510: $i] :
( ( ~ ( ( SV510 != SV198 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6953]) ).
thf(7223,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i] :
( ( ! [SY2921: $i,SY2922: $i] :
( ~ ( ( SY2922 != SY2921 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SY2922 ) @ SV511 ) ) @ SY2921 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SY2921 ) @ SV199 ) ) @ SY2922 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6954]) ).
thf(7224,plain,
! [SV200: $i,SV512: $i,SV769: $i,SV949: $i] :
( ( ~ ( c_Fun_Obij__betw @ SV949 @ SV769 @ SV512 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV769 @ tc_HOL_Obool ) ) )
| ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV949 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6955]) ).
thf(7225,plain,
! [SV201: $i,SV513: $i,SV770: $i,SV950: $i] :
( ( ~ ( class_Orderings_Oord @ SV950 )
| ( SV770 != SV513 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6956]) ).
thf(7226,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
| ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ~ ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6957]) ).
thf(7227,plain,
! [SV203: $i,SV515: $i,SV772: $i] :
( ( ( SV772 != SV515 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SV515 ) @ SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6958]) ).
thf(7228,plain,
! [SV204: $i,SV516: $i,SV773: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV773 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV773 ) @ SV204 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV773 @ tc_HOL_Obool ) ) ) ) ) )
= $true )
| ( ( SV516 = SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6959]) ).
thf(7229,plain,
! [SV205: $i,SV517: $i,SV774: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ SV517 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV774 ) @ SV205 ) @ SV517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6960]) ).
thf(7230,plain,
! [SV206: $i,SV518: $i,SV775: $i,SV952: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV952 @ SV775 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV518 @ tc_HOL_Obool ) ) @ SV952 ) @ SV206 ) @ SV775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6961]) ).
thf(7231,plain,
! [SV207: $i,SV519: $i] :
( ( ( class_Groups_Ominus @ SV519 )
= $false )
| ( ( class_Groups_Ominus @ ( tc_fun @ SV207 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6962]) ).
thf(7232,plain,
! [SV208: $i,SV520: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV520 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV208 @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6963]) ).
thf(7233,plain,
! [SV209: $i,SV521: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV521 ) @ SV209 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SV521 ) )
| ( SV521 = SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6964]) ).
thf(7234,plain,
! [SV210: $i,SV522: $i] :
( ( ( ~ ! [SY2337: $i] :
~ ( hBOOL @ ( hAPP @ SV522 @ SY2337 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6965]) ).
thf(7235,plain,
! [SV211: $i,SV523: $i,SV776: $i,SV953: $i] :
( ( ! [SY2923: $i,SY2924: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2924 @ SY2923 ) @ SV953 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SY2924 ) @ SY2923 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6966]) ).
thf(7236,plain,
! [SV212: $i,SV524: $i,SV777: $i,SV954: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV954 @ SV777 ) )
| ~ ( hBOOL @ ( hAPP @ SV524 @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SV954 ) @ SV524 ) @ SV777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6967]) ).
thf(7237,plain,
! [SV213: $i,SV525: $i,SV778: $i,SV955: $i] :
( ( ! [SY2925: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2925 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2925 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2925 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2925 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2925 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6968]) ).
thf(7238,plain,
! [SV214: $i,SV526: $i] :
( ( ( class_Orderings_Opreorder @ SV526 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV214 @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6969]) ).
thf(7239,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
| ~ ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6970]) ).
thf(7240,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i] :
( ( ! [SY2928: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2928 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2928 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ~ ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2928 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY2928 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2928 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6971]) ).
thf(7241,plain,
! [SV217: $i,SV529: $i] :
( ( ( class_Orderings_Obot @ SV529 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV529 ) @ ( c_Orderings_Obot__class_Obot @ SV529 ) ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6972]) ).
thf(7242,plain,
! [SV218: $i,SV530: $i,SV781: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV781 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6973]) ).
thf(7243,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i] :
( ( ! [SY2929: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2929 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2929 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6974]) ).
thf(7244,plain,
! [SV220: $i,SV532: $i,SV783: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV532 ) @ SV220 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV783 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV532 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6975]) ).
thf(7245,plain,
! [SV221: $i,SV533: $i,SV784: $i,SV959: $i] :
( ( ! [SY2930: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY2930 @ SV959 @ SV784 )
| ( ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6976]) ).
thf(7246,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i] :
( ( ! [SY2931: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2931 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SY2931 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6977]) ).
thf(7247,plain,
! [SV223: $i,SV535: $i,SV786: $i,SV961: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV961 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV786 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6978]) ).
thf(7248,plain,
! [SV224: $i,SV536: $i,SV787: $i,SV962: $i] :
( ( ~ ( class_Orderings_Oorder @ SV962 )
| ( SV787 != SV536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6979]) ).
thf(7249,plain,
! [SV225: $i,SV537: $i,SV788: $i,SV963: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV963 @ tc_HOL_Obool ) ) @ SV788 ) @ SV537 ) @ SV225 ) )
| ( hBOOL @ ( hAPP @ SV788 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6980]) ).
thf(7250,plain,
! [SV226: $i,SV538: $i] :
( ( ( ~ ( ~ ( class_Finite__Set_Ofinite @ SV538 )
| ~ ( class_Finite__Set_Ofinite @ SV226 ) ) )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6981]) ).
thf(7251,plain,
! [SV227: $i,SV539: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
| ( SV539 = SV227 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6982]) ).
thf(7252,plain,
! [SV227: $i,SV539: $i] :
( ( ~ ( ( SV539 != SV227 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6982]) ).
thf(7253,plain,
! [SV228: $i,SV540: $i,SV789: $i,SV964: $i] :
( ( ( SV964 != SV789 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV964 ) @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6983]) ).
thf(7254,plain,
! [SV229: $i,SV790: $i,SV541: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV541 ) @ SV790 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV541 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ SV790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6984]) ).
thf(7255,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i] :
( ( ! [SY2932: $i,SY2933: $i] :
~ ( ~ ( ( SY2933 != SY2932 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SY2932 @ SV230 ) @ SY2933 )
= SV230 ) )
| ~ ( ~ ( ( SY2933 != SY2932 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SY2932 @ SV230 ) @ SY2933 )
= ( hAPP @ SV542 @ SY2933 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6985]) ).
thf(7256,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
| ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6986]) ).
thf(7257,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ~ ( ( SV793 != SV544 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
| ( SV793 = SV544 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6987]) ).
thf(7258,plain,
! [SV233: $i,SV545: $i,SV794: $i,SV966: $i] :
( ( ~ ( c_Fun_Obij__betw @ SV966 @ SV794 @ SV545 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV966 @ tc_HOL_Obool ) ) @ SV233 )
| ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6988]) ).
thf(7259,plain,
! [SV234: $i,SV546: $i,SV795: $i,SV967: $i] :
( ( ! [SY2934: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2934 @ tc_HOL_Obool ) ) @ SV967 ) @ SV795 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2934 @ SV546 @ SV234 ) @ SV967 ) ) @ ( hAPP @ ( c_Set_Oimage @ SY2934 @ SV546 @ SV234 ) @ SV795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6989]) ).
thf(7260,plain,
! [SV235: $i,SV547: $i,SV796: $i,SV968: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one @ SV968 @ SV796 @ SV547 )
| ( ( hAPP @ SV547 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV968 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV968 @ tc_HOL_Obool ) ) ) )
= SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6990]) ).
thf(7261,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6991]) ).
thf(7262,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6992]) ).
thf(7263,plain,
! [SV238: $i,SV550: $i,SV799: $i,SV970: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) )
| ~ ( ( SV799 != SV550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6993]) ).
thf(7264,plain,
! [SV239: $i,SV551: $i,SV800: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6994]) ).
thf(7265,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6995]) ).
thf(7266,plain,
! [SV241: $i,SV553: $i,SV802: $i,SV971: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6996]) ).
thf(7267,plain,
! [SV242: $i,SV554: $i,SV803: $i,SV972: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ SV803 ) @ SV554 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV803 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6997]) ).
thf(7268,plain,
! [SV243: $i,SV555: $i,SV804: $i,SV973: $i] :
( ( ! [SY2935: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2935 @ SV973 @ SV804 ) @ SV555 ) @ SV243 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV804 @ SV243 ) @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6998]) ).
thf(7269,plain,
! [SV244: $i,SV556: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
| ( SV556 = SV244 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6999]) ).
thf(7270,plain,
! [SV244: $i,SV556: $i] :
( ( ~ ( ( SV556 != SV244 )
| ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6999]) ).
thf(7271,plain,
! [SV245: $i,SV557: $i,SV805: $i,SV974: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV557 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV245 ) )
| ( SV557 = SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7000]) ).
thf(7272,plain,
! [SV246: $i,SV558: $i,SV806: $i] :
( ( ( SV806
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV558 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV558 ) @ SV246 ) @ SV806 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7001]) ).
thf(7273,plain,
! [SV247: $i,SV559: $i,SV807: $i,SV975: $i] :
( ( ~ ( class_Orderings_Oord @ SV975 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
| ~ ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7002]) ).
thf(7274,plain,
! [SV248: $i,SV560: $i,SV808: $i,SV976: $i] :
( ( ! [SY2938: $i,SY2939: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2939 @ SY2938 ) @ SV976 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SY2938 ) @ SV976 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SY2939 ) @ SY2938 ) @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7003]) ).
thf(7275,plain,
! [SV249: $i,SV561: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
| ( SV561 = SV249 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7004]) ).
thf(7276,plain,
! [SV249: $i,SV561: $i] :
( ( ~ ( ( SV561 != SV249 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7004]) ).
thf(7277,plain,
! [SV250: $i,SV562: $i,SV809: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 )
= SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7005]) ).
thf(7278,plain,
! [SV251: $i,SV563: $i] :
( ( ( class_Orderings_Obot @ SV563 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV251 @ SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7006]) ).
thf(7279,plain,
! [SV252: $i,SV564: $i,SV810: $i,SV977: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV977 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7007]) ).
thf(7280,plain,
! [SV253: $i,SV565: $i,SV811: $i,SV978: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2941 @ SY2940 ) @ SV978 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SY2940 ) @ SV978 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SY2941 ) @ SV811 ) @ SY2940 ) @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7008]) ).
thf(7281,plain,
! [SV254: $i,SV566: $i] :
( ( ~ ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
| ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7009]) ).
thf(7282,plain,
! [SV566: $i,SV254: $i] :
( ( ~ ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7009]) ).
thf(7283,plain,
! [SV255: $i,SV567: $i] :
( ( ( ! [SY2421: $i] :
( ( hAPP @ SV567 @ SY2421 )
= ( hAPP @ SV255 @ SY2421 ) ) )
= $false )
| ( ( SV567 = SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7010]) ).
thf(7284,plain,
! [SV256: $i,SV568: $i] :
( ( ! [SY2422: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SY2422 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SY2422 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7011]) ).
thf(7285,plain,
! [SV257: $i,SV569: $i,SV812: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) )
| ( SV569 = SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7012]) ).
thf(7286,plain,
! [SV258: $i,SV570: $i,SV813: $i,SV979: $i] :
( ( ! [SY2942: $i,SY2943: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SY2943 @ SY2942 @ SV979 @ SV813 @ SV570 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2942 @ tc_HOL_Obool ) ) )
= SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7013]) ).
thf(7287,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i] :
( ( ! [SY2944: $i,SY2945: $i,SY2946: $i,SY2947: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2947 @ SY2946 @ SY2945 @ SY2944 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SY2946 @ SY2945 @ SV571 ) @ SV259 ) )
| ! [SY2948: $i] :
( ( hAPP @ SY2944 @ ( hAPP @ SV980 @ SY2948 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY2948 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7014]) ).
thf(7288,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i] :
( ( ! [SY2949: $i,SY2950: $i] :
( ~ ( ( SY2950 != SY2949 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SY2949 @ SV260 ) @ SY2950 )
= ( hAPP @ SV572 @ SY2950 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7015]) ).
thf(7289,plain,
! [SV261: $i,SV573: $i,SV816: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV816 ) )
= $true )
| ( ( ( SV573 != SV261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV816 ) @ SV573 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7016]) ).
thf(7290,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
| ( SV574 = SV262 ) )
| ~ ( ( SV574 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7017]) ).
thf(7291,plain,
! [SV263: $i,SV575: $i,SV818: $i,SV982: $i] :
( ( ! [SY2951: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2951 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2951 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2951 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2951 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2951 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7018]) ).
thf(7292,plain,
! [SV264: $i,SV576: $i,SV819: $i,SV983: $i] :
( ( ! [SY2952: $i,SY2953: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2953 @ SY2952 ) @ SV983 ) @ SV819 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY2953 @ SY2952 ) @ SV576 ) @ SV264 ) )
| ~ ( ( SV983 != SV576 )
| ( SV819 != SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7019]) ).
thf(7293,plain,
! [SV265: $i,SV577: $i,SV820: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV577 ) @ SV265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV820 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV820 @ SV577 ) ) @ ( c_Predicate_OPowp @ SV820 @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7020]) ).
thf(7294,plain,
! [SV266: $i,SV578: $i] :
( ( ( class_Orderings_Opreorder @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV578 ) @ SV266 ) @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7021]) ).
thf(7295,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i] :
( ( ! [SY2954: $i,SY2955: $i,SY2956: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2956 @ SY2955 @ SY2954 @ SV984 ) @ SV821 )
!= SV579 )
| ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7022]) ).
thf(7296,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
| ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7023]) ).
thf(7297,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ( ~ ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) )
| ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7023]) ).
thf(7298,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7024]) ).
thf(7299,plain,
! [SV270: $i,SV582: $i,SV823: $i,SV985: $i] :
( ( ! [SY2957: $i] :
( ~ ( c_Equiv__Relations_Oequivp @ SY2957 @ SV985 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7025]) ).
thf(7300,plain,
! [SV271: $i,SV583: $i,SV824: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV824 @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV824 ) @ SV583 ) @ SV271 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7026]) ).
thf(7301,plain,
! [SV272: $i,SV584: $i,SV825: $i,SV986: $i] :
( ( ( SV986 != SV825 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7027]) ).
thf(7302,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
| ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ~ ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7028]) ).
thf(7303,plain,
! [SV274: $i,SV586: $i] :
( ( ( SV586 = SV274 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ SV586 ) @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7029]) ).
thf(7304,plain,
! [SV275: $i,SV587: $i,SV827: $i,SV988: $i] :
( ( ! [SY2958: $i,SY2959: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2959 ) @ SY2958 ) @ SV988 )
!= SV827 )
| ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2959 ) @ SV988 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2959 ) @ SY2958 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2959 ) @ SV827 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7030]) ).
thf(7305,plain,
! [SV276: $i,SV588: $i,SV828: $i,SV989: $i] :
( ( ( SV989 != SV828 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7031]) ).
thf(7306,plain,
! [SV277: $i,SV589: $i,SV829: $i,SV990: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV990 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV829 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7032]) ).
thf(7307,plain,
! [SV278: $i,SV590: $i,SV830: $i,SV991: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7033]) ).
thf(7308,plain,
! [SV279: $i,SV591: $i] :
( ( ( class_Orderings_Oorder @ SV591 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV279 @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7034]) ).
thf(7309,plain,
! [SV280: $i,SV592: $i,SV831: $i,SV992: $i] :
( ( ( SV992
!= ( c_Finite__Set_Ofold1 @ SV831 @ SV592 ) )
| ( ( hAPP @ SV992 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV831 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV831 @ tc_HOL_Obool ) ) ) )
= SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7035]) ).
thf(7310,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i] :
( ( ! [SY2960: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY2961: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV593 ) @ SY2961 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SY2961 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV993 ) @ SY2961 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SY2961 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY2962: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV593 ) @ SY2962 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SY2962 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV993 ) @ SY2962 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SY2962 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY2960 ) @ SV593 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7036]) ).
thf(7311,plain,
! [SV282: $i,SV594: $i,SV833: $i] :
( ( ( SV833
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) @ SV833 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7037]) ).
thf(7312,plain,
! [SV284: $i,SV596: $i,SV834: $i,SV994: $i] :
( ( ! [SY2963: $i] :
( ~ ( c_Fun_Oinj__on @ SY2963 @ SV994 @ SV834 @ SV596 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY2963 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SY2963 @ SV994 @ SV834 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7039]) ).
thf(7313,plain,
! [SV285: $i,SV597: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
| ( SV597 = SV285 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7040]) ).
thf(7314,plain,
! [SV285: $i,SV597: $i] :
( ( ~ ( ( SV597 != SV285 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7040]) ).
thf(7315,plain,
! [SV286: $i,SV598: $i,SV835: $i,SV995: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7041]) ).
thf(7316,plain,
! [SV287: $i,SV599: $i] :
( ( ~ ( ~ ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
| ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7042]) ).
thf(7317,plain,
! [SV599: $i,SV287: $i] :
( ( ~ ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7042]) ).
thf(7318,plain,
! [SV289: $i,SV600: $i] :
( ( ~ ( ~ ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) )
| ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7043]) ).
thf(7319,plain,
! [SV600: $i,SV289: $i] :
( ( ~ ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
| ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7043]) ).
thf(7320,plain,
! [SV291: $i,SV601: $i,SV836: $i] :
( ( ( ~ ~ ! [SY2814: $i] :
~ ( hBOOL @ ( hAPP @ SV836 @ SY2814 ) ) )
= $true )
| ( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7044]) ).
thf(7321,plain,
! [SV292: $i,SV602: $i,SV837: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV602 ) @ SV292 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV292 ) @ SV602 )
= SV602 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7045]) ).
thf(7322,plain,
! [SV293: $i,SV603: $i] :
( ( ( class_Orderings_Oord @ SV603 )
= $false )
| ( ( class_Orderings_Oord @ ( tc_fun @ SV293 @ SV603 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7046]) ).
thf(7323,plain,
! [SV294: $i,SV604: $i,SV838: $i,SV996: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV996 @ SV838 ) )
| ( hBOOL @ ( hAPP @ SV604 @ SV838 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7047]) ).
thf(7324,plain,
! [SV295: $i,SV605: $i,SV839: $i,SV997: $i] :
( ( ! [SY2964: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SY2964 @ SV997 @ SV839 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2964 @ tc_HOL_Obool ) ) ) @ SV295 ) )
| ( SV295 = SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7048]) ).
thf(7325,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV840 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7049]) ).
thf(7326,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV998: $i] :
( ( ! [SY2965: $i] :
( ~ ( class_Orderings_Oord @ SY2965 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SY2965 ) ) @ SV841 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SY2965 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7050]) ).
thf(7327,plain,
! [SV298: $i,SV608: $i,SV842: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) @ SV298 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV298 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7051]) ).
thf(7328,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7052]) ).
thf(7329,plain,
! [SV300: $i,SV610: $i,SV844: $i,SV999: $i] :
( ( ! [SY2966: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2966 @ SV999 ) @ SV844 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SY2966 ) @ SV999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7053]) ).
thf(7330,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7054]) ).
thf(7331,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7055]) ).
thf(7332,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7055]) ).
thf(7333,plain,
! [SV303: $i,SV613: $i,SV846: $i,SV1000: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV1000 @ SV846 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7056]) ).
thf(7334,plain,
! [SV304: $i,SV614: $i,SV847: $i] :
( ( ( SV847 != SV614 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV304 @ tc_HOL_Obool ) ) @ SV847 ) @ SV614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7057]) ).
thf(7335,plain,
! [SV305: $i,SV615: $i,SV848: $i,SV1001: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ( SY2968 != SY2967 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SY2968 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SY2967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7058]) ).
thf(7336,plain,
! [SV306: $i,SV616: $i,SV849: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV849 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ SV849 ) ) @ SV306 )
= ( c_Orderings_Obot__class_Obot @ SV849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7059]) ).
thf(7337,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
| ~ ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7060]) ).
thf(7338,plain,
! [SV308: $i,SV618: $i,SV851: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 )
= SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7061]) ).
thf(7339,plain,
! [SV309: $i,SV619: $i,SV852: $i,SV1003: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SV619 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7062]) ).
thf(7340,plain,
! [SV310: $i,SV620: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV620 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV310 @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7063]) ).
thf(7341,plain,
! [SV311: $i,SV621: $i,SV853: $i,SV1004: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV1004 @ SV853 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SV1004 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SV853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7064]) ).
thf(7342,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SV622 = SV312 ) )
| ~ ( ( SV622 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7065]) ).
thf(7343,plain,
! [SV313: $i,SV623: $i,SV855: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) @ SV623 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) ) )
= $true )
| ( ( ( SV623
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) )
| ( SV623
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7066]) ).
thf(7344,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i] :
( ( ! [SY2971: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2971 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SY2971 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7067]) ).
thf(7345,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
| ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) )
| ~ ( ~ ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7068]) ).
thf(7346,plain,
! [SV316: $i,SV626: $i,SV858: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV626 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7069]) ).
thf(7347,plain,
! [SV317: $i,SV627: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV627 )
= ( hAPP @ c_Nat_OSuc @ SV317 ) )
= $false )
| ( ( SV627 = SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7070]) ).
thf(7348,plain,
! [SV318: $i,SV628: $i,SV859: $i,SV1006: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7071]) ).
thf(7349,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i] :
( ( ! [SY2972: $i,SY2973: $i] :
~ ( ~ ( ( SY2973 != SY2972 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SY2972 @ SV319 ) @ SY2973 )
= SV319 ) )
| ~ ( ~ ( ( SY2973 != SY2972 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SY2972 @ SV319 ) @ SY2973 )
= ( hAPP @ SV629 @ SY2973 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7072]) ).
thf(7350,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i] :
( ( ! [SY2974: $i,SY2975: $i,SY2976: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY2976 @ SY2975 @ SY2974 @ SV1008 @ SV861 @ SV630 )
| ( ( hAPP @ ( hAPP @ SY2974 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7073]) ).
thf(7351,plain,
! [SV321: $i,SV631: $i,SV862: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV631 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV321 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) ) )
= $true )
| ( ( SV631 = SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7074]) ).
thf(7352,plain,
! [SV322: $i,SV632: $i,SV863: $i,SV1009: $i] :
( ( ! [SY2977: $i,SY2978: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY2978 @ ( tc_fun @ SY2977 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7075]) ).
thf(7353,plain,
! [SV12: $i,SV332: $i,SV638: $i,SV865: $i,SV1010: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ SV1010 @ SV865 @ SV638 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1010 ) @ SV332 ) @ SV12 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV865 ) @ ( hAPP @ SV638 @ SV332 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1010 @ SV865 @ SV638 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7077]) ).
thf(7354,plain,
! [SV33: $i,SV351: $i,SV651: $i,SV873: $i,SV1011: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1011 @ SV873 @ SV651 @ SV351 @ SV33 ) @ SV351 )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7086]) ).
thf(7355,plain,
! [SV34: $i,SV352: $i,SV652: $i,SV874: $i,SV1012: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ SV1012 @ SV874 @ SV652 ) @ SV352 ) @ SV34 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_HOL_Obool ) ) )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7087]) ).
thf(7356,plain,
! [SV38: $i,SV355: $i,SV654: $i,SV875: $i,SV1013: $i] :
( ( ! [SY2979: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2979 @ SV1013 @ SV875 @ SV654 ) @ SV355 ) @ SV38 )
= ( hAPP @ SV654 @ ( hAPP @ SV355 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7088]) ).
thf(7357,plain,
! [SV39: $i,SV356: $i,SV655: $i,SV876: $i,SV1014: $i] :
( ( ! [SY2980: $i,SY2981: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY2981 @ SY2980 @ SV1014 @ SV876 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2981 @ SV1014 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY2980 @ SV1014 @ ( hAPP @ ( c_Fun_Ocomp @ SY2981 @ SY2980 @ SV655 @ SV876 ) @ SV356 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7089]) ).
thf(7358,plain,
! [SV40: $i,SV357: $i,SV656: $i,SV877: $i,SV1015: $i] :
( ( ! [SY2982: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY2982 @ SV1015 @ SV877 @ SV656 ) @ SV357 ) @ SV40 )
= ( hAPP @ SV656 @ ( hAPP @ SV357 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7090]) ).
thf(7359,plain,
! [SV43: $i,SV360: $i,SV658: $i,SV879: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV879 @ ( tc_fun @ SV658 @ tc_HOL_Obool ) ) ) @ SV360 ) @ SV43 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7092]) ).
thf(7360,plain,
! [SV76: $i,SV391: $i,SV677: $i,SV887: $i,SV1016: $i] :
( ( ! [SY2983: $i,SY2984: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2984 @ SY2983 @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2984 @ SV887 @ SY2983 ) @ SV677 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY2984 @ SV887 @ SV1016 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV887 @ SY2983 @ SV1016 ) @ SV391 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7100]) ).
thf(7361,plain,
! [SV80: $i,SV395: $i,SV680: $i,SV889: $i,SV1017: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV1017 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV1017 @ SV889 ) @ SV680 ) @ SV395 ) ) @ SV680 ) @ SV80 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV1017 @ SV889 ) @ SV680 ) @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7102]) ).
thf(7362,plain,
! [SV85: $i,SV400: $i,SV683: $i,SV892: $i,SV1018: $i] :
( ( ! [SY2985: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY2985 @ SV1018 @ SV892 ) @ SV683 ) @ SV400 ) @ SV85 )
= ( hAPP @ SV683 @ ( hAPP @ SV400 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7105]) ).
thf(7363,plain,
! [SV86: $i,SV401: $i,SV684: $i,SV893: $i,SV1019: $i] :
( ( ! [SY2986: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY2986 @ SV1019 @ SV893 ) @ SV684 ) @ SV401 ) @ SV86 )
= ( hAPP @ ( hAPP @ SV684 @ SV86 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7106]) ).
thf(7364,plain,
! [SV87: $i,SV402: $i,SV685: $i,SV894: $i,SV1020: $i] :
( ( ! [SY2987: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY2987 @ SV1020 @ SV894 ) @ SV685 ) @ SV402 ) @ SV87 )
= ( hAPP @ ( hAPP @ SV685 @ SV87 ) @ ( hAPP @ SV402 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7107]) ).
thf(7365,plain,
! [SV91: $i,SV404: $i] :
( ( ( hBOOL @ SV404 )
= $false )
| ( ( ~ ( hBOOL @ SV91 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV404 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7111]) ).
thf(7366,plain,
! [SV96: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ SV409 ) @ SV96 ) )
= $false )
| ( ( hBOOL @ SV409 )
= $true )
| ( ( hBOOL @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7116]) ).
thf(7367,plain,
! [SV99: $i,SV412: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV412 ) @ SV99 ) )
= $false )
| ( ( ~ ( hBOOL @ SV412 ) )
= $true )
| ( ( hBOOL @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7118]) ).
thf(7368,plain,
! [SV100: $i,SV413: $i,SV686: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV686 @ SV413 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV413 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7119]) ).
thf(7369,plain,
! [SV101: $i,SV414: $i,SV687: $i,SV895: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV895 @ SV687 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV414 @ tc_HOL_Obool ) ) @ SV101 ) @ SV895 ) @ SV687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7120]) ).
thf(7370,plain,
! [SV102: $i,SV415: $i,SV688: $i] :
( ( ( class_Orderings_Obot @ SV688 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV415 @ SV688 ) ) @ SV102 )
= ( c_Orderings_Obot__class_Obot @ SV688 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7121]) ).
thf(7371,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) )
| ~ ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7122]) ).
thf(7372,plain,
! [SV104: $i,SV417: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
| ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7123]) ).
thf(7373,plain,
! [SV417: $i,SV104: $i] :
( ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7124]) ).
thf(7374,plain,
! [SV105: $i,SV418: $i,SV690: $i,SV897: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7125]) ).
thf(7375,plain,
! [SV106: $i,SV419: $i,SV691: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV419 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7126]) ).
thf(7376,plain,
! [SV107: $i,SV420: $i,SV692: $i,SV898: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ SV420 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV898 ) @ SV107 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7127]) ).
thf(7377,plain,
! [SV108: $i,SV421: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
| ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7128]) ).
thf(7378,plain,
! [SV421: $i,SV108: $i] :
( ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7129]) ).
thf(7379,plain,
! [SV109: $i,SV422: $i,SV693: $i,SV899: $i,SV1021: $i] :
( ( ! [SY2988: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY2988 @ SV1021 @ SV899 )
| ( ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7130]) ).
thf(7380,plain,
! [SV110: $i,SV423: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
| ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7131]) ).
thf(7381,plain,
! [SV423: $i,SV110: $i] :
( ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) )
| ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7132]) ).
thf(7382,plain,
! [SV113: $i,SV426: $i,SV694: $i,SV900: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7135]) ).
thf(7383,plain,
! [SV114: $i,SV427: $i,SV695: $i,SV901: $i,SV1022: $i] :
( ( ! [SY2989: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2989 @ SV1022 ) @ SV901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SY2989 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7136]) ).
thf(7384,plain,
! [SV116: $i,SV428: $i,SV696: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV428 ) @ SV116 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV696 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV116 ) ) @ ( c_Complete__Lattice_OInf__class_OInf @ ( tc_fun @ SV696 @ tc_HOL_Obool ) @ SV428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7137]) ).
thf(7385,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ~ ( ~ ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) )
| ~ ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7138]) ).
thf(7386,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
| ~ ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7139]) ).
thf(7387,plain,
! [SV119: $i,SV431: $i,SV699: $i] :
( ( ( c_Wellfounded_OwfP @ SV699 @ SV431 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV699 @ ( tc_fun @ SV699 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) )
| ( c_Wellfounded_OwfP @ SV699 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7140]) ).
thf(7388,plain,
! [SV120: $i,SV432: $i,SV700: $i,SV904: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ SV432 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV904 ) @ SV120 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7141]) ).
thf(7389,plain,
! [SV122: $i,SV434: $i,SV702: $i,SV905: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV905 @ tc_HOL_Obool ) ) @ SV702 ) @ SV434 ) @ SV122 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV434 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7143]) ).
thf(7390,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7144]) ).
thf(7391,plain,
! [SV703: $i,SV435: $i,SV123: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7144]) ).
thf(7392,plain,
! [SV124: $i,SV436: $i,SV704: $i,SV906: $i,SV1025: $i] :
( ( ! [SY2990: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2990 @ ( tc_fun @ SV1025 @ tc_HOL_Obool ) ) ) @ SV906 ) @ SV704 ) @ SV436 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7145]) ).
thf(7393,plain,
! [SV437: $i,SV125: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SV437 ) ) )
= $true )
| ( ( SV437 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV437 ) @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7146]) ).
thf(7394,plain,
! [SV126: $i,SV438: $i,SV705: $i,SV907: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV907 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7147]) ).
thf(7395,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7148]) ).
thf(7396,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7148]) ).
thf(7397,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ( ~ ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) )
| ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7149]) ).
thf(7398,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ( ~ ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) )
| ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7149]) ).
thf(7399,plain,
! [SV129: $i,SV441: $i,SV708: $i,SV908: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV908 @ SV708 @ SV441 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV708 @ SV129 ) @ SV129 )
= SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7150]) ).
thf(7400,plain,
! [SV130: $i,SV442: $i,SV709: $i] :
( ( ( c_Predicate_Oreflp @ SV709 @ SV442 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV442 @ SV130 ) @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7151]) ).
thf(7401,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i] :
( ( ! [SY2991: $i,SY2992: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2992 @ SY2991 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY2992 @ SY2991 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7152]) ).
thf(7402,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i] :
( ( ! [SY2995: $i,SY2996: $i,SY2997: $i,SY2998: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY2998 @ SY2997 @ SY2996 @ SY2995 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SY2997 @ SY2996 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SY2995 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7153]) ).
thf(7403,plain,
! [SV133: $i,SV445: $i,SV712: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV712 @ tc_HOL_Obool ) ) @ SV445 ) @ SV133 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV712 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV445 ) ) @ ( hAPP @ ( c_Set_OPow @ SV712 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7154]) ).
thf(7404,plain,
! [SV134: $i,SV446: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
| ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7155]) ).
thf(7405,plain,
! [SV446: $i,SV134: $i] :
( ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7156]) ).
thf(7406,plain,
! [SV135: $i,SV447: $i,SV713: $i,SV911: $i,SV1028: $i] :
( ( ! [SY2999: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY2999 @ ( tc_fun @ SV1028 @ tc_HOL_Obool ) ) ) @ SV911 ) @ SV713 ) @ SV447 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV911 @ SV447 ) @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7157]) ).
thf(7407,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7158]) ).
thf(7408,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7158]) ).
thf(7409,plain,
! [SV137: $i,SV449: $i,SV715: $i,SV912: $i] :
( ( ( ~ ( c_Predicate_Osymp @ SV912 @ SV715 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7159]) ).
thf(7410,plain,
! [SV138: $i,SV450: $i,SV716: $i] :
( ( ( class_Orderings_Olinorder @ SV716 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV450 ) @ SV138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV138 ) @ SV450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7160]) ).
thf(7411,plain,
! [SV142: $i,SV454: $i,SV718: $i,SV913: $i,SV1029: $i] :
( ( ! [SY3000: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SY3000 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7164]) ).
thf(7412,plain,
! [SV143: $i,SV455: $i,SV719: $i,SV914: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV914 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV719 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SV455 @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7165]) ).
thf(7413,plain,
! [SV144: $i,SV456: $i,SV720: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV720 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV144 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7166]) ).
thf(7414,plain,
! [SV145: $i,SV457: $i,SV721: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV457 ) @ SV145 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV721 @ tc_HOL_Obool ) ) @ SV145 ) @ SV457 )
= SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7167]) ).
thf(7415,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i] :
( ( ! [SY3001: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3001 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3001 @ SV1030 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
| ~ ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3001 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3001 @ SV1030 ) @ SV458 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7168]) ).
thf(7416,plain,
! [SV147: $i,SV459: $i,SV723: $i,SV916: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV916 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV723 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7169]) ).
thf(7417,plain,
! [SV148: $i,SV460: $i,SV724: $i,SV917: $i,SV1031: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7170]) ).
thf(7418,plain,
! [SV149: $i,SV461: $i,SV725: $i] :
( ( ( class_Orderings_Oorder @ SV725 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7171]) ).
thf(7419,plain,
! [SV150: $i,SV462: $i,SV726: $i,SV918: $i,SV1032: $i] :
( ( ( ( hAPP @ SV1032 @ SV918 )
!= SV726 )
| ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SV1032 @ SV918 @ SV726 )
= SV1032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7172]) ).
thf(7420,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7173]) ).
thf(7421,plain,
! [SV727: $i,SV151: $i,SV463: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7173]) ).
thf(7422,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i] :
( ( ! [SY3002: $i,SY3003: $i,SY3004: $i,SY3005: $i,SY3006: $i,SY3007: $i] :
( ( ( hAPP @ SY3007 @ ( hAPP @ SY3006 @ SY3005 ) )
!= ( hAPP @ SY3004 @ ( hAPP @ SY3003 @ SY3002 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3007 ) @ SY3006 ) @ SY3005 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SY3004 ) @ SY3003 ) @ SY3002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7175]) ).
thf(7423,plain,
! [SV154: $i,SV466: $i,SV730: $i,SV920: $i,SV1034: $i] :
( ( ~ ( c_Predicate_Otransp @ SV1034 @ SV920 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7176]) ).
thf(7424,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
| ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7177]) ).
thf(7425,plain,
! [SV731: $i,SV155: $i,SV467: $i] :
( ( ~ ( ~ ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7177]) ).
thf(7426,plain,
! [SV156: $i,SV468: $i,SV732: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV732 ) @ SV468 ) @ SV156 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV732 ) @ SV468 ) @ SV156 )
= SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7178]) ).
thf(7427,plain,
! [SV157: $i,SV469: $i] :
( ( ( ! [SY2236: $i] :
~ ( hBOOL @ ( hAPP @ SV469 @ SY2236 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7179]) ).
thf(7428,plain,
! [SV158: $i,SV470: $i,SV733: $i,SV921: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV921 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7180]) ).
thf(7429,plain,
! [SV159: $i,SV471: $i,SV734: $i,SV922: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV922 @ SV734 @ SV471 ) @ SV159 ) ) )
= $true )
| ( ( SV471
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV922 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7181]) ).
thf(7430,plain,
! [SV160: $i,SV472: $i,SV735: $i,SV923: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7182]) ).
thf(7431,plain,
! [SV161: $i,SV473: $i] :
( ( ~ ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) )
| ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7183]) ).
thf(7432,plain,
! [SV473: $i,SV161: $i] :
( ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) )
| ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7184]) ).
thf(7433,plain,
! [SV162: $i,SV474: $i,SV736: $i,SV924: $i] :
( ( ( SV924 != SV736 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7185]) ).
thf(7434,plain,
! [SV163: $i,SV475: $i,SV737: $i,SV925: $i,SV1035: $i] :
( ( ! [SY3008: $i] :
( ~ ( c_Typedef_Otype__definition @ SY3008 @ SV1035 @ SV925 @ SV737 @ SV475 )
| ( ( hAPP @ SV737 @ ( hAPP @ SV925 @ SV163 ) )
= SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7186]) ).
thf(7435,plain,
! [SV164: $i,SV476: $i,SV738: $i,SV926: $i,SV1036: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1036 @ tc_HOL_Obool ) ) @ SV926 ) @ SV738 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV926 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7187]) ).
thf(7436,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i] :
( ( ! [SY3009: $i,SY3010: $i,SY3011: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3011 @ SY3010 ) @ SY3009 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SY3009 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SY3011 @ SV1037 ) @ SY3010 ) @ SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7188]) ).
thf(7437,plain,
! [SV167: $i,SV479: $i,SV740: $i] :
( ( ( hBOOL @ ( hAPP @ SV740 @ SV479 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV740 @ ( c_Hilbert__Choice_OEps @ SV167 @ SV740 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7190]) ).
thf(7438,plain,
! [SV168: $i,SV480: $i,SV741: $i] :
( ( ( class_Orderings_Oorder @ SV741 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7191]) ).
thf(7439,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
| ( SV481 = SV169 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7192]) ).
thf(7440,plain,
! [SV742: $i,SV169: $i,SV481: $i] :
( ( ~ ( ( SV481 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7192]) ).
thf(7441,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7193]) ).
thf(7442,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( class_Orderings_Oorder @ SV744 )
= $false )
| ( ( ~ ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7194]) ).
thf(7443,plain,
! [SV173: $i,SV485: $i] :
( ( ( ~ ( class_Enum_Oenum @ SV485 )
| ~ ( class_Enum_Oenum @ SV173 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7196]) ).
thf(7444,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i,SV1038: $i] :
( ( ! [SY3012: $i,SY3013: $i] :
( ~ ( c_Typedef_Otype__definition @ SY3013 @ SY3012 @ SV1038 @ SV929 @ SV745 )
| ~ ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7197]) ).
thf(7445,plain,
! [SV175: $i,SV487: $i,SV746: $i,SV930: $i,SV1039: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7198]) ).
thf(7446,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
| ( SV747 = SV176 ) )
| ~ ( ( SV747 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7199]) ).
thf(7447,plain,
! [SV177: $i,SV489: $i,SV748: $i,SV932: $i,SV1040: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1040 @ SV932 ) @ SV748 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SV1040 ) @ SV748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7200]) ).
thf(7448,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
| ( SV490 = SV178 ) )
| ~ ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7201]) ).
thf(7449,plain,
! [SV179: $i,SV491: $i,SV750: $i,SV934: $i,SV1041: $i] :
( ( ! [SY3014: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SY3014 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7202]) ).
thf(7450,plain,
! [SV180: $i,SV492: $i,SV751: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV492 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV751 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7203]) ).
thf(7451,plain,
! [SV181: $i,SV493: $i,SV752: $i,SV935: $i,SV1042: $i] :
( ( ! [SY3015: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3015 @ SV1042 ) @ SV935 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SY3015 ) @ SV181 ) @ SV1042 ) @ SV935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7204]) ).
thf(7452,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
| ~ ( ~ ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7205]) ).
thf(7453,plain,
! [SV183: $i,SV495: $i,SV754: $i] :
( ( ( SV754 = SV495 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7206]) ).
thf(7454,plain,
! [SV184: $i,SV496: $i,SV755: $i,SV937: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7207]) ).
thf(7455,plain,
! [SV185: $i,SV497: $i,SV756: $i,SV938: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV938 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
| ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7208]) ).
thf(7456,plain,
! [SV186: $i,SV498: $i,SV757: $i,SV939: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV939 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
| ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7209]) ).
thf(7457,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV940: $i,SV1044: $i] :
( ( ~ ( class_Orderings_Oord @ SV1044 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SV1044 ) ) @ SV758 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1044 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7210]) ).
thf(7458,plain,
! [SV188: $i,SV500: $i,SV759: $i,SV941: $i,SV1045: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1045 @ SV941 ) @ SV759 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SV1045 ) @ SV759 ) @ SV941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7211]) ).
thf(7459,plain,
! [SV189: $i,SV501: $i,SV760: $i,SV942: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7212]) ).
thf(7460,plain,
! [SV190: $i,SV502: $i,SV761: $i,SV943: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7213]) ).
thf(7461,plain,
! [SV191: $i,SV503: $i,SV762: $i,SV944: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV944 @ SV762 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7214]) ).
thf(7462,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) )
| ( SV763 = SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7215]) ).
thf(7463,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7216]) ).
thf(7464,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7218]) ).
thf(7465,plain,
! [SV196: $i,SV508: $i,SV766: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) ) @ SV508 ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV766 @ tc_HOL_Obool ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV196 ) ) @ ( c_Wellfounded_Oaccp @ SV766 @ SV508 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7219]) ).
thf(7466,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
!= SV197 )
| ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7220]) ).
thf(7467,plain,
! [SV197: $i,SV767: $i,SV509: $i] :
( ( ~ ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7220]) ).
thf(7468,plain,
! [SV198: $i,SV510: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
| ( SV510 = SV198 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7221]) ).
thf(7469,plain,
! [SV198: $i,SV510: $i] :
( ( ( SV510 != SV198 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7222]) ).
thf(7470,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i,SV1046: $i] :
( ( ! [SY3018: $i] :
( ~ ( ( SY3018 != SV1046 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SY3018 ) @ SV511 ) ) @ SV1046 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1046 ) @ SV199 ) ) @ SY3018 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7223]) ).
thf(7471,plain,
! [SV200: $i,SV512: $i,SV769: $i,SV949: $i] :
( ( ( ~ ( c_Fun_Obij__betw @ SV949 @ SV769 @ SV512 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV769 @ tc_HOL_Obool ) ) ) )
= $true )
| ( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV949 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7224]) ).
thf(7472,plain,
! [SV201: $i,SV513: $i,SV770: $i,SV950: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV950 ) )
= $true )
| ( ( ( SV770 != SV513 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7225]) ).
thf(7473,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
| ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ~ ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7226]) ).
thf(7474,plain,
! [SV203: $i,SV515: $i,SV772: $i] :
( ( ( SV772 = SV515 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV203 @ tc_HOL_Obool ) ) @ SV515 ) @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7227]) ).
thf(7475,plain,
! [SV204: $i,SV516: $i,SV773: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV773 ) @ SV516 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV773 ) @ SV204 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV773 @ tc_HOL_Obool ) ) ) ) )
= $false )
| ( ( SV516 = SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7228]) ).
thf(7476,plain,
! [SV205: $i,SV517: $i,SV774: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ SV517 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV774 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV774 ) @ SV205 ) @ SV517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7229]) ).
thf(7477,plain,
! [SV206: $i,SV518: $i,SV775: $i,SV952: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV952 @ SV775 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV518 @ tc_HOL_Obool ) ) @ SV952 ) @ SV206 ) @ SV775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7230]) ).
thf(7478,plain,
! [SV521: $i,SV209: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SV521 ) ) )
= $true )
| ( ( SV521 = SV209 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV521 ) @ SV209 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7233]) ).
thf(7479,plain,
! [SV210: $i,SV522: $i] :
( ( ( ! [SY2337: $i] :
~ ( hBOOL @ ( hAPP @ SV522 @ SY2337 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7234]) ).
thf(7480,plain,
! [SV211: $i,SV523: $i,SV776: $i,SV953: $i,SV1047: $i] :
( ( ! [SY3019: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3019 @ SV1047 ) @ SV953 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SY3019 ) @ SV1047 ) @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7235]) ).
thf(7481,plain,
! [SV212: $i,SV524: $i,SV777: $i,SV954: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV954 @ SV777 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV524 @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SV954 ) @ SV524 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7236]) ).
thf(7482,plain,
! [SV213: $i,SV525: $i,SV778: $i,SV955: $i,SV1048: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7237]) ).
thf(7483,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
| ~ ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7239]) ).
thf(7484,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ~ ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7240]) ).
thf(7485,plain,
! [SV218: $i,SV530: $i,SV781: $i] :
( ( ( class_Orderings_Oorder @ SV781 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7242]) ).
thf(7486,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7243]) ).
thf(7487,plain,
! [SV220: $i,SV532: $i,SV783: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ SV532 ) @ SV220 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV783 @ tc_HOL_Obool ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV532 ) ) @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ SV783 @ tc_HOL_Obool ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7244]) ).
thf(7488,plain,
! [SV221: $i,SV533: $i,SV784: $i,SV959: $i,SV1051: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV1051 @ SV959 @ SV784 )
| ( ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7245]) ).
thf(7489,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7246]) ).
thf(7490,plain,
! [SV223: $i,SV535: $i,SV786: $i,SV961: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV961 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV786 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV535 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7247]) ).
thf(7491,plain,
! [SV224: $i,SV536: $i,SV787: $i,SV962: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV962 ) )
= $true )
| ( ( ( SV787 != SV536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7248]) ).
thf(7492,plain,
! [SV225: $i,SV537: $i,SV788: $i,SV963: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV963 @ tc_HOL_Obool ) ) @ SV788 ) @ SV537 ) @ SV225 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV788 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7249]) ).
thf(7493,plain,
! [SV226: $i,SV538: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV538 )
| ~ ( class_Finite__Set_Ofinite @ SV226 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7250]) ).
thf(7494,plain,
! [SV227: $i,SV539: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
| ( SV539 = SV227 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7251]) ).
thf(7495,plain,
! [SV227: $i,SV539: $i] :
( ( ( SV539 != SV227 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7252]) ).
thf(7496,plain,
! [SV228: $i,SV540: $i,SV789: $i,SV964: $i] :
( ( ( SV964 != SV789 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV964 ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7253]) ).
thf(7497,plain,
! [SV229: $i,SV790: $i,SV541: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV541 ) @ SV790 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV541 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV229 @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7254]) ).
thf(7498,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i] :
( ( ! [SY3020: $i] :
~ ( ~ ( ( SY3020 != SV1053 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SY3020 )
= SV230 ) )
| ~ ( ~ ( ( SY3020 != SV1053 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SY3020 )
= ( hAPP @ SV542 @ SY3020 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7255]) ).
thf(7499,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
| ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7256]) ).
thf(7500,plain,
! [SV231: $i,SV792: $i,SV543: $i] :
( ( ~ ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7256]) ).
thf(7501,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ~ ( ( SV793 != SV544 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7257]) ).
thf(7502,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
| ( SV793 = SV544 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7257]) ).
thf(7503,plain,
! [SV233: $i,SV545: $i,SV794: $i,SV966: $i] :
( ( ( ~ ( c_Fun_Obij__betw @ SV966 @ SV794 @ SV545 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV966 @ tc_HOL_Obool ) ) @ SV233 ) )
= $true )
| ( ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7258]) ).
thf(7504,plain,
! [SV234: $i,SV546: $i,SV795: $i,SV967: $i,SV1054: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1054 @ tc_HOL_Obool ) ) @ SV967 ) @ SV795 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV967 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7259]) ).
thf(7505,plain,
! [SV235: $i,SV547: $i,SV796: $i,SV968: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one @ SV968 @ SV796 @ SV547 ) )
= $true )
| ( ( ( hAPP @ SV547 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV968 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV968 @ tc_HOL_Obool ) ) ) )
= SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7260]) ).
thf(7506,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) ) )
| ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7261]) ).
thf(7507,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7262]) ).
thf(7508,plain,
! [SV237: $i,SV798: $i,SV549: $i] :
( ( ~ ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7262]) ).
thf(7509,plain,
! [SV238: $i,SV550: $i,SV799: $i,SV970: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) ) )
= $true )
| ( ( ~ ( ( SV799 != SV550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7263]) ).
thf(7510,plain,
! [SV239: $i,SV551: $i,SV800: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV800 @ tc_HOL_Obool ) ) @ SV551 ) @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7264]) ).
thf(7511,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7265]) ).
thf(7512,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ~ ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7265]) ).
thf(7513,plain,
! [SV241: $i,SV553: $i,SV802: $i,SV971: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV553 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7266]) ).
thf(7514,plain,
! [SV242: $i,SV554: $i,SV803: $i,SV972: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ SV803 ) @ SV554 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV803 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV554 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7267]) ).
thf(7515,plain,
! [SV243: $i,SV555: $i,SV804: $i,SV973: $i,SV1055: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1055 @ SV973 @ SV804 ) @ SV555 ) @ SV243 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV804 @ SV243 ) @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7268]) ).
thf(7516,plain,
! [SV244: $i,SV556: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
| ( SV556 = SV244 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7269]) ).
thf(7517,plain,
! [SV244: $i,SV556: $i] :
( ( ( SV556 != SV244 )
| ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7270]) ).
thf(7518,plain,
! [SV245: $i,SV557: $i,SV805: $i,SV974: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV557 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV245 ) )
| ( SV557 = SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7271]) ).
thf(7519,plain,
! [SV246: $i,SV558: $i,SV806: $i] :
( ( ( SV806
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV558 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV558 ) @ SV246 ) @ SV806 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7272]) ).
thf(7520,plain,
! [SV247: $i,SV559: $i,SV807: $i,SV975: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV975 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
| ~ ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7273]) ).
thf(7521,plain,
! [SV248: $i,SV560: $i,SV808: $i,SV976: $i,SV1056: $i] :
( ( ! [SY3021: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3021 @ SV1056 ) @ SV976 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SV1056 ) @ SV976 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SY3021 ) @ SV1056 ) @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7274]) ).
thf(7522,plain,
! [SV249: $i,SV561: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
| ( SV561 = SV249 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7275]) ).
thf(7523,plain,
! [SV249: $i,SV561: $i] :
( ( ( SV561 != SV249 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7276]) ).
thf(7524,plain,
! [SV250: $i,SV562: $i,SV809: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV809 @ tc_HOL_Obool ) ) @ SV562 ) @ SV250 )
= SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7277]) ).
thf(7525,plain,
! [SV252: $i,SV564: $i,SV810: $i,SV977: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV564 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV977 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7279]) ).
thf(7526,plain,
! [SV253: $i,SV565: $i,SV811: $i,SV978: $i,SV1057: $i] :
( ( ! [SY3022: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3022 @ SV1057 ) @ SV978 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SY3022 ) @ SV811 ) @ SV1057 ) @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7280]) ).
thf(7527,plain,
! [SV254: $i,SV566: $i] :
( ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
| ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7281]) ).
thf(7528,plain,
! [SV566: $i,SV254: $i] :
( ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) )
| ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7282]) ).
thf(7529,plain,
! [SV255: $i,SV567: $i] :
( ( ( ( hAPP @ SV567 @ ( sK1_SY2421 @ SV255 @ SV567 ) )
= ( hAPP @ SV255 @ ( sK1_SY2421 @ SV255 @ SV567 ) ) )
= $false )
| ( ( SV567 = SV255 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7283]) ).
thf(7530,plain,
! [SV256: $i,SV1058: $i,SV568: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7284]) ).
thf(7531,plain,
! [SV257: $i,SV569: $i,SV812: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) )
| ( SV569 = SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7285]) ).
thf(7532,plain,
! [SV258: $i,SV570: $i,SV813: $i,SV979: $i,SV1059: $i] :
( ( ! [SY3023: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple @ SY3023 @ SV1059 @ SV979 @ SV813 @ SV570 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1059 @ tc_HOL_Obool ) ) )
= SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7286]) ).
thf(7533,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i] :
( ( ! [SY3024: $i,SY3025: $i,SY3026: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3026 @ SY3025 @ SY3024 @ SV1060 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SY3025 @ SY3024 @ SV571 ) @ SV259 ) )
| ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7287]) ).
thf(7534,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i,SV1061: $i] :
( ( ! [SY3028: $i] :
( ~ ( ( SY3028 != SV1061 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SV1061 @ SV260 ) @ SY3028 )
= ( hAPP @ SV572 @ SY3028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7288]) ).
thf(7535,plain,
! [SV261: $i,SV573: $i,SV816: $i] :
( ( ( class_Orderings_Opreorder @ SV816 )
= $false )
| ( ( ( SV573 != SV261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV816 ) @ SV573 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7289]) ).
thf(7536,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
| ( SV574 = SV262 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7290]) ).
thf(7537,plain,
! [SV817: $i,SV262: $i,SV574: $i] :
( ( ~ ( ( SV574 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7290]) ).
thf(7538,plain,
! [SV263: $i,SV575: $i,SV818: $i,SV982: $i,SV1062: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7291]) ).
thf(7539,plain,
! [SV264: $i,SV576: $i,SV819: $i,SV983: $i,SV1063: $i] :
( ( ! [SY3029: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3029 @ SV1063 ) @ SV983 ) @ SV819 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY3029 @ SV1063 ) @ SV576 ) @ SV264 ) )
| ~ ( ( SV983 != SV576 )
| ( SV819 != SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7292]) ).
thf(7540,plain,
! [SV265: $i,SV577: $i,SV820: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV820 @ tc_HOL_Obool ) ) @ SV577 ) @ SV265 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ SV820 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( c_Predicate_OPowp @ SV820 @ SV577 ) ) @ ( c_Predicate_OPowp @ SV820 @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7293]) ).
thf(7541,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i,SV1064: $i] :
( ( ! [SY3030: $i,SY3031: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3031 @ SY3030 @ SV1064 @ SV984 ) @ SV821 )
!= SV579 )
| ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7295]) ).
thf(7542,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
| ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7296]) ).
thf(7543,plain,
! [SV268: $i,SV580: $i] :
( ( ~ ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) )
| ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7297]) ).
thf(7544,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7298]) ).
thf(7545,plain,
! [SV581: $i,SV269: $i,SV822: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7298]) ).
thf(7546,plain,
! [SV270: $i,SV582: $i,SV823: $i,SV985: $i,SV1065: $i] :
( ( ~ ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7299]) ).
thf(7547,plain,
! [SV272: $i,SV584: $i,SV825: $i,SV986: $i] :
( ( ( SV986 != SV825 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7301]) ).
thf(7548,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
| ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ~ ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7302]) ).
thf(7549,plain,
! [SV275: $i,SV587: $i,SV827: $i,SV988: $i,SV1066: $i] :
( ( ! [SY3032: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY3032 ) @ SV1066 ) @ SV988 )
!= SV827 )
| ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY3032 ) @ SV988 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY3032 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY3032 ) @ SV827 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7304]) ).
thf(7550,plain,
! [SV276: $i,SV588: $i,SV828: $i,SV989: $i] :
( ( ( SV989 != SV828 )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7305]) ).
thf(7551,plain,
! [SV277: $i,SV589: $i,SV829: $i,SV990: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV990 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV829 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7306]) ).
thf(7552,plain,
! [SV278: $i,SV590: $i,SV830: $i,SV991: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7307]) ).
thf(7553,plain,
! [SV280: $i,SV592: $i,SV831: $i,SV992: $i] :
( ( ( SV992
!= ( c_Finite__Set_Ofold1 @ SV831 @ SV592 ) )
= $true )
| ( ( ( hAPP @ SV992 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV831 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV831 @ tc_HOL_Obool ) ) ) )
= SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7309]) ).
thf(7554,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7310]) ).
thf(7555,plain,
! [SV282: $i,SV594: $i,SV833: $i] :
( ( ( SV833
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ SV594 @ SV594 ) @ tc_HOL_Obool ) ) @ SV833 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7311]) ).
thf(7556,plain,
! [SV284: $i,SV596: $i,SV834: $i,SV994: $i,SV1068: $i] :
( ( ~ ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV596 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1068 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7312]) ).
thf(7557,plain,
! [SV285: $i,SV597: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
| ( SV597 = SV285 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7313]) ).
thf(7558,plain,
! [SV285: $i,SV597: $i] :
( ( ( SV597 != SV285 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7314]) ).
thf(7559,plain,
! [SV286: $i,SV598: $i,SV835: $i,SV995: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7315]) ).
thf(7560,plain,
! [SV287: $i,SV599: $i] :
( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
| ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7316]) ).
thf(7561,plain,
! [SV599: $i,SV287: $i] :
( ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
| ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7317]) ).
thf(7562,plain,
! [SV289: $i,SV600: $i] :
( ( ~ ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) )
| ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7318]) ).
thf(7563,plain,
! [SV600: $i,SV289: $i] :
( ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
| ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7319]) ).
thf(7564,plain,
! [SV291: $i,SV601: $i,SV836: $i] :
( ( ( ~ ! [SY2814: $i] :
~ ( hBOOL @ ( hAPP @ SV836 @ SY2814 ) ) )
= $false )
| ( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7320]) ).
thf(7565,plain,
! [SV292: $i,SV602: $i,SV837: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV602 ) @ SV292 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV837 @ tc_HOL_Obool ) ) @ SV292 ) @ SV602 )
= SV602 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7321]) ).
thf(7566,plain,
! [SV294: $i,SV604: $i,SV838: $i,SV996: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ SV996 @ SV838 ) )
| ( hBOOL @ ( hAPP @ SV604 @ SV838 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7323]) ).
thf(7567,plain,
! [SV295: $i,SV605: $i,SV839: $i,SV997: $i,SV1069: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SV1069 @ SV997 @ SV839 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1069 @ tc_HOL_Obool ) ) ) @ SV295 ) )
| ( SV295 = SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7324]) ).
thf(7568,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ( class_Orderings_Olinorder @ SV840 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7325]) ).
thf(7569,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV998: $i,SV1070: $i] :
( ( ~ ( class_Orderings_Oord @ SV1070 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SV1070 ) ) @ SV841 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1070 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7326]) ).
thf(7570,plain,
! [SV298: $i,SV608: $i,SV842: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) @ SV298 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV298 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV842 @ tc_HOL_Obool ) ) @ SV608 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7327]) ).
thf(7571,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7328]) ).
thf(7572,plain,
! [SV609: $i,SV299: $i,SV843: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7328]) ).
thf(7573,plain,
! [SV300: $i,SV610: $i,SV844: $i,SV999: $i,SV1071: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1071 @ SV999 ) @ SV844 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SV1071 ) @ SV999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7329]) ).
thf(7574,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7330]) ).
thf(7575,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7330]) ).
thf(7576,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7331]) ).
thf(7577,plain,
! [SV302: $i,SV612: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7332]) ).
thf(7578,plain,
! [SV303: $i,SV613: $i,SV846: $i,SV1000: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV1000 @ SV846 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7333]) ).
thf(7579,plain,
! [SV304: $i,SV614: $i,SV847: $i] :
( ( ( SV847 = SV614 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV304 @ tc_HOL_Obool ) ) @ SV847 ) @ SV614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7334]) ).
thf(7580,plain,
! [SV305: $i,SV615: $i,SV848: $i,SV1001: $i,SV1072: $i] :
( ( ! [SY3035: $i] :
( ( SY3035 != SV1072 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SY3035 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7335]) ).
thf(7581,plain,
! [SV306: $i,SV616: $i,SV849: $i] :
( ( ( class_Orderings_Obot @ SV849 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ SV849 ) ) @ SV306 )
= ( c_Orderings_Obot__class_Obot @ SV849 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7336]) ).
thf(7582,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
| ~ ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7337]) ).
thf(7583,plain,
! [SV308: $i,SV618: $i,SV851: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV851 @ tc_HOL_Obool ) ) @ SV618 ) @ SV308 )
= SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7338]) ).
thf(7584,plain,
! [SV309: $i,SV619: $i,SV852: $i,SV1003: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SV619 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7339]) ).
thf(7585,plain,
! [SV311: $i,SV621: $i,SV853: $i,SV1004: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1004 @ SV853 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SV1004 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SV853 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7341]) ).
thf(7586,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ~ ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SV622 = SV312 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7342]) ).
thf(7587,plain,
! [SV854: $i,SV312: $i,SV622: $i] :
( ( ~ ( ( SV622 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7342]) ).
thf(7588,plain,
! [SV313: $i,SV623: $i,SV855: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) @ SV623 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
= $false )
| ( ( ( SV623
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) )
| ( SV623
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7343]) ).
thf(7589,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7344]) ).
thf(7590,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
| ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7345]) ).
thf(7591,plain,
! [SV857: $i,SV315: $i,SV625: $i] :
( ( ~ ( ~ ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7345]) ).
thf(7592,plain,
! [SV316: $i,SV626: $i,SV858: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV626 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7346]) ).
thf(7593,plain,
! [SV318: $i,SV628: $i,SV859: $i,SV1006: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7348]) ).
thf(7594,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i] :
( ( ! [SY3036: $i] :
~ ( ~ ( ( SY3036 != SV1074 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SY3036 )
= SV319 ) )
| ~ ( ~ ( ( SY3036 != SV1074 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SY3036 )
= ( hAPP @ SV629 @ SY3036 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7349]) ).
thf(7595,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i,SV1075: $i] :
( ( ! [SY3037: $i,SY3038: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY3038 @ SY3037 @ SV1075 @ SV1008 @ SV861 @ SV630 )
| ( ( hAPP @ ( hAPP @ SV1075 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7350]) ).
thf(7596,plain,
! [SV321: $i,SV631: $i,SV862: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV631 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV862 ) @ SV321 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV862 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( SV631 = SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7351]) ).
thf(7597,plain,
! [SV322: $i,SV632: $i,SV863: $i,SV1009: $i,SV1076: $i] :
( ( ! [SY3039: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SY3039 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7352]) ).
thf(7598,plain,
! [SV38: $i,SV355: $i,SV654: $i,SV875: $i,SV1013: $i,SV1077: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1077 @ SV1013 @ SV875 @ SV654 ) @ SV355 ) @ SV38 )
= ( hAPP @ SV654 @ ( hAPP @ SV355 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7356]) ).
thf(7599,plain,
! [SV39: $i,SV356: $i,SV655: $i,SV876: $i,SV1014: $i,SV1078: $i] :
( ( ! [SY3040: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY3040 @ SV1078 @ SV1014 @ SV876 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SY3040 @ SV1014 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SV1078 @ SV1014 @ ( hAPP @ ( c_Fun_Ocomp @ SY3040 @ SV1078 @ SV655 @ SV876 ) @ SV356 ) ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7357]) ).
thf(7600,plain,
! [SV40: $i,SV357: $i,SV656: $i,SV877: $i,SV1015: $i,SV1079: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1079 @ SV1015 @ SV877 @ SV656 ) @ SV357 ) @ SV40 )
= ( hAPP @ SV656 @ ( hAPP @ SV357 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7358]) ).
thf(7601,plain,
! [SV76: $i,SV391: $i,SV677: $i,SV887: $i,SV1016: $i,SV1080: $i] :
( ( ! [SY3041: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY3041 @ SV1080 @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY3041 @ SV887 @ SV1080 ) @ SV677 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY3041 @ SV887 @ SV1016 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV887 @ SV1080 @ SV1016 ) @ SV391 ) @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7360]) ).
thf(7602,plain,
! [SV85: $i,SV400: $i,SV683: $i,SV892: $i,SV1018: $i,SV1081: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV1081 @ SV1018 @ SV892 ) @ SV683 ) @ SV400 ) @ SV85 )
= ( hAPP @ SV683 @ ( hAPP @ SV400 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7362]) ).
thf(7603,plain,
! [SV86: $i,SV401: $i,SV684: $i,SV893: $i,SV1019: $i,SV1082: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV1082 @ SV1019 @ SV893 ) @ SV684 ) @ SV401 ) @ SV86 )
= ( hAPP @ ( hAPP @ SV684 @ SV86 ) @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7363]) ).
thf(7604,plain,
! [SV87: $i,SV402: $i,SV685: $i,SV894: $i,SV1020: $i,SV1083: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV1083 @ SV1020 @ SV894 ) @ SV685 ) @ SV402 ) @ SV87 )
= ( hAPP @ ( hAPP @ SV685 @ SV87 ) @ ( hAPP @ SV402 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7364]) ).
thf(7605,plain,
! [SV404: $i,SV91: $i] :
( ( ( hBOOL @ SV91 )
= $false )
| ( ( hBOOL @ SV404 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ SV404 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7365]) ).
thf(7606,plain,
! [SV99: $i,SV412: $i] :
( ( ( hBOOL @ SV412 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ SV412 ) @ SV99 ) )
= $false )
| ( ( hBOOL @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7367]) ).
thf(7607,plain,
! [SV101: $i,SV414: $i,SV687: $i,SV895: $i] :
( ( ( hBOOL @ ( hAPP @ SV895 @ SV687 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV414 @ tc_HOL_Obool ) ) @ SV101 ) @ SV895 ) @ SV687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7369]) ).
thf(7608,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7371]) ).
thf(7609,plain,
! [SV689: $i,SV896: $i,SV103: $i,SV416: $i] :
( ( ~ ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7371]) ).
thf(7610,plain,
! [SV104: $i,SV417: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) ) )
= $true )
| ( ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7372]) ).
thf(7611,plain,
! [SV417: $i,SV104: $i] :
( ( ( SV104
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7373]) ).
thf(7612,plain,
! [SV105: $i,SV418: $i,SV690: $i,SV897: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7374]) ).
thf(7613,plain,
! [SV691: $i,SV106: $i,SV419: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV419 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7375]) ).
thf(7614,plain,
! [SV107: $i,SV420: $i,SV692: $i,SV898: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ SV420 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV898 @ tc_HOL_Obool ) ) @ SV692 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV898 ) @ SV107 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7376]) ).
thf(7615,plain,
! [SV108: $i,SV421: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7377]) ).
thf(7616,plain,
! [SV421: $i,SV108: $i] :
( ( ( SV108
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7378]) ).
thf(7617,plain,
! [SV109: $i,SV422: $i,SV693: $i,SV899: $i,SV1021: $i,SV1084: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV1084 @ SV1021 @ SV899 )
| ( ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7379]) ).
thf(7618,plain,
! [SV110: $i,SV423: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 ) )
= $true )
| ( ( ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7380]) ).
thf(7619,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7381]) ).
thf(7620,plain,
! [SV113: $i,SV426: $i,SV694: $i,SV900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7382]) ).
thf(7621,plain,
! [SV114: $i,SV427: $i,SV695: $i,SV901: $i,SV1022: $i,SV1085: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1085 @ SV1022 ) @ SV901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SV1085 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7383]) ).
thf(7622,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) )
| ~ ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7385]) ).
thf(7623,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
| ~ ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7386]) ).
thf(7624,plain,
! [SV431: $i,SV119: $i,SV699: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV699 @ ( tc_fun @ SV699 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) ) )
= $true )
| ( ( c_Wellfounded_OwfP @ SV699 @ SV119 )
= $true )
| ( ( c_Wellfounded_OwfP @ SV699 @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7387]) ).
thf(7625,plain,
! [SV120: $i,SV432: $i,SV700: $i,SV904: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ SV432 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV904 ) @ SV700 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV904 ) @ SV120 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7388]) ).
thf(7626,plain,
! [SV122: $i,SV434: $i,SV702: $i,SV905: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV905 @ tc_HOL_Obool ) ) @ SV702 ) @ SV434 ) @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV434 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7389]) ).
thf(7627,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
| ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7390]) ).
thf(7628,plain,
! [SV703: $i,SV435: $i,SV123: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7391]) ).
thf(7629,plain,
! [SV124: $i,SV436: $i,SV704: $i,SV906: $i,SV1025: $i,SV1086: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1086 @ ( tc_fun @ SV1025 @ tc_HOL_Obool ) ) ) @ SV906 ) @ SV704 ) @ SV436 ) @ SV124 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7392]) ).
thf(7630,plain,
! [SV437: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV125 ) @ SV437 ) )
= $false )
| ( ( SV437 = SV125 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV437 ) @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7393]) ).
thf(7631,plain,
! [SV126: $i,SV438: $i,SV705: $i,SV907: $i] :
( ( ( class_Orderings_Oorder @ SV907 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7394]) ).
thf(7632,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7395]) ).
thf(7633,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7396]) ).
thf(7634,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) )
| ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7397]) ).
thf(7635,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ~ ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) )
| ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7398]) ).
thf(7636,plain,
! [SV129: $i,SV441: $i,SV708: $i,SV908: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV908 @ SV708 @ SV441 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV708 @ SV129 ) @ SV129 )
= SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7399]) ).
thf(7637,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i] :
( ( ! [SY3042: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY3042 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SY3042 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7401]) ).
thf(7638,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i] :
( ( ! [SY3045: $i,SY3046: $i,SY3047: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3047 @ SY3046 @ SY3045 @ SV1088 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SY3046 @ SY3045 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7402]) ).
thf(7639,plain,
! [SV134: $i,SV446: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $true )
| ( ( ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7404]) ).
thf(7640,plain,
! [SV446: $i,SV134: $i] :
( ( ( ~ ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7405]) ).
thf(7641,plain,
! [SV135: $i,SV447: $i,SV713: $i,SV911: $i,SV1028: $i,SV1089: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1089 @ ( tc_fun @ SV1028 @ tc_HOL_Obool ) ) ) @ SV911 ) @ SV713 ) @ SV447 ) @ SV135 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV911 @ SV447 ) @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7406]) ).
thf(7642,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7407]) ).
thf(7643,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7408]) ).
thf(7644,plain,
! [SV137: $i,SV449: $i,SV715: $i,SV912: $i] :
( ( ( c_Predicate_Osymp @ SV912 @ SV715 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7409]) ).
thf(7645,plain,
! [SV138: $i,SV450: $i,SV716: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV450 ) @ SV138 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV716 ) @ SV138 ) @ SV450 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV716 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7410]) ).
thf(7646,plain,
! [SV142: $i,SV454: $i,SV718: $i,SV913: $i,SV1029: $i,SV1090: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1090 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7411]) ).
thf(7647,plain,
! [SV143: $i,SV455: $i,SV719: $i,SV914: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV914 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV719 @ SV143 ) )
| ( hBOOL @ ( hAPP @ SV455 @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7412]) ).
thf(7648,plain,
! [SV456: $i,SV144: $i,SV720: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV144 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV456 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV720 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7413]) ).
thf(7649,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
| ~ ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7415]) ).
thf(7650,plain,
! [SV147: $i,SV459: $i,SV723: $i,SV916: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV916 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV723 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7416]) ).
thf(7651,plain,
! [SV148: $i,SV460: $i,SV724: $i,SV917: $i,SV1031: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7417]) ).
thf(7652,plain,
! [SV149: $i,SV461: $i,SV725: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV725 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7418]) ).
thf(7653,plain,
! [SV150: $i,SV462: $i,SV726: $i,SV918: $i,SV1032: $i] :
( ( ( ( hAPP @ SV1032 @ SV918 )
!= SV726 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SV1032 @ SV918 @ SV726 )
= SV1032 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7419]) ).
thf(7654,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7420]) ).
thf(7655,plain,
! [SV727: $i,SV151: $i,SV463: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
| ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7421]) ).
thf(7656,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i] :
( ( ! [SY3048: $i,SY3049: $i,SY3050: $i,SY3051: $i,SY3052: $i] :
( ( ( hAPP @ SY3052 @ ( hAPP @ SY3051 @ SY3050 ) )
!= ( hAPP @ SY3049 @ ( hAPP @ SY3048 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3052 ) @ SY3051 ) @ SY3050 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SY3049 ) @ SY3048 ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7422]) ).
thf(7657,plain,
! [SV154: $i,SV466: $i,SV730: $i,SV920: $i,SV1034: $i] :
( ( ( ~ ( c_Predicate_Otransp @ SV1034 @ SV920 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7423]) ).
thf(7658,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
| ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7424]) ).
thf(7659,plain,
! [SV731: $i,SV155: $i,SV467: $i] :
( ( ~ ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7425]) ).
thf(7660,plain,
! [SV157: $i,SV1093: $i,SV469: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV469 @ SV1093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7427]) ).
thf(7661,plain,
! [SV158: $i,SV470: $i,SV733: $i,SV921: $i] :
( ( ( class_Orderings_Opreorder @ SV921 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7428]) ).
thf(7662,plain,
! [SV159: $i,SV471: $i,SV734: $i,SV922: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV922 @ SV734 @ SV471 ) @ SV159 ) )
= $false )
| ( ( SV471
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV922 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7429]) ).
thf(7663,plain,
! [SV160: $i,SV472: $i,SV735: $i,SV923: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7430]) ).
thf(7664,plain,
! [SV161: $i,SV473: $i] :
( ( ( ~ ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) ) )
= $true )
| ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7431]) ).
thf(7665,plain,
! [SV473: $i,SV161: $i] :
( ( ( ~ ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7432]) ).
thf(7666,plain,
! [SV162: $i,SV474: $i,SV736: $i,SV924: $i] :
( ( ( SV924 = SV736 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7433]) ).
thf(7667,plain,
! [SV163: $i,SV475: $i,SV737: $i,SV925: $i,SV1035: $i,SV1094: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV1094 @ SV1035 @ SV925 @ SV737 @ SV475 )
| ( ( hAPP @ SV737 @ ( hAPP @ SV925 @ SV163 ) )
= SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7434]) ).
thf(7668,plain,
! [SV164: $i,SV476: $i,SV738: $i,SV926: $i,SV1036: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1036 @ tc_HOL_Obool ) ) @ SV926 ) @ SV738 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV926 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7435]) ).
thf(7669,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i,SV1095: $i] :
( ( ! [SY3053: $i,SY3054: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3054 @ SY3053 ) @ SV1095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SY3054 @ SV1037 ) @ SY3053 ) @ SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7436]) ).
thf(7670,plain,
! [SV168: $i,SV480: $i,SV741: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7438]) ).
thf(7671,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
| ( SV481 = SV169 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7439]) ).
thf(7672,plain,
! [SV742: $i,SV169: $i,SV481: $i] :
( ( ( SV481 != SV169 )
| ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7440]) ).
thf(7673,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ~ ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7441]) ).
thf(7674,plain,
! [SV482: $i,SV928: $i,SV743: $i,SV170: $i] :
( ( ~ ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7441]) ).
thf(7675,plain,
! [SV744: $i,SV171: $i,SV483: $i] :
( ( ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7442]) ).
thf(7676,plain,
! [SV173: $i,SV485: $i] :
( ( ( ~ ( class_Enum_Oenum @ SV485 ) )
= $true )
| ( ( ~ ( class_Enum_Oenum @ SV173 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7443]) ).
thf(7677,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i,SV1038: $i,SV1096: $i] :
( ( ! [SY3055: $i] :
( ~ ( c_Typedef_Otype__definition @ SY3055 @ SV1096 @ SV1038 @ SV929 @ SV745 )
| ~ ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7444]) ).
thf(7678,plain,
! [SV175: $i,SV487: $i,SV746: $i,SV930: $i,SV1039: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7445]) ).
thf(7679,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
| ( SV747 = SV176 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7446]) ).
thf(7680,plain,
! [SV488: $i,SV931: $i,SV176: $i,SV747: $i] :
( ( ~ ( ( SV747 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7446]) ).
thf(7681,plain,
! [SV177: $i,SV489: $i,SV748: $i,SV932: $i,SV1040: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1040 @ SV932 ) @ SV748 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SV1040 ) @ SV748 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7447]) ).
thf(7682,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
| ( SV490 = SV178 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7448]) ).
thf(7683,plain,
! [SV749: $i,SV933: $i,SV178: $i,SV490: $i] :
( ( ~ ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7448]) ).
thf(7684,plain,
! [SV179: $i,SV491: $i,SV750: $i,SV934: $i,SV1041: $i,SV1097: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7449]) ).
thf(7685,plain,
! [SV492: $i,SV180: $i,SV751: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV751 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV180 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV492 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7450]) ).
thf(7686,plain,
! [SV181: $i,SV493: $i,SV752: $i,SV935: $i,SV1042: $i,SV1098: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1098 @ SV1042 ) @ SV935 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SV1098 ) @ SV181 ) @ SV1042 ) @ SV935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7451]) ).
thf(7687,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
| ~ ( ~ ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7452]) ).
thf(7688,plain,
! [SV495: $i,SV754: $i,SV183: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) ) )
= $false )
| ( ( SV754 = SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7453]) ).
thf(7689,plain,
! [SV184: $i,SV496: $i,SV755: $i,SV937: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7454]) ).
thf(7690,plain,
! [SV185: $i,SV497: $i,SV756: $i,SV938: $i] :
( ( ( class_Orderings_Oord @ SV938 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
| ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7455]) ).
thf(7691,plain,
! [SV186: $i,SV498: $i,SV757: $i,SV939: $i] :
( ( ( class_Orderings_Oorder @ SV939 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
| ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7456]) ).
thf(7692,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV940: $i,SV1044: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1044 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SV1044 ) ) @ SV758 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1044 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7457]) ).
thf(7693,plain,
! [SV188: $i,SV500: $i,SV759: $i,SV941: $i,SV1045: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1045 @ SV941 ) @ SV759 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SV1045 ) @ SV759 ) @ SV941 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7458]) ).
thf(7694,plain,
! [SV189: $i,SV501: $i,SV760: $i,SV942: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7459]) ).
thf(7695,plain,
! [SV190: $i,SV502: $i,SV761: $i,SV943: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7460]) ).
thf(7696,plain,
! [SV191: $i,SV503: $i,SV762: $i,SV944: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV944 @ SV762 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7461]) ).
thf(7697,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) )
| ( SV763 = SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7462]) ).
thf(7698,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7463]) ).
thf(7699,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7463]) ).
thf(7700,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7464]) ).
thf(7701,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
!= SV197 )
| ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7466]) ).
thf(7702,plain,
! [SV197: $i,SV767: $i,SV509: $i] :
( ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
| ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7467]) ).
thf(7703,plain,
! [SV198: $i,SV510: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
= $true )
| ( ( SV510 = SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7468]) ).
thf(7704,plain,
! [SV198: $i,SV510: $i] :
( ( ( SV510 != SV198 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7469]) ).
thf(7705,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i,SV1046: $i,SV1099: $i] :
( ( ~ ( ( SV1099 != SV1046 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1099 ) @ SV511 ) ) @ SV1046 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1046 ) @ SV199 ) ) @ SV1099 ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7470]) ).
thf(7706,plain,
! [SV200: $i,SV512: $i,SV769: $i,SV949: $i] :
( ( ( c_Fun_Obij__betw @ SV949 @ SV769 @ SV512 @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV769 @ tc_HOL_Obool ) ) )
= $false )
| ( ( SV200
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV949 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7471]) ).
thf(7707,plain,
! [SV201: $i,SV513: $i,SV770: $i,SV950: $i] :
( ( ( class_Orderings_Oord @ SV950 )
= $false )
| ( ( ( SV770 != SV513 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7472]) ).
thf(7708,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
| ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7473]) ).
thf(7709,plain,
! [SV951: $i,SV514: $i,SV202: $i,SV771: $i] :
( ( ~ ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7473]) ).
thf(7710,plain,
! [SV206: $i,SV518: $i,SV775: $i,SV952: $i] :
( ( ( hBOOL @ ( hAPP @ SV952 @ SV775 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV518 @ tc_HOL_Obool ) ) @ SV952 ) @ SV206 ) @ SV775 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7477]) ).
thf(7711,plain,
! [SV521: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV209 ) @ SV521 ) )
= $false )
| ( ( SV521 = SV209 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV521 ) @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7478]) ).
thf(7712,plain,
! [SV210: $i,SV1100: $i,SV522: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV522 @ SV1100 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7479]) ).
thf(7713,plain,
! [SV211: $i,SV523: $i,SV776: $i,SV953: $i,SV1047: $i,SV1101: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1101 @ SV1047 ) @ SV953 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SV1101 ) @ SV1047 ) @ SV953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7480]) ).
thf(7714,plain,
! [SV212: $i,SV524: $i,SV777: $i,SV954: $i] :
( ( ( hBOOL @ ( hAPP @ SV954 @ SV777 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV524 @ SV777 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SV954 ) @ SV524 ) @ SV777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7481]) ).
thf(7715,plain,
! [SV213: $i,SV525: $i,SV778: $i,SV955: $i,SV1048: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7482]) ).
thf(7716,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7483]) ).
thf(7717,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ~ ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7483]) ).
thf(7718,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ~ ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7484]) ).
thf(7719,plain,
! [SV218: $i,SV530: $i,SV781: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7485]) ).
thf(7720,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7486]) ).
thf(7721,plain,
! [SV221: $i,SV533: $i,SV784: $i,SV959: $i,SV1051: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV1051 @ SV959 @ SV784 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7488]) ).
thf(7722,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7489]) ).
thf(7723,plain,
! [SV223: $i,SV535: $i,SV786: $i,SV961: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV961 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV786 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV535 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7490]) ).
thf(7724,plain,
! [SV224: $i,SV536: $i,SV787: $i,SV962: $i] :
( ( ( class_Orderings_Oorder @ SV962 )
= $false )
| ( ( ( SV787 != SV536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7491]) ).
thf(7725,plain,
! [SV225: $i,SV537: $i,SV788: $i,SV963: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV963 @ tc_HOL_Obool ) ) @ SV788 ) @ SV537 ) @ SV225 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV788 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7492]) ).
thf(7726,plain,
! [SV226: $i,SV538: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV538 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV226 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7493]) ).
thf(7727,plain,
! [SV227: $i,SV539: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
= $true )
| ( ( SV539 = SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7494]) ).
thf(7728,plain,
! [SV227: $i,SV539: $i] :
( ( ( SV539 != SV227 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7495]) ).
thf(7729,plain,
! [SV228: $i,SV540: $i,SV789: $i,SV964: $i] :
( ( ( SV964 = SV789 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV964 ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7496]) ).
thf(7730,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ~ ( ~ ( ( SV1102 != SV1053 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 ) )
| ~ ( ~ ( ( SV1102 != SV1053 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7498]) ).
thf(7731,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
| ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7499]) ).
thf(7732,plain,
! [SV231: $i,SV792: $i,SV543: $i] :
( ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7500]) ).
thf(7733,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ( SV793 != SV544 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7501]) ).
thf(7734,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
| ( SV793 = SV544 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7502]) ).
thf(7735,plain,
! [SV233: $i,SV545: $i,SV794: $i,SV966: $i] :
( ( ( c_Fun_Obij__betw @ SV966 @ SV794 @ SV545 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV966 @ tc_HOL_Obool ) ) @ SV233 )
= $false )
| ( ( SV233
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV794 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7503]) ).
thf(7736,plain,
! [SV234: $i,SV546: $i,SV795: $i,SV967: $i,SV1054: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1054 @ tc_HOL_Obool ) ) @ SV967 ) @ SV795 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV967 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7504]) ).
thf(7737,plain,
! [SV235: $i,SV547: $i,SV796: $i,SV968: $i] :
( ( ( c_Finite__Set_Ofolding__one @ SV968 @ SV796 @ SV547 )
= $false )
| ( ( ( hAPP @ SV547 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV968 ) @ SV235 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV968 @ tc_HOL_Obool ) ) ) )
= SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7505]) ).
thf(7738,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ~ ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7506]) ).
thf(7739,plain,
! [SV548: $i,SV797: $i,SV969: $i,SV236: $i] :
( ( ~ ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7506]) ).
thf(7740,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
| ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7507]) ).
thf(7741,plain,
! [SV237: $i,SV798: $i,SV549: $i] :
( ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7508]) ).
thf(7742,plain,
! [SV238: $i,SV550: $i,SV799: $i,SV970: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) )
= $false )
| ( ( ~ ( ( SV799 != SV550 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7509]) ).
thf(7743,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7511]) ).
thf(7744,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7512]) ).
thf(7745,plain,
! [SV241: $i,SV553: $i,SV802: $i,SV971: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV553 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7513]) ).
thf(7746,plain,
! [SV242: $i,SV554: $i,SV803: $i,SV972: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ SV803 ) @ SV554 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV972 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV803 ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV972 ) @ SV242 ) @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7514]) ).
thf(7747,plain,
! [SV243: $i,SV555: $i,SV804: $i,SV973: $i,SV1055: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1055 @ SV973 @ SV804 ) @ SV555 ) @ SV243 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV804 @ SV243 ) @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7515]) ).
thf(7748,plain,
! [SV244: $i,SV556: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
!= ( hAPP @ c_Nat_OSuc @ SV244 ) )
= $true )
| ( ( SV556 = SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7516]) ).
thf(7749,plain,
! [SV244: $i,SV556: $i] :
( ( ( SV556 != SV244 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7517]) ).
thf(7750,plain,
! [SV245: $i,SV557: $i,SV805: $i,SV974: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV557 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV245 ) )
| ( SV557 = SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7518]) ).
thf(7751,plain,
! [SV806: $i,SV246: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV558 ) @ SV246 ) @ SV806 ) )
= $false )
| ( ( SV806
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV558 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7519]) ).
thf(7752,plain,
! [SV247: $i,SV559: $i,SV807: $i,SV975: $i] :
( ( ( class_Orderings_Oord @ SV975 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
| ~ ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7520]) ).
thf(7753,plain,
! [SV248: $i,SV560: $i,SV808: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SV1056 ) @ SV976 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7521]) ).
thf(7754,plain,
! [SV249: $i,SV561: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
!= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
= $true )
| ( ( SV561 = SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7522]) ).
thf(7755,plain,
! [SV249: $i,SV561: $i] :
( ( ( SV561 != SV249 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7523]) ).
thf(7756,plain,
! [SV252: $i,SV564: $i,SV810: $i,SV977: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV564 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV977 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7525]) ).
thf(7757,plain,
! [SV253: $i,SV565: $i,SV811: $i,SV978: $i,SV1057: $i,SV1104: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1104 @ SV1057 ) @ SV978 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SV1104 ) @ SV811 ) @ SV1057 ) @ SV978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7526]) ).
thf(7758,plain,
! [SV254: $i,SV566: $i] :
( ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7527]) ).
thf(7759,plain,
! [SV566: $i,SV254: $i] :
( ( ( ~ ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7528]) ).
thf(7760,plain,
! [SV256: $i,SV1058: $i,SV568: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7530]) ).
thf(7761,plain,
! [SV569: $i,SV257: $i,SV812: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) ) )
= $true )
| ( ( SV569 = SV257 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7531]) ).
thf(7762,plain,
! [SV258: $i,SV570: $i,SV813: $i,SV979: $i,SV1059: $i,SV1105: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple @ SV1105 @ SV1059 @ SV979 @ SV813 @ SV570 @ SV258 )
| ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1059 @ tc_HOL_Obool ) ) )
= SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7532]) ).
thf(7763,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i,SV1106: $i] :
( ( ! [SY3056: $i,SY3057: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3057 @ SY3056 @ SV1106 @ SV1060 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SY3056 @ SV1106 @ SV571 ) @ SV259 ) )
| ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7533]) ).
thf(7764,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i,SV1061: $i,SV1107: $i] :
( ( ~ ( ( SV1107 != SV1061 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SV1061 @ SV260 ) @ SV1107 )
= ( hAPP @ SV572 @ SV1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7534]) ).
thf(7765,plain,
! [SV816: $i,SV261: $i,SV573: $i] :
( ( ( SV573 != SV261 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV816 ) @ SV573 ) @ SV261 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV816 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7535]) ).
thf(7766,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
| ( SV574 = SV262 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7536]) ).
thf(7767,plain,
! [SV817: $i,SV262: $i,SV574: $i] :
( ( ( SV574 != SV262 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7537]) ).
thf(7768,plain,
! [SV263: $i,SV575: $i,SV818: $i,SV982: $i,SV1062: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7538]) ).
thf(7769,plain,
! [SV264: $i,SV576: $i,SV819: $i,SV983: $i,SV1063: $i,SV1108: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
| ~ ( ( SV983 != SV576 )
| ( SV819 != SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7539]) ).
thf(7770,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i,SV1064: $i,SV1109: $i] :
( ( ! [SY3059: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3059 @ SV1109 @ SV1064 @ SV984 ) @ SV821 )
!= SV579 )
| ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7541]) ).
thf(7771,plain,
! [SV268: $i,SV580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) ) )
= $true )
| ( ( ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7542]) ).
thf(7772,plain,
! [SV268: $i,SV580: $i] :
( ( ( ~ ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7543]) ).
thf(7773,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7544]) ).
thf(7774,plain,
! [SV581: $i,SV269: $i,SV822: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7545]) ).
thf(7775,plain,
! [SV270: $i,SV582: $i,SV823: $i,SV985: $i,SV1065: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7546]) ).
thf(7776,plain,
! [SV272: $i,SV584: $i,SV825: $i,SV986: $i] :
( ( ( SV986 = SV825 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
| ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7547]) ).
thf(7777,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
| ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7548]) ).
thf(7778,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ~ ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7548]) ).
thf(7779,plain,
! [SV275: $i,SV587: $i,SV827: $i,SV988: $i,SV1066: $i,SV1110: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV988 )
!= SV827 )
| ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV988 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV827 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7549]) ).
thf(7780,plain,
! [SV276: $i,SV588: $i,SV828: $i,SV989: $i] :
( ( ( SV989 = SV828 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7550]) ).
thf(7781,plain,
! [SV277: $i,SV589: $i,SV829: $i,SV990: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV990 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV829 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7551]) ).
thf(7782,plain,
! [SV278: $i,SV590: $i,SV830: $i,SV991: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7552]) ).
thf(7783,plain,
! [SV280: $i,SV592: $i,SV831: $i,SV992: $i] :
( ( ( SV992
= ( c_Finite__Set_Ofold1 @ SV831 @ SV592 ) )
= $false )
| ( ( ( hAPP @ SV992 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV831 ) @ SV280 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV831 @ tc_HOL_Obool ) ) ) )
= SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7553]) ).
thf(7784,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
| ~ ( ~ ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7554]) ).
thf(7785,plain,
! [SV284: $i,SV596: $i,SV834: $i,SV994: $i,SV1068: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV596 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1068 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7556]) ).
thf(7786,plain,
! [SV285: $i,SV597: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
= $true )
| ( ( SV597 = SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7557]) ).
thf(7787,plain,
! [SV285: $i,SV597: $i] :
( ( ( SV597 != SV285 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7558]) ).
thf(7788,plain,
! [SV286: $i,SV598: $i,SV835: $i,SV995: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7559]) ).
thf(7789,plain,
! [SV287: $i,SV599: $i] :
( ( ( ~ ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7560]) ).
thf(7790,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7561]) ).
thf(7791,plain,
! [SV289: $i,SV600: $i] :
( ( ( ~ ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) ) )
= $true )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7562]) ).
thf(7792,plain,
! [SV600: $i,SV289: $i] :
( ( ( SV289
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7563]) ).
thf(7793,plain,
! [SV291: $i,SV601: $i,SV836: $i] :
( ( ( ! [SY2814: $i] :
~ ( hBOOL @ ( hAPP @ SV836 @ SY2814 ) ) )
= $true )
| ( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7564]) ).
thf(7794,plain,
! [SV294: $i,SV604: $i,SV838: $i,SV996: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV996 @ SV838 ) )
| ( hBOOL @ ( hAPP @ SV604 @ SV838 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7566]) ).
thf(7795,plain,
! [SV295: $i,SV605: $i,SV839: $i,SV997: $i,SV1069: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SV1069 @ SV997 @ SV839 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1069 @ tc_HOL_Obool ) ) ) @ SV295 ) ) )
= $true )
| ( ( SV295 = SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7567]) ).
thf(7796,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV840 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7568]) ).
thf(7797,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV998: $i,SV1070: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1070 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SV1070 ) ) @ SV841 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1070 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7569]) ).
thf(7798,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7571]) ).
thf(7799,plain,
! [SV609: $i,SV299: $i,SV843: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7572]) ).
thf(7800,plain,
! [SV300: $i,SV610: $i,SV844: $i,SV999: $i,SV1071: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1071 @ SV999 ) @ SV844 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SV1071 ) @ SV999 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7573]) ).
thf(7801,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7574]) ).
thf(7802,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7575]) ).
thf(7803,plain,
! [SV302: $i,SV612: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7576]) ).
thf(7804,plain,
! [SV302: $i,SV612: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7577]) ).
thf(7805,plain,
! [SV303: $i,SV613: $i,SV846: $i,SV1000: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV1000 @ SV846 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7578]) ).
thf(7806,plain,
! [SV305: $i,SV615: $i,SV848: $i,SV1001: $i,SV1072: $i,SV1111: $i] :
( ( ( SV1111 != SV1072 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1111 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7580]) ).
thf(7807,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7582]) ).
thf(7808,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7582]) ).
thf(7809,plain,
! [SV309: $i,SV619: $i,SV852: $i,SV1003: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) )
| ( hBOOL @ ( hAPP @ SV619 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7584]) ).
thf(7810,plain,
! [SV311: $i,SV621: $i,SV853: $i,SV1004: $i] :
( ( ( hBOOL @ ( hAPP @ SV1004 @ SV853 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SV1004 ) @ SV311 ) )
| ( hBOOL @ ( hAPP @ SV311 @ SV853 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7585]) ).
thf(7811,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
| ( SV622 = SV312 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7586]) ).
thf(7812,plain,
! [SV854: $i,SV312: $i,SV622: $i] :
( ( ( SV622 != SV312 )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7587]) ).
thf(7813,plain,
! [SV313: $i,SV855: $i,SV623: $i] :
( ( ( SV623
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) )
= $true )
| ( ( SV623
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) @ SV623 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV855 ) @ SV313 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV855 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7588]) ).
thf(7814,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7589]) ).
thf(7815,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
| ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7590]) ).
thf(7816,plain,
! [SV857: $i,SV315: $i,SV625: $i] :
( ( ~ ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7591]) ).
thf(7817,plain,
! [SV858: $i,SV316: $i,SV626: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV316 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV626 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7592]) ).
thf(7818,plain,
! [SV318: $i,SV628: $i,SV859: $i,SV1006: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7593]) ).
thf(7819,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ~ ( ~ ( ( SV1112 != SV1074 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 ) )
| ~ ( ~ ( ( SV1112 != SV1074 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7594]) ).
thf(7820,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i,SV1075: $i,SV1113: $i] :
( ( ! [SY3060: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY3060 @ SV1113 @ SV1075 @ SV1008 @ SV861 @ SV630 )
| ( ( hAPP @ ( hAPP @ SV1075 @ SV320 ) @ SV320 )
= SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7595]) ).
thf(7821,plain,
! [SV322: $i,SV632: $i,SV863: $i,SV1009: $i,SV1076: $i,SV1114: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7597]) ).
thf(7822,plain,
! [SV39: $i,SV356: $i,SV655: $i,SV876: $i,SV1014: $i,SV1078: $i,SV1115: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV1115 @ SV1078 @ SV1014 @ SV876 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SV1115 @ SV1014 @ SV356 ) @ SV39 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV655 @ SV1078 @ SV1014 @ ( hAPP @ ( c_Fun_Ocomp @ SV1115 @ SV1078 @ SV655 @ SV876 ) @ SV356 ) ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7599]) ).
thf(7823,plain,
! [SV76: $i,SV391: $i,SV677: $i,SV887: $i,SV1016: $i,SV1080: $i,SV1116: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV1116 @ SV1080 @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV1116 @ SV887 @ SV1080 ) @ SV677 ) @ SV391 ) ) @ SV76 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV1116 @ SV887 @ SV1016 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV887 @ SV1080 @ SV1016 ) @ SV391 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7601]) ).
thf(7824,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
| ( SV416 = SV103 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7608]) ).
thf(7825,plain,
! [SV689: $i,SV896: $i,SV103: $i,SV416: $i] :
( ( ( SV416 != SV103 )
| ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7609]) ).
thf(7826,plain,
! [SV104: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
= $false )
| ( ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7610]) ).
thf(7827,plain,
! [SV417: $i,SV104: $i] :
( ( ( SV104
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV417 @ tc_HOL_Obool ) ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7611]) ).
thf(7828,plain,
! [SV690: $i,SV105: $i,SV418: $i,SV897: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7612]) ).
thf(7829,plain,
! [SV691: $i,SV106: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV419 ) @ SV106 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint ) @ SV691 ) @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7613]) ).
thf(7830,plain,
! [SV108: $i,SV421: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7615]) ).
thf(7831,plain,
! [SV421: $i,SV108: $i] :
( ( ( SV108
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) @ SV108 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV421 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7616]) ).
thf(7832,plain,
! [SV109: $i,SV422: $i,SV693: $i,SV899: $i,SV1021: $i,SV1084: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV1084 @ SV1021 @ SV899 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7617]) ).
thf(7833,plain,
! [SV110: $i,SV423: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false )
| ( ( ! [SY1376: $i,SY1377: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) )
| ( ( hAPP @ SV110 @ SY1376 )
= ( hAPP @ SV110 @ SY1377 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1376 )
!= ( hAPP @ SV110 @ SY1377 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1376 ) @ SY1377 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7618]) ).
thf(7834,plain,
! [SV423: $i,SV110: $i] :
( ( ( ! [SY1378: $i,SY1379: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) )
| ( ( hAPP @ SV110 @ SY1378 )
= ( hAPP @ SV110 @ SY1379 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SY1378 )
!= ( hAPP @ SV110 @ SY1379 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1378 ) @ SY1379 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7619]) ).
thf(7835,plain,
! [SV113: $i,SV426: $i,SV694: $i,SV900: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7620]) ).
thf(7836,plain,
! [SV114: $i,SV427: $i,SV695: $i,SV901: $i,SV1022: $i,SV1085: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1085 @ SV1022 ) @ SV901 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SV1085 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7621]) ).
thf(7837,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7622]) ).
thf(7838,plain,
! [SV902: $i,SV1023: $i,SV117: $i,SV429: $i,SV697: $i] :
( ( ~ ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7622]) ).
thf(7839,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7623]) ).
thf(7840,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ~ ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7623]) ).
thf(7841,plain,
! [SV431: $i,SV119: $i,SV699: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV699 @ ( tc_fun @ SV699 @ tc_HOL_Obool ) ) ) @ SV119 ) @ SV431 ) )
= $false )
| ( ( c_Wellfounded_OwfP @ SV699 @ SV119 )
= $true )
| ( ( c_Wellfounded_OwfP @ SV699 @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7624]) ).
thf(7842,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7627]) ).
thf(7843,plain,
! [SV703: $i,SV435: $i,SV123: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV123 @ SV435 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7628]) ).
thf(7844,plain,
! [SV124: $i,SV436: $i,SV704: $i,SV906: $i,SV1025: $i,SV1086: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1086 @ ( tc_fun @ SV1025 @ tc_HOL_Obool ) ) ) @ SV906 ) @ SV704 ) @ SV436 ) @ SV124 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7629]) ).
thf(7845,plain,
! [SV126: $i,SV438: $i,SV705: $i,SV907: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV907 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7631]) ).
thf(7846,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7632]) ).
thf(7847,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7633]) ).
thf(7848,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( ~ ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) ) )
= $true )
| ( ( ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7634]) ).
thf(7849,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( ~ ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) ) )
= $true )
| ( ( ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7635]) ).
thf(7850,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7637]) ).
thf(7851,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i,SV1118: $i] :
( ( ! [SY3063: $i,SY3064: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3064 @ SY3063 @ SV1118 @ SV1088 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SY3063 @ SV1118 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7638]) ).
thf(7852,plain,
! [SV134: $i,SV446: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $false )
| ( ( ! [SY1455: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7639]) ).
thf(7853,plain,
! [SV446: $i,SV134: $i] :
( ( ( ! [SY1456: $i] :
~ ( hBOOL @ ( hAPP @ SV134 @ SY1456 ) ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7640]) ).
thf(7854,plain,
! [SV135: $i,SV447: $i,SV713: $i,SV911: $i,SV1028: $i,SV1089: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1089 @ ( tc_fun @ SV1028 @ tc_HOL_Obool ) ) ) @ SV911 ) @ SV713 ) @ SV447 ) @ SV135 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV911 @ SV447 ) @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7641]) ).
thf(7855,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7642]) ).
thf(7856,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7643]) ).
thf(7857,plain,
! [SV912: $i,SV137: $i,SV449: $i,SV715: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV912 @ SV715 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7644]) ).
thf(7858,plain,
! [SV142: $i,SV454: $i,SV718: $i,SV913: $i,SV1029: $i,SV1090: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1090 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7646]) ).
thf(7859,plain,
! [SV914: $i,SV455: $i,SV143: $i,SV719: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV719 @ SV143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV455 @ SV143 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV914 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7647]) ).
thf(7860,plain,
! [SV456: $i,SV144: $i,SV720: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV144 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV720 ) @ SV456 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV720 @ tc_HOL_Obool ) ) @ SV456 ) @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7648]) ).
thf(7861,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
| ~ ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7649]) ).
thf(7862,plain,
! [SV459: $i,SV723: $i,SV147: $i,SV916: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV723 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV459 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV916 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7650]) ).
thf(7863,plain,
! [SV148: $i,SV460: $i,SV724: $i,SV917: $i,SV1031: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7651]) ).
thf(7864,plain,
! [SV149: $i,SV461: $i,SV725: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
| ( SV149 = SV461 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV725 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7652]) ).
thf(7865,plain,
! [SV150: $i,SV462: $i,SV726: $i,SV918: $i,SV1032: $i] :
( ( ( ( hAPP @ SV1032 @ SV918 )
= SV726 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV462 @ SV150 @ SV1032 @ SV918 @ SV726 )
= SV1032 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7653]) ).
thf(7866,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7654]) ).
thf(7867,plain,
! [SV727: $i,SV151: $i,SV463: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7655]) ).
thf(7868,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i] :
( ( ! [SY3065: $i,SY3066: $i,SY3067: $i,SY3068: $i] :
( ( ( hAPP @ SY3068 @ ( hAPP @ SY3067 @ SY3066 ) )
!= ( hAPP @ SY3065 @ ( hAPP @ SV1119 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3068 ) @ SY3067 ) @ SY3066 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SY3065 ) @ SV1119 ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7656]) ).
thf(7869,plain,
! [SV154: $i,SV466: $i,SV730: $i,SV920: $i,SV1034: $i] :
( ( ( c_Predicate_Otransp @ SV1034 @ SV920 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7657]) ).
thf(7870,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) ) )
= $true )
| ( ( ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7658]) ).
thf(7871,plain,
! [SV731: $i,SV155: $i,SV467: $i] :
( ( ( ~ ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7659]) ).
thf(7872,plain,
! [SV157: $i,SV1093: $i,SV469: $i] :
( ( ( hBOOL @ ( hAPP @ SV469 @ SV1093 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV469 @ ( c_Hilbert__Choice_OEps @ SV157 @ SV469 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7660]) ).
thf(7873,plain,
! [SV158: $i,SV470: $i,SV733: $i,SV921: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV921 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7661]) ).
thf(7874,plain,
! [SV159: $i,SV734: $i,SV922: $i,SV471: $i] :
( ( ( SV471
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV922 @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV922 @ SV734 @ SV471 ) @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7662]) ).
thf(7875,plain,
! [SV735: $i,SV472: $i,SV160: $i,SV923: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7663]) ).
thf(7876,plain,
! [SV161: $i,SV473: $i] :
( ( ( ~ ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) ) )
= $false )
| ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7664]) ).
thf(7877,plain,
! [SV473: $i,SV161: $i] :
( ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7665]) ).
thf(7878,plain,
! [SV736: $i,SV162: $i,SV924: $i,SV474: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) ) )
= $false )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7666]) ).
thf(7879,plain,
! [SV163: $i,SV475: $i,SV737: $i,SV925: $i,SV1035: $i,SV1094: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV1094 @ SV1035 @ SV925 @ SV737 @ SV475 ) )
= $true )
| ( ( ( hAPP @ SV737 @ ( hAPP @ SV925 @ SV163 ) )
= SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7667]) ).
thf(7880,plain,
! [SV164: $i,SV476: $i,SV738: $i,SV926: $i,SV1036: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1036 @ tc_HOL_Obool ) ) @ SV926 ) @ SV738 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV476 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV926 ) ) @ ( hAPP @ ( c_Set_Ovimage @ SV476 @ SV1036 @ SV164 ) @ SV738 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7668]) ).
thf(7881,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i,SV1095: $i,SV1120: $i] :
( ( ! [SY3069: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3069 @ SV1120 ) @ SV1095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SY3069 @ SV1037 ) @ SV1120 ) @ SV927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7669]) ).
thf(7882,plain,
! [SV168: $i,SV480: $i,SV741: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7670]) ).
thf(7883,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
!= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
= $true )
| ( ( SV481 = SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7671]) ).
thf(7884,plain,
! [SV742: $i,SV169: $i,SV481: $i] :
( ( ( SV481 != SV169 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7672]) ).
thf(7885,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
| ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7673]) ).
thf(7886,plain,
! [SV482: $i,SV928: $i,SV743: $i,SV170: $i] :
( ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7674]) ).
thf(7887,plain,
! [SV744: $i,SV171: $i,SV483: $i] :
( ( ( ~ ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7675]) ).
thf(7888,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7675]) ).
thf(7889,plain,
! [SV173: $i,SV485: $i] :
( ( ( class_Enum_Oenum @ SV485 )
= $false )
| ( ( ~ ( class_Enum_Oenum @ SV173 ) )
= $true )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7676]) ).
thf(7890,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i,SV1038: $i,SV1096: $i,SV1121: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
| ~ ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7677]) ).
thf(7891,plain,
! [SV175: $i,SV487: $i,SV746: $i,SV930: $i,SV1039: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7678]) ).
thf(7892,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
| ( SV747 = SV176 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7679]) ).
thf(7893,plain,
! [SV488: $i,SV931: $i,SV176: $i,SV747: $i] :
( ( ( SV747 != SV176 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7680]) ).
thf(7894,plain,
! [SV177: $i,SV489: $i,SV748: $i,SV932: $i,SV1040: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1040 @ SV932 ) @ SV748 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV489 @ SV177 @ SV1040 ) @ SV748 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7681]) ).
thf(7895,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
| ( SV490 = SV178 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7682]) ).
thf(7896,plain,
! [SV749: $i,SV933: $i,SV178: $i,SV490: $i] :
( ( ( SV490 != SV178 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7683]) ).
thf(7897,plain,
! [SV179: $i,SV491: $i,SV750: $i,SV934: $i,SV1041: $i,SV1097: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7684]) ).
thf(7898,plain,
! [SV492: $i,SV180: $i,SV751: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV751 @ tc_HOL_Obool ) ) @ SV180 ) @ SV492 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV180 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV751 ) @ SV492 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7685]) ).
thf(7899,plain,
! [SV181: $i,SV493: $i,SV752: $i,SV935: $i,SV1042: $i,SV1098: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1098 @ SV1042 ) @ SV935 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SV1098 ) @ SV181 ) @ SV1042 ) @ SV935 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7686]) ).
thf(7900,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7687]) ).
thf(7901,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ~ ( ~ ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7687]) ).
thf(7902,plain,
! [SV495: $i,SV754: $i,SV183: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) ) )
= $false )
| ( ( SV754 = SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7688]) ).
thf(7903,plain,
! [SV754: $i,SV495: $i,SV183: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) ) )
= $false )
| ( ( SV754 = SV495 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7688]) ).
thf(7904,plain,
! [SV755: $i,SV184: $i,SV496: $i,SV937: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7689]) ).
thf(7905,plain,
! [SV185: $i,SV497: $i,SV756: $i,SV938: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) ) )
= $true )
| ( ( ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV938 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7690]) ).
thf(7906,plain,
! [SV186: $i,SV498: $i,SV757: $i,SV939: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) ) )
= $true )
| ( ( ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV939 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7691]) ).
thf(7907,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV940: $i,SV1044: $i] :
( ( ( class_Orderings_Oord @ SV1044 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SV1044 ) ) @ SV758 ) @ SV499 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1044 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7692]) ).
thf(7908,plain,
! [SV188: $i,SV500: $i,SV759: $i,SV941: $i,SV1045: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1045 @ SV941 ) @ SV759 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV500 @ SV188 @ SV1045 ) @ SV759 ) @ SV941 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7693]) ).
thf(7909,plain,
! [SV501: $i,SV189: $i,SV760: $i,SV942: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7694]) ).
thf(7910,plain,
! [SV761: $i,SV190: $i,SV502: $i,SV943: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7695]) ).
thf(7911,plain,
! [SV944: $i,SV191: $i,SV503: $i,SV762: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV944 @ SV762 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7696]) ).
thf(7912,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7697]) ).
thf(7913,plain,
! [SV504: $i,SV945: $i,SV192: $i,SV763: $i] :
( ( ( SV763 = SV192 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7697]) ).
thf(7914,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7698]) ).
thf(7915,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7699]) ).
thf(7916,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
| ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7700]) ).
thf(7917,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
!= SV197 )
= $true )
| ( ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7701]) ).
thf(7918,plain,
! [SV197: $i,SV767: $i,SV509: $i] :
( ( ( SV509
!= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7702]) ).
thf(7919,plain,
! [SV198: $i,SV510: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
= $false )
| ( ( SV510 = SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7703]) ).
thf(7920,plain,
! [SV198: $i,SV510: $i] :
( ( ( SV510 = SV198 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV510 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7704]) ).
thf(7921,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i,SV1046: $i,SV1099: $i] :
( ( ( ~ ( ( SV1099 != SV1046 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1099 ) @ SV511 ) ) @ SV1046 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1046 ) @ SV199 ) ) @ SV1099 ) @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7705]) ).
thf(7922,plain,
! [SV201: $i,SV950: $i,SV513: $i,SV770: $i] :
( ( ( SV770 != SV513 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV950 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7707]) ).
thf(7923,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
| ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7708]) ).
thf(7924,plain,
! [SV951: $i,SV514: $i,SV202: $i,SV771: $i] :
( ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7709]) ).
thf(7925,plain,
! [SV210: $i,SV1100: $i,SV522: $i] :
( ( ( hBOOL @ ( hAPP @ SV522 @ SV1100 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV522 @ ( c_Hilbert__Choice_OEps @ SV210 @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7712]) ).
thf(7926,plain,
! [SV211: $i,SV523: $i,SV776: $i,SV953: $i,SV1047: $i,SV1101: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1101 @ SV1047 ) @ SV953 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SV1101 ) @ SV1047 ) @ SV953 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7713]) ).
thf(7927,plain,
! [SV954: $i,SV212: $i,SV777: $i,SV524: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV524 @ SV777 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SV954 ) @ SV524 ) @ SV777 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV954 @ SV777 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7714]) ).
thf(7928,plain,
! [SV213: $i,SV525: $i,SV778: $i,SV955: $i,SV1048: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7715]) ).
thf(7929,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
| ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7716]) ).
thf(7930,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7717]) ).
thf(7931,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7718]) ).
thf(7932,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ~ ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7718]) ).
thf(7933,plain,
! [SV218: $i,SV530: $i,SV781: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
| ( SV530 = SV218 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7719]) ).
thf(7934,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7720]) ).
thf(7935,plain,
! [SV958: $i,SV1050: $i,SV531: $i,SV219: $i,SV782: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7720]) ).
thf(7936,plain,
! [SV221: $i,SV533: $i,SV784: $i,SV959: $i,SV1051: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV1051 @ SV959 @ SV784 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= ( hAPP @ ( hAPP @ SV784 @ SV533 ) @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7721]) ).
thf(7937,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7722]) ).
thf(7938,plain,
! [SV960: $i,SV1052: $i,SV222: $i,SV785: $i,SV534: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7722]) ).
thf(7939,plain,
! [SV535: $i,SV786: $i,SV223: $i,SV961: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV786 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV535 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV961 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7723]) ).
thf(7940,plain,
! [SV224: $i,SV962: $i,SV536: $i,SV787: $i] :
( ( ( SV787 != SV536 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV962 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7724]) ).
thf(7941,plain,
! [SV226: $i,SV538: $i] :
( ( ( class_Finite__Set_Ofinite @ SV538 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV226 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7726]) ).
thf(7942,plain,
! [SV227: $i,SV539: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
= $false )
| ( ( SV539 = SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7727]) ).
thf(7943,plain,
! [SV227: $i,SV539: $i] :
( ( ( SV539 = SV227 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV539 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7728]) ).
thf(7944,plain,
! [SV964: $i,SV228: $i,SV789: $i,SV540: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV964 ) @ SV228 ) )
= $true )
| ( ( SV964 = SV789 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7729]) ).
thf(7945,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ~ ( ( SV1102 != SV1053 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 ) )
| ~ ( ~ ( ( SV1102 != SV1053 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7730]) ).
thf(7946,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
!= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
= $true )
| ( ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7731]) ).
thf(7947,plain,
! [SV231: $i,SV792: $i,SV543: $i] :
( ( ( SV543
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7732]) ).
thf(7948,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ( SV793 != SV544 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7733]) ).
thf(7949,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
= $true )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7734]) ).
thf(7950,plain,
! [SV234: $i,SV546: $i,SV795: $i,SV967: $i,SV1054: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1054 @ tc_HOL_Obool ) ) @ SV967 ) @ SV795 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV546 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV967 ) ) @ ( hAPP @ ( c_Set_Oimage @ SV1054 @ SV546 @ SV234 ) @ SV795 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7736]) ).
thf(7951,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
| ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7738]) ).
thf(7952,plain,
! [SV548: $i,SV797: $i,SV969: $i,SV236: $i] :
( ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
| ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7739]) ).
thf(7953,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $true )
| ( ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7740]) ).
thf(7954,plain,
! [SV237: $i,SV798: $i,SV549: $i] :
( ( ( SV549
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7741]) ).
thf(7955,plain,
! [SV238: $i,SV970: $i,SV550: $i,SV799: $i] :
( ( ( ~ ( ( SV799 != SV550 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7742]) ).
thf(7956,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7743]) ).
thf(7957,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( ~ ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7744]) ).
thf(7958,plain,
! [SV971: $i,SV553: $i,SV241: $i,SV802: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV241 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7745]) ).
thf(7959,plain,
! [SV243: $i,SV555: $i,SV804: $i,SV973: $i,SV1055: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1055 @ SV973 @ SV804 ) @ SV555 ) @ SV243 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV804 @ SV243 ) @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7747]) ).
thf(7960,plain,
! [SV244: $i,SV556: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) )
= $false )
| ( ( SV556 = SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7748]) ).
thf(7961,plain,
! [SV244: $i,SV556: $i] :
( ( ( SV556 = SV244 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV556 )
= ( hAPP @ c_Nat_OSuc @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7749]) ).
thf(7962,plain,
! [SV557: $i,SV245: $i,SV805: $i,SV974: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV245 ) ) )
= $true )
| ( ( SV557 = SV245 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV557 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7750]) ).
thf(7963,plain,
! [SV247: $i,SV559: $i,SV975: $i,SV807: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
| ~ ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7752]) ).
thf(7964,plain,
! [SV248: $i,SV560: $i,SV808: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SV1056 ) @ SV976 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7753]) ).
thf(7965,plain,
! [SV249: $i,SV561: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
= $false )
| ( ( SV561 = SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7754]) ).
thf(7966,plain,
! [SV249: $i,SV561: $i] :
( ( ( SV561 = SV249 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV561 )
= ( hAPP @ c_Int_ORep__Integ @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7755]) ).
thf(7967,plain,
! [SV810: $i,SV252: $i,SV564: $i,SV977: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV977 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV252 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV564 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7756]) ).
thf(7968,plain,
! [SV253: $i,SV565: $i,SV811: $i,SV978: $i,SV1057: $i,SV1104: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1104 @ SV1057 ) @ SV978 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SV1104 ) @ SV811 ) @ SV1057 ) @ SV978 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7757]) ).
thf(7969,plain,
! [SV254: $i,SV566: $i] :
( ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ! [SY1808: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7758]) ).
thf(7970,plain,
! [SV566: $i,SV254: $i] :
( ( ( ! [SY1809: $i] :
~ ( hBOOL @ ( hAPP @ SV254 @ SY1809 ) ) )
= $false )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7759]) ).
thf(7971,plain,
! [SV256: $i,SV1058: $i,SV568: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7760]) ).
thf(7972,plain,
! [SV569: $i,SV257: $i,SV812: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV257 ) @ SV569 ) )
= $false )
| ( ( SV569 = SV257 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV812 @ tc_HOL_Obool ) ) @ SV569 ) @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7761]) ).
thf(7973,plain,
! [SV258: $i,SV570: $i,SV813: $i,SV979: $i,SV1059: $i,SV1105: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple @ SV1105 @ SV1059 @ SV979 @ SV813 @ SV570 @ SV258 ) )
= $true )
| ( ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1059 @ tc_HOL_Obool ) ) )
= SV813 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7762]) ).
thf(7974,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i,SV1106: $i,SV1122: $i] :
( ( ! [SY3070: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3070 @ SV1122 @ SV1106 @ SV1060 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SV1122 @ SV1106 @ SV571 ) @ SV259 ) )
| ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7763]) ).
thf(7975,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i,SV1061: $i,SV1107: $i] :
( ( ( ~ ( ( SV1107 != SV1061 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SV1061 @ SV260 ) @ SV1107 )
= ( hAPP @ SV572 @ SV1107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7764]) ).
thf(7976,plain,
! [SV816: $i,SV261: $i,SV573: $i] :
( ( ( SV573 = SV261 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV816 ) @ SV573 ) @ SV261 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV816 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7765]) ).
thf(7977,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) ) )
= $true )
| ( ( SV574 = SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7766]) ).
thf(7978,plain,
! [SV817: $i,SV262: $i,SV574: $i] :
( ( ( SV574 != SV262 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7767]) ).
thf(7979,plain,
! [SV263: $i,SV575: $i,SV818: $i,SV982: $i,SV1062: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7768]) ).
thf(7980,plain,
! [SV264: $i,SV576: $i,SV819: $i,SV983: $i,SV1063: $i,SV1108: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $true )
| ( ( ~ ( ( SV983 != SV576 )
| ( SV819 != SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7769]) ).
thf(7981,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i,SV1064: $i,SV1109: $i,SV1123: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1123 @ SV1109 @ SV1064 @ SV984 ) @ SV821 )
!= SV579 )
| ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7770]) ).
thf(7982,plain,
! [SV268: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $false )
| ( ( ~ ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7771]) ).
thf(7983,plain,
! [SV268: $i,SV580: $i] :
( ( ( ~ ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7772]) ).
thf(7984,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7773]) ).
thf(7985,plain,
! [SV581: $i,SV269: $i,SV822: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7774]) ).
thf(7986,plain,
! [SV270: $i,SV582: $i,SV823: $i,SV985: $i,SV1065: $i] :
( ( ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7775]) ).
thf(7987,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7776]) ).
thf(7988,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
| ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7777]) ).
thf(7989,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7778]) ).
thf(7990,plain,
! [SV275: $i,SV587: $i,SV827: $i,SV988: $i,SV1066: $i,SV1110: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV988 )
!= SV827 )
= $true )
| ( ( ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV988 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV827 ) @ SV275 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7779]) ).
thf(7991,plain,
! [SV828: $i,SV989: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) ) )
= $false )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7780]) ).
thf(7992,plain,
! [SV589: $i,SV829: $i,SV277: $i,SV990: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV829 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV589 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV990 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7781]) ).
thf(7993,plain,
! [SV830: $i,SV278: $i,SV590: $i,SV991: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7782]) ).
thf(7994,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7784]) ).
thf(7995,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ~ ( ~ ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7784]) ).
thf(7996,plain,
! [SV284: $i,SV596: $i,SV834: $i,SV994: $i,SV1068: $i] :
( ( ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV596 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1068 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
| ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7785]) ).
thf(7997,plain,
! [SV285: $i,SV597: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
= $false )
| ( ( SV597 = SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7786]) ).
thf(7998,plain,
! [SV285: $i,SV597: $i] :
( ( ( SV597 = SV285 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV597 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7787]) ).
thf(7999,plain,
! [SV995: $i,SV598: $i,SV286: $i,SV835: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7788]) ).
thf(8000,plain,
! [SV287: $i,SV599: $i] :
( ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false )
| ( ( ~ ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7789]) ).
thf(8001,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7790]) ).
thf(8002,plain,
! [SV289: $i,SV600: $i] :
( ( ( ! [SY2494: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2494 ) @ SV289 ) ) )
= $false )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7791]) ).
thf(8003,plain,
! [SV600: $i,SV289: $i] :
( ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ! [SY2495: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SY2495 ) @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7792]) ).
thf(8004,plain,
! [SV291: $i,SV601: $i,SV1124: $i,SV836: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV836 @ SV1124 ) ) )
= $true )
| ( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[7793]) ).
thf(8005,plain,
! [SV604: $i,SV294: $i,SV838: $i,SV996: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV996 @ SV838 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7794]) ).
thf(8006,plain,
! [SV996: $i,SV294: $i,SV838: $i,SV604: $i] :
( ( ( hBOOL @ ( hAPP @ SV604 @ SV838 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[7794]) ).
thf(8007,plain,
! [SV295: $i,SV605: $i,SV839: $i,SV997: $i,SV1069: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ SV1069 @ SV997 @ SV839 @ SV605 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1069 @ tc_HOL_Obool ) ) ) @ SV295 ) )
= $false )
| ( ( SV295 = SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7795]) ).
thf(8008,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV840 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7796]) ).
thf(8009,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV998: $i,SV1070: $i] :
( ( ( class_Orderings_Oord @ SV1070 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SV1070 ) ) @ SV841 ) @ SV607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1070 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7797]) ).
thf(8010,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7798]) ).
thf(8011,plain,
! [SV609: $i,SV299: $i,SV843: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7799]) ).
thf(8012,plain,
! [SV300: $i,SV610: $i,SV844: $i,SV999: $i,SV1071: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1071 @ SV999 ) @ SV844 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV610 @ SV300 @ SV1071 ) @ SV999 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7800]) ).
thf(8013,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7801]) ).
thf(8014,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
!= SV301 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7802]) ).
thf(8015,plain,
! [SV302: $i,SV612: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7803]) ).
thf(8016,plain,
! [SV302: $i,SV612: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV612 ) @ SV302 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_HOL_Obool ) ) @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7804]) ).
thf(8017,plain,
! [SV1000: $i,SV303: $i,SV613: $i,SV846: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1000 @ SV846 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7805]) ).
thf(8018,plain,
! [SV305: $i,SV615: $i,SV848: $i,SV1001: $i,SV1072: $i,SV1111: $i] :
( ( ( SV1111 != SV1072 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1111 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1072 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7806]) ).
thf(8019,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
| ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7807]) ).
thf(8020,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) )
| ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7808]) ).
thf(8021,plain,
! [SV1003: $i,SV619: $i,SV309: $i,SV852: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV619 @ SV309 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7809]) ).
thf(8022,plain,
! [SV853: $i,SV311: $i,SV1004: $i,SV621: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SV1004 ) @ SV311 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV853 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1004 @ SV853 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7810]) ).
thf(8023,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
= $true )
| ( ( SV622 = SV312 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7811]) ).
thf(8024,plain,
! [SV854: $i,SV312: $i,SV622: $i] :
( ( ( SV622 != SV312 )
= $true )
| ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7812]) ).
thf(8025,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7814]) ).
thf(8026,plain,
! [SV1005: $i,SV1073: $i,SV624: $i,SV314: $i,SV856: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7814]) ).
thf(8027,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) ) )
= $true )
| ( ( ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7815]) ).
thf(8028,plain,
! [SV857: $i,SV315: $i,SV625: $i] :
( ( ( ~ ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7816]) ).
thf(8029,plain,
! [SV858: $i,SV316: $i,SV626: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV626 ) @ SV316 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV316 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ SV858 ) @ SV626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7817]) ).
thf(8030,plain,
! [SV859: $i,SV318: $i,SV628: $i,SV1006: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7818]) ).
thf(8031,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ~ ( ( SV1112 != SV1074 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 ) )
| ~ ( ~ ( ( SV1112 != SV1074 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7819]) ).
thf(8032,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i,SV1075: $i,SV1113: $i,SV1125: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV1125 @ SV1113 @ SV1075 @ SV1008 @ SV861 @ SV630 )
| ( ( hAPP @ ( hAPP @ SV1075 @ SV320 ) @ SV320 )
= SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7820]) ).
thf(8033,plain,
! [SV322: $i,SV632: $i,SV863: $i,SV1009: $i,SV1076: $i,SV1114: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7821]) ).
thf(8034,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) ) )
= $true )
| ( ( SV416 = SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7824]) ).
thf(8035,plain,
! [SV689: $i,SV896: $i,SV103: $i,SV416: $i] :
( ( ( SV416 != SV103 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7825]) ).
thf(8036,plain,
! [SV690: $i,SV105: $i,SV418: $i,SV897: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV418 ) @ SV105 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV897 @ tc_HOL_Obool ) ) @ SV690 ) @ SV418 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7828]) ).
thf(8037,plain,
! [SV109: $i,SV422: $i,SV693: $i,SV899: $i,SV1021: $i,SV1084: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV1084 @ SV1021 @ SV899 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ SV109 ) )
= ( hAPP @ ( hAPP @ SV899 @ SV422 ) @ ( hAPP @ ( hAPP @ SV899 @ SV693 ) @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7832]) ).
thf(8038,plain,
! [SV423: $i,SV1126: $i,SV110: $i] :
( ( ( ! [SY3072: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SY3072 ) )
| ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SY3072 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SY3072 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SY3072 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7833]) ).
thf(8039,plain,
! [SV423: $i,SV110: $i] :
( ( ( ! [SY3073: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ SY3073 ) )
| ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ SY3073 ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ SY3073 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ SY3073 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7834]) ).
thf(8040,plain,
! [SV113: $i,SV694: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7835]) ).
thf(8041,plain,
! [SV114: $i,SV427: $i,SV695: $i,SV901: $i,SV1022: $i,SV1085: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1085 @ SV1022 ) @ SV901 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SV1085 ) @ SV114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7836]) ).
thf(8042,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
| ( ( hAPP @ SV697 @ SV429 )
= SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7837]) ).
thf(8043,plain,
! [SV902: $i,SV1023: $i,SV117: $i,SV429: $i,SV697: $i] :
( ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
| ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7838]) ).
thf(8044,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
| ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7839]) ).
thf(8045,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7840]) ).
thf(8046,plain,
! [SV123: $i,SV435: $i,SV703: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7842]) ).
thf(8047,plain,
! [SV703: $i,SV435: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ SV123 @ SV435 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV703 ) @ SV435 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7843]) ).
thf(8048,plain,
! [SV124: $i,SV436: $i,SV704: $i,SV906: $i,SV1025: $i,SV1086: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1086 @ ( tc_fun @ SV1025 @ tc_HOL_Obool ) ) ) @ SV906 ) @ SV704 ) @ SV436 ) @ SV124 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV704 @ SV436 ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7844]) ).
thf(8049,plain,
! [SV126: $i,SV438: $i,SV705: $i,SV907: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV907 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7845]) ).
thf(8050,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7846]) ).
thf(8051,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7847]) ).
thf(8052,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( ! [SY2628: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2628 ) ) )
= $false )
| ( ( ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7848]) ).
thf(8053,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( ! [SY2631: $i,SY2632: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2631 ) @ SY2632 ) ) ) )
= $false )
| ( ( ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7849]) ).
thf(8054,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
| ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7850]) ).
thf(8055,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i,SV1118: $i,SV1127: $i] :
( ( ! [SY3074: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY3074 @ SV1127 @ SV1118 @ SV1088 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SV1127 @ SV1118 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7851]) ).
thf(8056,plain,
! [SV446: $i,SV1128: $i,SV134: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV134 @ SV1128 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7852]) ).
thf(8057,plain,
! [SV446: $i,SV134: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV134 @ ( sK3_SY1456 @ SV446 @ SV134 ) ) ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7853]) ).
thf(8058,plain,
! [SV135: $i,SV447: $i,SV713: $i,SV911: $i,SV1028: $i,SV1089: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1089 @ ( tc_fun @ SV1028 @ tc_HOL_Obool ) ) ) @ SV911 ) @ SV713 ) @ SV447 ) @ SV135 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV911 @ SV447 ) @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7854]) ).
thf(8059,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7855]) ).
thf(8060,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
| ( SV448 = SV136 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7856]) ).
thf(8061,plain,
! [SV912: $i,SV137: $i,SV449: $i,SV715: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV449 ) @ SV137 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV715 @ SV137 ) @ SV449 ) )
= $true )
| ( ( c_Predicate_Osymp @ SV912 @ SV715 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7857]) ).
thf(8062,plain,
! [SV142: $i,SV454: $i,SV718: $i,SV913: $i,SV1029: $i,SV1090: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1090 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7858]) ).
thf(8063,plain,
! [SV914: $i,SV455: $i,SV143: $i,SV719: $i] :
( ( ( hBOOL @ ( hAPP @ SV719 @ SV143 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV455 @ SV143 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV914 @ tc_HOL_Obool ) ) @ SV719 ) @ SV455 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7859]) ).
thf(8064,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7861]) ).
thf(8065,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ~ ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7861]) ).
thf(8066,plain,
! [SV459: $i,SV723: $i,SV147: $i,SV916: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV723 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV916 ) @ SV147 ) @ SV459 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV916 @ tc_HOL_Obool ) ) @ SV723 ) @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7862]) ).
thf(8067,plain,
! [SV1031: $i,SV148: $i,SV460: $i,SV724: $i,SV917: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7863]) ).
thf(8068,plain,
! [SV461: $i,SV149: $i,SV725: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) ) )
= $true )
| ( ( SV149 = SV461 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV725 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7864]) ).
thf(8069,plain,
! [SV151: $i,SV463: $i,SV727: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7866]) ).
thf(8070,plain,
! [SV727: $i,SV151: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV463 @ SV151 ) @ SV151 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Quotient_ORespects @ SV727 @ SV463 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7867]) ).
thf(8071,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i] :
( ( ! [SY3075: $i,SY3076: $i,SY3077: $i] :
( ( ( hAPP @ SY3077 @ ( hAPP @ SY3076 @ SY3075 ) )
!= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3077 ) @ SY3076 ) @ SY3075 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7868]) ).
thf(8072,plain,
! [SV1034: $i,SV154: $i,SV466: $i,SV730: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV1034 @ SV920 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7869]) ).
thf(8073,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $false )
| ( ( ! [SY2673: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2673 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2673 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7870]) ).
thf(8074,plain,
! [SV731: $i,SV155: $i,SV467: $i] :
( ( ( ! [SY2674: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SY2674 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SY2674 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7871]) ).
thf(8075,plain,
! [SV158: $i,SV470: $i,SV733: $i,SV921: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV921 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7873]) ).
thf(8076,plain,
! [SV735: $i,SV472: $i,SV160: $i,SV923: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV160 ) @ SV472 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV160 ) ) @ SV472 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV923 @ tc_HOL_Obool ) ) @ SV735 ) @ SV472 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7875]) ).
thf(8077,plain,
! [SV161: $i,SV473: $i] :
( ( ( ! [SY2243: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2243 ) @ SV161 ) ) )
= $true )
| ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7876]) ).
thf(8078,plain,
! [SV473: $i,SV161: $i] :
( ( ( SV161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ~ ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7877]) ).
thf(8079,plain,
! [SV736: $i,SV162: $i,SV924: $i,SV474: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) ) )
= $false )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7878]) ).
thf(8080,plain,
! [SV924: $i,SV162: $i,SV736: $i,SV474: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) ) )
= $false )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7878]) ).
thf(8081,plain,
! [SV163: $i,SV475: $i,SV737: $i,SV925: $i,SV1035: $i,SV1094: $i] :
( ( ( c_Typedef_Otype__definition @ SV1094 @ SV1035 @ SV925 @ SV737 @ SV475 )
= $false )
| ( ( ( hAPP @ SV737 @ ( hAPP @ SV925 @ SV163 ) )
= SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7879]) ).
thf(8082,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i,SV1095: $i,SV1120: $i,SV1130: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1130 @ SV1120 ) @ SV1095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SV1130 @ SV1037 ) @ SV1120 ) @ SV927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7881]) ).
thf(8083,plain,
! [SV480: $i,SV168: $i,SV741: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
| ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7882]) ).
thf(8084,plain,
! [SV169: $i,SV481: $i,SV742: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
= $false )
| ( ( SV481 = SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7883]) ).
thf(8085,plain,
! [SV742: $i,SV169: $i,SV481: $i] :
( ( ( SV481 = SV169 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV742 ) @ SV481 )
= ( hAPP @ ( c_List_Orev @ SV742 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7884]) ).
thf(8086,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
!= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
= $true )
| ( ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7885]) ).
thf(8087,plain,
! [SV482: $i,SV928: $i,SV743: $i,SV170: $i] :
( ( ( SV170
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7886]) ).
thf(8088,plain,
! [SV744: $i,SV171: $i,SV483: $i] :
( ( ( ( SV483 != SV171 )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7887]) ).
thf(8089,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
| ( SV483 = SV171 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7888]) ).
thf(8090,plain,
! [SV485: $i,SV173: $i] :
( ( ( class_Enum_Oenum @ SV173 )
= $false )
| ( ( class_Enum_Oenum @ SV485 )
= $false )
| ( ( class_Enum_Oenum @ ( tc_fun @ SV485 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7889]) ).
thf(8091,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i,SV1038: $i,SV1096: $i,SV1121: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7890]) ).
thf(8092,plain,
! [SV746: $i,SV930: $i,SV175: $i,SV487: $i,SV1039: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7891]) ).
thf(8093,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
= $true )
| ( ( SV747 = SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7892]) ).
thf(8094,plain,
! [SV488: $i,SV931: $i,SV176: $i,SV747: $i] :
( ( ( SV747 != SV176 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7893]) ).
thf(8095,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
= $true )
| ( ( SV490 = SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7895]) ).
thf(8096,plain,
! [SV749: $i,SV933: $i,SV178: $i,SV490: $i] :
( ( ( SV490 != SV178 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7896]) ).
thf(8097,plain,
! [SV179: $i,SV491: $i,SV750: $i,SV934: $i,SV1041: $i,SV1097: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7897]) ).
thf(8098,plain,
! [SV181: $i,SV493: $i,SV752: $i,SV935: $i,SV1042: $i,SV1098: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1098 @ SV1042 ) @ SV935 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV752 @ ( tc_fun @ SV493 @ tc_HOL_Obool ) ) ) @ SV1098 ) @ SV181 ) @ SV1042 ) @ SV935 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7899]) ).
thf(8099,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
| ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7900]) ).
thf(8100,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ~ ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7901]) ).
thf(8101,plain,
! [SV495: $i,SV754: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV754 ) @ SV495 ) )
= $true )
| ( ( SV754 = SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7902]) ).
thf(8102,plain,
! [SV754: $i,SV495: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV183 @ tc_HOL_Obool ) ) @ SV495 ) @ SV754 ) )
= $true )
| ( ( SV754 = SV495 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[7903]) ).
thf(8103,plain,
! [SV755: $i,SV184: $i,SV496: $i,SV937: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV496 ) @ SV184 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV184 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV937 @ tc_HOL_Obool ) ) @ SV755 ) @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7904]) ).
thf(8104,plain,
! [SV185: $i,SV497: $i,SV756: $i,SV938: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
= $false )
| ( ( ( SV497 != SV185 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV938 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7905]) ).
thf(8105,plain,
! [SV186: $i,SV498: $i,SV757: $i,SV939: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
= $false )
| ( ( ( SV757 != SV186 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV939 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7906]) ).
thf(8106,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV1044: $i,SV940: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SV1044 ) ) @ SV758 ) @ SV499 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1044 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV1044 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7907]) ).
thf(8107,plain,
! [SV501: $i,SV189: $i,SV760: $i,SV942: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV189 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV501 ) @ SV189 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV942 @ tc_HOL_Obool ) ) @ SV760 ) @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7909]) ).
thf(8108,plain,
! [SV761: $i,SV190: $i,SV502: $i,SV943: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV502 ) @ SV190 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV943 @ tc_HOL_Obool ) ) @ SV761 ) @ SV502 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7910]) ).
thf(8109,plain,
! [SV944: $i,SV191: $i,SV503: $i,SV762: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV503 ) @ SV191 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV762 @ SV191 ) @ SV503 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV944 @ SV762 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7911]) ).
thf(8110,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7912]) ).
thf(8111,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7914]) ).
thf(8112,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7915]) ).
thf(8113,plain,
! [SV507: $i,SV195: $i,SV765: $i,SV947: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7916]) ).
thf(8114,plain,
! [SV197: $i,SV509: $i,SV767: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 )
= $false )
| ( ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7917]) ).
thf(8115,plain,
! [SV197: $i,SV767: $i,SV509: $i] :
( ( ( SV509
= ( hAPP @ ( c_List_Orev @ SV767 ) @ SV197 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV767 ) @ SV509 )
= SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7918]) ).
thf(8116,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i,SV1046: $i,SV1099: $i] :
( ( ( SV1099 != SV1046 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1099 ) @ SV511 ) ) @ SV1046 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1046 ) @ SV199 ) ) @ SV1099 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7921]) ).
thf(8117,plain,
! [SV201: $i,SV950: $i,SV513: $i,SV770: $i] :
( ( ( SV770 = SV513 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV950 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7922]) ).
thf(8118,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) ) )
= $true )
| ( ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7923]) ).
thf(8119,plain,
! [SV951: $i,SV514: $i,SV202: $i,SV771: $i] :
( ( ( ~ ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7924]) ).
thf(8120,plain,
! [SV211: $i,SV523: $i,SV776: $i,SV953: $i,SV1047: $i,SV1101: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1101 @ SV1047 ) @ SV953 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV776 @ ( tc_fun @ SV523 @ tc_HOL_Obool ) ) ) @ SV211 ) @ SV1101 ) @ SV1047 ) @ SV953 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7926]) ).
thf(8121,plain,
! [SV954: $i,SV212: $i,SV777: $i,SV524: $i] :
( ( ( hBOOL @ ( hAPP @ SV524 @ SV777 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV212 @ tc_HOL_Obool ) ) @ SV954 ) @ SV524 ) @ SV777 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV954 @ SV777 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7927]) ).
thf(8122,plain,
! [SV778: $i,SV955: $i,SV213: $i,SV525: $i,SV1048: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7928]) ).
thf(8123,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) ) )
= $true )
| ( ( ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7929]) ).
thf(8124,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ( ~ ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7930]) ).
thf(8125,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
| ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7931]) ).
thf(8126,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7932]) ).
thf(8127,plain,
! [SV530: $i,SV218: $i,SV781: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) ) )
= $true )
| ( ( SV530 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7933]) ).
thf(8128,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7934]) ).
thf(8129,plain,
! [SV958: $i,SV1050: $i,SV531: $i,SV219: $i,SV782: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7935]) ).
thf(8130,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
| ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7937]) ).
thf(8131,plain,
! [SV960: $i,SV1052: $i,SV222: $i,SV785: $i,SV534: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7938]) ).
thf(8132,plain,
! [SV535: $i,SV786: $i,SV223: $i,SV961: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV786 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV961 ) @ SV223 ) @ SV535 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV961 @ tc_HOL_Obool ) ) @ SV786 ) @ SV535 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7939]) ).
thf(8133,plain,
! [SV224: $i,SV962: $i,SV536: $i,SV787: $i] :
( ( ( SV787 = SV536 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV962 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7940]) ).
thf(8134,plain,
! [SV538: $i,SV226: $i] :
( ( ( class_Finite__Set_Ofinite @ SV226 )
= $false )
| ( ( class_Finite__Set_Ofinite @ SV538 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV538 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7941]) ).
thf(8135,plain,
! [SV964: $i,SV228: $i,SV789: $i,SV540: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV789 ) @ SV228 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV540 ) @ SV964 ) @ SV228 ) )
= $true )
| ( ( SV964 = SV789 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7944]) ).
thf(8136,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ~ ( ( SV1102 != SV1053 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7945]) ).
thf(8137,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ~ ( ~ ( ( SV1102 != SV1053 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[7945]) ).
thf(8138,plain,
! [SV231: $i,SV543: $i,SV792: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
= $false )
| ( ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7946]) ).
thf(8139,plain,
! [SV231: $i,SV792: $i,SV543: $i] :
( ( ( SV543
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV792 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV792 @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV792 ) @ SV543 ) @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7947]) ).
thf(8140,plain,
! [SV232: $i,SV544: $i,SV793: $i] :
( ( ( SV793 = SV544 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7948]) ).
thf(8141,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) ) )
= $false )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7949]) ).
thf(8142,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
= $true )
| ( ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7951]) ).
thf(8143,plain,
! [SV548: $i,SV797: $i,SV969: $i,SV236: $i] :
( ( ( SV236
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7952]) ).
thf(8144,plain,
! [SV237: $i,SV549: $i,SV798: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $false )
| ( ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7953]) ).
thf(8145,plain,
! [SV237: $i,SV798: $i,SV549: $i] :
( ( ( SV549
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV798 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Equiv__Relations_Oquotient @ SV798 ) @ SV549 ) @ SV237 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ SV798 @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7954]) ).
thf(8146,plain,
! [SV238: $i,SV970: $i,SV550: $i,SV799: $i] :
( ( ( SV799 != SV550 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7955]) ).
thf(8147,plain,
! [SV240: $i,SV552: $i,SV801: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7956]) ).
thf(8148,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( ~ ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7957]) ).
thf(8149,plain,
! [SV971: $i,SV553: $i,SV241: $i,SV802: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV802 @ SV241 ) @ SV553 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV241 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV971 @ SV802 ) @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7958]) ).
thf(8150,plain,
! [SV557: $i,SV245: $i,SV805: $i,SV974: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV245 ) )
= $false )
| ( ( SV557 = SV245 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ SV974 @ SV805 ) @ SV557 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7962]) ).
thf(8151,plain,
! [SV247: $i,SV559: $i,SV975: $i,SV807: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7963]) ).
thf(8152,plain,
! [SV807: $i,SV247: $i,SV559: $i,SV975: $i] :
( ( ( ~ ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) ) )
= $false )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7963]) ).
thf(8153,plain,
! [SV248: $i,SV560: $i,SV808: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SV1056 ) @ SV976 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7964]) ).
thf(8154,plain,
! [SV810: $i,SV252: $i,SV564: $i,SV977: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV977 @ tc_HOL_Obool ) ) @ SV564 ) @ SV252 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV252 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV977 ) @ SV810 ) @ SV564 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7967]) ).
thf(8155,plain,
! [SV253: $i,SV565: $i,SV811: $i,SV978: $i,SV1057: $i,SV1104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1104 @ SV1057 ) @ SV978 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SV1104 ) @ SV811 ) @ SV1057 ) @ SV978 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7968]) ).
thf(8156,plain,
! [SV566: $i,SV1131: $i,SV254: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV254 @ SV1131 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[7969]) ).
thf(8157,plain,
! [SV566: $i,SV254: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV254 @ ( sK4_SY1809 @ SV566 @ SV254 ) ) ) )
= $false )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[7970]) ).
thf(8158,plain,
! [SV256: $i,SV1058: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7971]) ).
thf(8159,plain,
! [SV258: $i,SV570: $i,SV813: $i,SV979: $i,SV1059: $i,SV1105: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple @ SV1105 @ SV1059 @ SV979 @ SV813 @ SV570 @ SV258 )
= $false )
| ( ( ( hAPP @ SV258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1059 @ tc_HOL_Obool ) ) )
= SV813 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7973]) ).
thf(8160,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i,SV1106: $i,SV1122: $i,SV1132: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1132 @ SV1122 @ SV1106 @ SV1060 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SV1122 @ SV1106 @ SV571 ) @ SV259 ) )
| ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7974]) ).
thf(8161,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i,SV1061: $i,SV1107: $i] :
( ( ( SV1107 != SV1061 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SV1061 @ SV260 ) @ SV1107 )
= ( hAPP @ SV572 @ SV1107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7975]) ).
thf(8162,plain,
! [SV262: $i,SV574: $i,SV817: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
= $false )
| ( ( SV574 = SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7977]) ).
thf(8163,plain,
! [SV817: $i,SV262: $i,SV574: $i] :
( ( ( SV574 = SV262 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV817 ) @ SV574 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV817 ) @ SV262 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV817 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7978]) ).
thf(8164,plain,
! [SV818: $i,SV982: $i,SV263: $i,SV575: $i,SV1062: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7979]) ).
thf(8165,plain,
! [SV264: $i,SV576: $i,SV819: $i,SV983: $i,SV1063: $i,SV1108: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false )
| ( ( ~ ( ( SV983 != SV576 )
| ( SV819 != SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7980]) ).
thf(8166,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i,SV1064: $i,SV1109: $i,SV1123: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1123 @ SV1109 @ SV1064 @ SV984 ) @ SV821 )
!= SV579 )
= $true )
| ( ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7981]) ).
thf(8167,plain,
! [SV268: $i,SV580: $i] :
( ( ( ! [SY2454: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2454 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7982]) ).
thf(8168,plain,
! [SV268: $i,SV580: $i] :
( ( ( ! [SY2455: $i] :
~ ( hBOOL @ ( hAPP @ SV580 @ SY2455 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[7983]) ).
thf(8169,plain,
! [SV269: $i,SV581: $i,SV822: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7984]) ).
thf(8170,plain,
! [SV581: $i,SV269: $i,SV822: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) @ SV581 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV581 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV822 @ tc_HOL_Obool ) ) @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7985]) ).
thf(8171,plain,
! [SV1065: $i,SV270: $i,SV582: $i,SV823: $i,SV985: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7986]) ).
thf(8172,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7987]) ).
thf(8173,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) ) )
= $true )
| ( ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7988]) ).
thf(8174,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ( ~ ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7989]) ).
thf(8175,plain,
! [SV275: $i,SV587: $i,SV827: $i,SV988: $i,SV1066: $i,SV1110: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV988 )
= SV827 )
= $false )
| ( ( ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV988 ) @ SV275 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV827 ) @ SV275 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7990]) ).
thf(8176,plain,
! [SV828: $i,SV989: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) ) )
= $false )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7991]) ).
thf(8177,plain,
! [SV989: $i,SV828: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) ) )
= $false )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7991]) ).
thf(8178,plain,
! [SV589: $i,SV829: $i,SV277: $i,SV990: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV829 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV990 ) @ SV277 ) @ SV589 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV990 @ tc_HOL_Obool ) ) @ SV829 ) @ SV589 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7992]) ).
thf(8179,plain,
! [SV830: $i,SV278: $i,SV590: $i,SV991: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV590 ) @ SV278 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV278 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV991 @ tc_HOL_Obool ) ) @ SV830 ) @ SV590 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7993]) ).
thf(8180,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
| ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7994]) ).
thf(8181,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ~ ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7995]) ).
thf(8182,plain,
! [SV834: $i,SV994: $i,SV596: $i,SV284: $i,SV1068: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1068 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV284 )
= $true )
| ( ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV596 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7996]) ).
thf(8183,plain,
! [SV598: $i,SV995: $i,SV286: $i,SV835: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV835 @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7999]) ).
thf(8184,plain,
! [SV835: $i,SV995: $i,SV286: $i,SV598: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV598 @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[7999]) ).
thf(8185,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) )
| ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8000]) ).
thf(8186,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) )
| ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8001]) ).
thf(8187,plain,
! [SV289: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ ( sK5_SY2494 @ SV289 @ SV600 ) ) @ SV289 ) ) )
= $false )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8002]) ).
thf(8188,plain,
! [SV289: $i,SV1133: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SV1133 ) @ SV289 ) ) )
= $true )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8003]) ).
thf(8189,plain,
! [SV291: $i,SV601: $i,SV1124: $i,SV836: $i] :
( ( ( hBOOL @ ( hAPP @ SV836 @ SV1124 ) )
= $false )
| ( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
| ( hBOOL @ ( hAPP @ SV836 @ SV601 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8004]) ).
thf(8190,plain,
! [SV604: $i,SV294: $i,SV838: $i,SV996: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV996 @ SV838 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8005]) ).
thf(8191,plain,
! [SV296: $i,SV606: $i,SV840: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV606 ) @ SV296 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV840 ) @ SV296 ) @ SV606 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV840 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8008]) ).
thf(8192,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV1070: $i,SV998: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SV1070 ) ) @ SV841 ) @ SV607 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1070 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV1070 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8009]) ).
thf(8193,plain,
! [SV299: $i,SV609: $i,SV843: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8010]) ).
thf(8194,plain,
! [SV609: $i,SV299: $i,SV843: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ SV299 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ SV843 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV843 ) @ SV609 ) @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8011]) ).
thf(8195,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8013]) ).
thf(8196,plain,
! [SV301: $i,SV611: $i,SV845: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 )
= SV301 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV845 @ tc_HOL_Obool ) ) @ SV611 ) @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8014]) ).
thf(8197,plain,
! [SV1000: $i,SV303: $i,SV613: $i,SV846: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV613 ) @ SV303 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV846 @ SV303 ) @ SV613 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1000 @ SV846 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8017]) ).
thf(8198,plain,
! [SV305: $i,SV615: $i,SV848: $i,SV1001: $i,SV1072: $i,SV1111: $i] :
( ( ( SV1111 = SV1072 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1111 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV1001 @ SV848 @ SV615 ) @ SV305 ) @ SV1072 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8018]) ).
thf(8199,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) ) )
= $true )
| ( ( ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8019]) ).
thf(8200,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8020]) ).
thf(8201,plain,
! [SV1003: $i,SV619: $i,SV309: $i,SV852: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV852 @ SV309 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV619 @ SV309 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8021]) ).
thf(8202,plain,
! [SV853: $i,SV311: $i,SV1004: $i,SV621: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV621 @ tc_HOL_Obool ) ) @ SV1004 ) @ SV311 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV853 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1004 @ SV853 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8022]) ).
thf(8203,plain,
! [SV312: $i,SV622: $i,SV854: $i] :
( ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
= $false )
| ( ( SV622 = SV312 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8023]) ).
thf(8204,plain,
! [SV854: $i,SV312: $i,SV622: $i] :
( ( ( SV622 = SV312 )
= $false )
| ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV622 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ SV854 @ tc_HOL_Obool ) ) @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8024]) ).
thf(8205,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8025]) ).
thf(8206,plain,
! [SV1005: $i,SV1073: $i,SV624: $i,SV314: $i,SV856: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8026]) ).
thf(8207,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $false )
| ( ( ! [SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2833 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2833 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8027]) ).
thf(8208,plain,
! [SV857: $i,SV315: $i,SV625: $i] :
( ( ( ! [SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY2834 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SY2834 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8028]) ).
thf(8209,plain,
! [SV859: $i,SV318: $i,SV628: $i,SV1006: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ SV318 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV628 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV318 ) @ SV859 ) )
= SV859 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1006 @ tc_HOL_Obool ) ) @ SV859 ) @ SV628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8030]) ).
thf(8210,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ~ ( ( SV1112 != SV1074 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8031]) ).
thf(8211,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ~ ( ~ ( ( SV1112 != SV1074 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8031]) ).
thf(8212,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i,SV1075: $i,SV1113: $i,SV1125: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV1125 @ SV1113 @ SV1075 @ SV1008 @ SV861 @ SV630 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV1075 @ SV320 ) @ SV320 )
= SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8032]) ).
thf(8213,plain,
! [SV322: $i,SV632: $i,SV863: $i,SV1009: $i,SV1076: $i,SV1114: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8033]) ).
thf(8214,plain,
! [SV103: $i,SV416: $i,SV689: $i,SV896: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
= $false )
| ( ( SV416 = SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8034]) ).
thf(8215,plain,
! [SV689: $i,SV896: $i,SV103: $i,SV416: $i] :
( ( ( SV416 = SV103 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV896 @ SV689 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV896 ) @ SV416 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV896 @ tc_HOL_Obool ) ) ) ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8035]) ).
thf(8216,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
| ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SV1134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8038]) ).
thf(8217,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8039]) ).
thf(8218,plain,
! [SV113: $i,SV694: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8040]) ).
thf(8219,plain,
! [SV694: $i,SV113: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8040]) ).
thf(8220,plain,
! [SV901: $i,SV1022: $i,SV114: $i,SV1085: $i,SV427: $i,SV695: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SV1085 ) @ SV114 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1085 @ SV1022 ) @ SV901 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8041]) ).
thf(8221,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
!= SV697 )
= $true )
| ( ( ( hAPP @ SV697 @ SV429 )
= SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8042]) ).
thf(8222,plain,
! [SV902: $i,SV1023: $i,SV117: $i,SV429: $i,SV697: $i] :
( ( ( ( hAPP @ SV697 @ SV429 )
!= SV117 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8043]) ).
thf(8223,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true )
| ( ( ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8044]) ).
thf(8224,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( ~ ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8045]) ).
thf(8225,plain,
! [SV438: $i,SV705: $i,SV126: $i,SV907: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV907 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8049]) ).
thf(8226,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8050]) ).
thf(8227,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
| ~ ( ( SV439 != SV127 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8051]) ).
thf(8228,plain,
! [SV440: $i,SV128: $i,SV707: $i] :
( ( ( hBOOL @ ( hAPP @ SV707 @ ( sK7_SY2628 @ SV128 @ SV440 @ SV707 ) ) )
= $false )
| ( ( ! [SY2629: $i,SY2630: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SY2629 ) @ SY2630 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8052]) ).
thf(8229,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( ! [SY3079: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ ( sK8_SY2631 @ SV128 @ SV440 @ SV707 ) ) @ SY3079 ) ) ) )
= $false )
| ( ( ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8053]) ).
thf(8230,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8054]) ).
thf(8231,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ~ ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8054]) ).
thf(8232,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i,SV1118: $i,SV1127: $i,SV1135: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1135 @ SV1127 @ SV1118 @ SV1088 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SV1127 @ SV1118 @ SV711 ) @ SV444 ) )
| ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8055]) ).
thf(8233,plain,
! [SV446: $i,SV1128: $i,SV134: $i] :
( ( ( hBOOL @ ( hAPP @ SV134 @ SV1128 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8056]) ).
thf(8234,plain,
! [SV446: $i,SV134: $i] :
( ( ( hBOOL @ ( hAPP @ SV134 @ ( sK3_SY1456 @ SV446 @ SV134 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_OCollect @ SV446 ) @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8057]) ).
thf(8235,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $true )
| ( ( SV448 = SV136 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8059]) ).
thf(8236,plain,
! [SV136: $i,SV448: $i,SV714: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8060]) ).
thf(8237,plain,
! [SV714: $i,SV136: $i,SV448: $i] :
( ( ( SV448 = SV136 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV714 @ tc_HOL_Obool ) ) @ SV448 ) @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8060]) ).
thf(8238,plain,
! [SV1029: $i,SV1090: $i,SV718: $i,SV142: $i,SV454: $i,SV913: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1090 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8062]) ).
thf(8239,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
| ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8064]) ).
thf(8240,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8065]) ).
thf(8241,plain,
! [SV1031: $i,SV148: $i,SV460: $i,SV724: $i,SV917: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8067]) ).
thf(8242,plain,
! [SV461: $i,SV149: $i,SV725: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV149 ) @ SV461 ) )
= $false )
| ( ( SV149 = SV461 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV725 ) @ SV461 ) @ SV149 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV725 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8068]) ).
thf(8243,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i,SV1136: $i] :
( ( ! [SY3080: $i,SY3081: $i] :
( ( ( hAPP @ SY3081 @ ( hAPP @ SY3080 @ SV1136 ) )
!= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3081 ) @ SY3080 ) @ SV1136 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8071]) ).
thf(8244,plain,
! [SV1034: $i,SV154: $i,SV466: $i,SV730: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) ) )
= $true )
| ( ( c_Predicate_Otransp @ SV1034 @ SV920 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8072]) ).
thf(8245,plain,
! [SV731: $i,SV155: $i,SV1137: $i,SV467: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SV1137 ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV1137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8073]) ).
thf(8246,plain,
! [SV155: $i,SV731: $i,SV467: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ ( sK9_SY2674 @ SV731 @ SV155 @ SV467 ) ) @ SV155 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ ( sK9_SY2674 @ SV731 @ SV155 @ SV467 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8074]) ).
thf(8247,plain,
! [SV733: $i,SV158: $i,SV470: $i,SV921: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
= $false )
| ( ( class_Orderings_Opreorder @ SV921 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8075]) ).
thf(8248,plain,
! [SV161: $i,SV1138: $i,SV473: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SV1138 ) @ SV161 ) ) )
= $true )
| ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8077]) ).
thf(8249,plain,
! [SV161: $i,SV473: $i] :
( ( ( ! [SY2244: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SY2244 ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8078]) ).
thf(8250,plain,
! [SV736: $i,SV162: $i,SV924: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8079]) ).
thf(8251,plain,
! [SV924: $i,SV162: $i,SV736: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8080]) ).
thf(8252,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i,SV1095: $i,SV1120: $i,SV1130: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1130 @ SV1120 ) @ SV1095 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SV1130 @ SV1037 ) @ SV1120 ) @ SV927 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8082]) ).
thf(8253,plain,
! [SV480: $i,SV168: $i,SV741: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8083]) ).
thf(8254,plain,
! [SV741: $i,SV480: $i,SV168: $i] :
( ( ( ~ ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8083]) ).
thf(8255,plain,
! [SV170: $i,SV482: $i,SV743: $i,SV928: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
= $false )
| ( ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8086]) ).
thf(8256,plain,
! [SV482: $i,SV928: $i,SV743: $i,SV170: $i] :
( ( ( SV170
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV743 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV928 @ tc_HOL_Obool ) )
= ( hAPP @ ( c_Set_Oimage @ SV743 @ SV928 @ SV482 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8087]) ).
thf(8257,plain,
! [SV744: $i,SV171: $i,SV483: $i] :
( ( ( SV483 != SV171 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8088]) ).
thf(8258,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
= $true )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8089]) ).
thf(8259,plain,
! [SV174: $i,SV486: $i,SV745: $i,SV929: $i,SV1038: $i,SV1096: $i,SV1121: $i] :
( ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8091]) ).
thf(8260,plain,
! [SV746: $i,SV930: $i,SV175: $i,SV487: $i,SV1039: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV487 ) @ SV175 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV175 ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV746 ) @ SV487 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1039 @ tc_HOL_Obool ) ) @ SV930 ) @ SV746 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8092]) ).
thf(8261,plain,
! [SV176: $i,SV488: $i,SV747: $i,SV931: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
= $false )
| ( ( SV747 = SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8093]) ).
thf(8262,plain,
! [SV488: $i,SV931: $i,SV176: $i,SV747: $i] :
( ( ( SV747 = SV176 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV747 ) @ SV488 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV931 ) @ SV176 ) @ SV488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8094]) ).
thf(8263,plain,
! [SV178: $i,SV490: $i,SV749: $i,SV933: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
= $false )
| ( ( SV490 = SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8095]) ).
thf(8264,plain,
! [SV749: $i,SV933: $i,SV178: $i,SV490: $i] :
( ( ( SV490 = SV178 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV490 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV933 ) @ SV749 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8096]) ).
thf(8265,plain,
! [SV1041: $i,SV1097: $i,SV750: $i,SV179: $i,SV491: $i,SV934: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8097]) ).
thf(8266,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) ) )
= $true )
| ( ( ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8099]) ).
thf(8267,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ( ~ ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8100]) ).
thf(8268,plain,
! [SV756: $i,SV938: $i,SV185: $i,SV497: $i] :
( ( ( SV497 != SV185 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
= $false )
| ( ( class_Orderings_Oord @ SV938 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8104]) ).
thf(8269,plain,
! [SV498: $i,SV939: $i,SV186: $i,SV757: $i] :
( ( ( SV757 != SV186 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV939 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8105]) ).
thf(8270,plain,
! [SV187: $i,SV499: $i,SV758: $i,SV1044: $i,SV940: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV940 @ SV1044 ) ) @ SV758 ) @ SV499 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1044 ) @ ( hAPP @ SV758 @ SV187 ) ) @ ( hAPP @ SV499 @ SV187 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV1044 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8106]) ).
thf(8271,plain,
! [SV192: $i,SV504: $i,SV763: $i,SV945: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ SV504 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV945 ) @ SV763 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV945 ) @ SV192 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8110]) ).
thf(8272,plain,
! [SV193: $i,SV505: $i,SV764: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8111]) ).
thf(8273,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8112]) ).
thf(8274,plain,
! [SV507: $i,SV195: $i,SV765: $i,SV947: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8113]) ).
thf(8275,plain,
! [SV199: $i,SV511: $i,SV768: $i,SV948: $i,SV1046: $i,SV1099: $i] :
( ( ( SV1099 = SV1046 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1099 ) @ SV511 ) ) @ SV1046 ) @ SV199 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV948 @ SV768 ) @ SV1046 ) @ SV199 ) ) @ SV1099 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8116]) ).
thf(8276,plain,
! [SV770: $i,SV201: $i,SV513: $i,SV950: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) )
= $true )
| ( ( SV770 = SV513 )
= $false )
| ( ( class_Orderings_Oord @ SV950 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8117]) ).
thf(8277,plain,
! [SV202: $i,SV514: $i,SV771: $i,SV951: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $false )
| ( ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8118]) ).
thf(8278,plain,
! [SV951: $i,SV514: $i,SV202: $i,SV771: $i] :
( ( ( ( SV771 = SV202 )
| ( hBOOL @ ( hAPP @ SV514 @ SV202 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8119]) ).
thf(8279,plain,
! [SV778: $i,SV955: $i,SV213: $i,SV525: $i,SV1048: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV525 ) @ SV213 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV525 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV778 ) @ SV213 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1048 @ tc_HOL_Obool ) ) @ SV955 ) @ SV778 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8122]) ).
thf(8280,plain,
! [SV215: $i,SV527: $i,SV779: $i,SV956: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $false )
| ( ( ~ ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8123]) ).
thf(8281,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ( ~ ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8124]) ).
thf(8282,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true )
| ( ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8125]) ).
thf(8283,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ~ ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8126]) ).
thf(8284,plain,
! [SV530: $i,SV218: $i,SV781: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV218 ) @ SV530 ) )
= $false )
| ( ( SV530 = SV218 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV781 ) @ SV530 ) @ SV218 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8127]) ).
thf(8285,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8128]) ).
thf(8286,plain,
! [SV958: $i,SV1050: $i,SV531: $i,SV219: $i,SV782: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8129]) ).
thf(8287,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8130]) ).
thf(8288,plain,
! [SV960: $i,SV1052: $i,SV222: $i,SV785: $i,SV534: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8131]) ).
thf(8289,plain,
! [SV787: $i,SV536: $i,SV224: $i,SV962: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) )
= $true )
| ( ( SV787 = SV536 )
= $false )
| ( ( class_Orderings_Oorder @ SV962 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8133]) ).
thf(8290,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( SV1102 != SV1053 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8136]) ).
thf(8291,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ~ ( ( SV1102 != SV1053 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8137]) ).
thf(8292,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
= $false )
| ( ( SV793 = SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8140]) ).
thf(8293,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
= $true )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8141]) ).
thf(8294,plain,
! [SV236: $i,SV548: $i,SV797: $i,SV969: $i] :
( ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
= $false )
| ( ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8142]) ).
thf(8295,plain,
! [SV548: $i,SV797: $i,SV969: $i,SV236: $i] :
( ( ( SV236
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV969 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( hAPP @ ( c_Set_Oimage @ SV969 @ SV797 @ SV548 ) @ SV236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV797 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8143]) ).
thf(8296,plain,
! [SV238: $i,SV970: $i,SV550: $i,SV799: $i] :
( ( ( SV799 = SV550 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ SV238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV970 ) @ SV799 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV970 ) @ SV550 ) @ SV238 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8146]) ).
thf(8297,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8147]) ).
thf(8298,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
| ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8148]) ).
thf(8299,plain,
! [SV247: $i,SV559: $i,SV975: $i,SV807: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
| ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8151]) ).
thf(8300,plain,
! [SV807: $i,SV247: $i,SV559: $i,SV975: $i] :
( ( ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8152]) ).
thf(8301,plain,
! [SV808: $i,SV248: $i,SV560: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8153]) ).
thf(8302,plain,
! [SV1103: $i,SV248: $i,SV560: $i,SV976: $i,SV1056: $i,SV808: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV808 @ SV1056 ) @ SV976 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8153]) ).
thf(8303,plain,
! [SV1104: $i,SV253: $i,SV565: $i,SV978: $i,SV1057: $i,SV811: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SV1104 ) @ SV811 ) @ SV1057 ) @ SV978 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1104 @ SV1057 ) @ SV978 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8155]) ).
thf(8304,plain,
! [SV566: $i,SV1131: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ SV1131 ) )
= $false )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8156]) ).
thf(8305,plain,
! [SV566: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ ( sK4_SY1809 @ SV566 @ SV254 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Set_OCollect @ SV566 ) @ SV254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV566 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8157]) ).
thf(8306,plain,
! [SV256: $i,SV1058: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8158]) ).
thf(8307,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i,SV1106: $i,SV1122: $i,SV1132: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1132 @ SV1122 @ SV1106 @ SV1060 ) @ SV980 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SV1122 @ SV1106 @ SV571 ) @ SV259 ) )
= $true )
| ( ( ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8160]) ).
thf(8308,plain,
! [SV260: $i,SV572: $i,SV815: $i,SV981: $i,SV1061: $i,SV1107: $i] :
( ( ( SV1107 = SV1061 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV981 @ SV815 @ SV572 @ SV1061 @ SV260 ) @ SV1107 )
= ( hAPP @ SV572 @ SV1107 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8161]) ).
thf(8309,plain,
! [SV818: $i,SV982: $i,SV263: $i,SV575: $i,SV1062: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV575 ) @ SV263 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV575 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV818 ) @ SV263 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1062 @ tc_HOL_Obool ) ) @ SV982 ) @ SV818 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8164]) ).
thf(8310,plain,
! [SV1063: $i,SV1108: $i,SV264: $i,SV819: $i,SV576: $i,SV983: $i] :
( ( ( ( SV983 != SV576 )
| ( SV819 != SV264 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8165]) ).
thf(8311,plain,
! [SV267: $i,SV579: $i,SV821: $i,SV984: $i,SV1064: $i,SV1109: $i,SV1123: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1123 @ SV1109 @ SV1064 @ SV984 ) @ SV821 )
= SV579 )
= $false )
| ( ( ( hAPP @ SV984 @ ( hAPP @ SV821 @ SV267 ) )
= ( hAPP @ SV579 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8166]) ).
thf(8312,plain,
! [SV268: $i,SV580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV580 @ ( sK10_SY2454 @ SV268 @ SV580 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8167]) ).
thf(8313,plain,
! [SV268: $i,SV1139: $i,SV580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV580 @ SV1139 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8168]) ).
thf(8314,plain,
! [SV1065: $i,SV270: $i,SV582: $i,SV823: $i,SV985: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8171]) ).
thf(8315,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8172]) ).
thf(8316,plain,
! [SV986: $i,SV825: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8172]) ).
thf(8317,plain,
! [SV273: $i,SV585: $i,SV826: $i,SV987: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $false )
| ( ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8173]) ).
thf(8318,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ( ( SV826 = SV585 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8174]) ).
thf(8319,plain,
! [SV827: $i,SV1066: $i,SV275: $i,SV988: $i,SV1110: $i,SV587: $i] :
( ( ( SV587
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV988 ) @ SV275 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV827 ) @ SV275 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV988 )
= SV827 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8175]) ).
thf(8320,plain,
! [SV828: $i,SV989: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8176]) ).
thf(8321,plain,
! [SV989: $i,SV828: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8177]) ).
thf(8322,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8180]) ).
thf(8323,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8181]) ).
thf(8324,plain,
! [SV834: $i,SV994: $i,SV596: $i,SV284: $i,SV1068: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1068 @ tc_HOL_Obool ) ) @ SV284 ) @ SV596 ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV284 )
= $true )
| ( ( c_Fun_Oinj__on @ SV1068 @ SV994 @ SV834 @ SV596 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8182]) ).
thf(8325,plain,
! [SV598: $i,SV995: $i,SV286: $i,SV835: $i] :
( ( ( hBOOL @ ( hAPP @ SV835 @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8183]) ).
thf(8326,plain,
! [SV835: $i,SV995: $i,SV286: $i,SV598: $i] :
( ( ( hBOOL @ ( hAPP @ SV598 @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV995 @ tc_HOL_Obool ) ) @ SV835 ) @ SV598 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8184]) ).
thf(8327,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8185]) ).
thf(8328,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8185]) ).
thf(8329,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) ) )
= $true )
| ( ( ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8186]) ).
thf(8330,plain,
! [SV289: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ ( sK5_SY2494 @ SV289 @ SV600 ) ) @ SV289 ) )
= $true )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8187]) ).
thf(8331,plain,
! [SV289: $i,SV1133: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV600 ) @ SV1133 ) @ SV289 ) )
= $false )
| ( ( SV289
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8188]) ).
thf(8332,plain,
! [SV1124: $i,SV836: $i,SV291: $i,SV601: $i] :
( ( ( SV601
!= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV836 @ SV601 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV836 @ SV1124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8189]) ).
thf(8333,plain,
! [SV604: $i,SV294: $i,SV838: $i,SV996: $i] :
( ( ( hBOOL @ ( hAPP @ SV996 @ SV838 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV294 @ tc_HOL_Obool ) ) @ SV604 ) @ SV996 ) @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8190]) ).
thf(8334,plain,
! [SV297: $i,SV607: $i,SV841: $i,SV1070: $i,SV998: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV998 @ SV1070 ) ) @ SV841 ) @ SV607 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV1070 ) @ ( hAPP @ SV841 @ SV297 ) ) @ ( hAPP @ SV607 @ SV297 ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV1070 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8192]) ).
thf(8335,plain,
! [SV307: $i,SV617: $i,SV850: $i,SV1002: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $false )
| ( ( ~ ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8199]) ).
thf(8336,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ( ~ ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8200]) ).
thf(8337,plain,
! [SV1003: $i,SV619: $i,SV309: $i,SV852: $i] :
( ( ( hBOOL @ ( hAPP @ SV852 @ SV309 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV619 @ SV309 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1003 @ tc_HOL_Obool ) ) @ SV852 ) @ SV619 ) @ SV309 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8201]) ).
thf(8338,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8205]) ).
thf(8339,plain,
! [SV1005: $i,SV1073: $i,SV624: $i,SV314: $i,SV856: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8206]) ).
thf(8340,plain,
! [SV857: $i,SV315: $i,SV1140: $i,SV625: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1140 ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV1140 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8207]) ).
thf(8341,plain,
! [SV315: $i,SV857: $i,SV625: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ ( sK11_SY2834 @ SV857 @ SV315 @ SV625 ) ) @ SV315 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ ( sK11_SY2834 @ SV857 @ SV315 @ SV625 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8208]) ).
thf(8342,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( SV1112 != SV1074 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8210]) ).
thf(8343,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ~ ( ( SV1112 != SV1074 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8211]) ).
thf(8344,plain,
! [SV320: $i,SV630: $i,SV861: $i,SV1008: $i,SV1075: $i,SV1113: $i,SV1125: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV1125 @ SV1113 @ SV1075 @ SV1008 @ SV861 @ SV630 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV1075 @ SV320 ) @ SV320 )
= SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8212]) ).
thf(8345,plain,
! [SV1076: $i,SV1114: $i,SV863: $i,SV322: $i,SV632: $i,SV1009: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8213]) ).
thf(8346,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
| ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) ) )
| ~ ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SV1134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8216]) ).
thf(8347,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
| ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8217]) ).
thf(8348,plain,
! [SV113: $i,SV694: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8218]) ).
thf(8349,plain,
! [SV694: $i,SV113: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8219]) ).
thf(8350,plain,
! [SV901: $i,SV1022: $i,SV114: $i,SV1085: $i,SV427: $i,SV695: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV695 @ ( tc_fun @ SV427 @ tc_HOL_Obool ) ) ) @ SV1085 ) @ SV114 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV114 @ SV1022 ) @ SV901 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1085 @ SV1022 ) @ SV901 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8220]) ).
thf(8351,plain,
! [SV117: $i,SV429: $i,SV697: $i,SV902: $i,SV1023: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 )
= $false )
| ( ( ( hAPP @ SV697 @ SV429 )
= SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8221]) ).
thf(8352,plain,
! [SV902: $i,SV1023: $i,SV117: $i,SV429: $i,SV697: $i] :
( ( ( ( hAPP @ SV697 @ SV429 )
= SV117 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV1023 @ SV902 @ SV697 @ SV429 @ SV117 )
= SV697 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8222]) ).
thf(8353,plain,
! [SV118: $i,SV430: $i,SV698: $i,SV903: $i,SV1024: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false )
| ( ( ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8223]) ).
thf(8354,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( ~ ( ( SV903 != SV430 )
| ( SV698 != SV118 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8224]) ).
thf(8355,plain,
! [SV438: $i,SV705: $i,SV126: $i,SV907: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV705 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV126 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV907 ) @ SV705 ) @ SV438 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV907 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8225]) ).
thf(8356,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8226]) ).
thf(8357,plain,
! [SV706: $i,SV127: $i,SV439: $i] :
( ( ( ~ ( ( SV439 != SV127 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8226]) ).
thf(8358,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) ) )
= $true )
| ( ( ~ ( ( SV439 != SV127 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8227]) ).
thf(8359,plain,
! [SV1141: $i,SV128: $i,SV440: $i,SV707: $i] :
( ( ( ! [SY3082: $i] : ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SV1141 ) @ SY3082 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV707 @ ( sK7_SY2628 @ SV128 @ SV440 @ SV707 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8228]) ).
thf(8360,plain,
! [SV128: $i,SV440: $i,SV707: $i] :
( ( ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ ( sK8_SY2631 @ SV128 @ SV440 @ SV707 ) ) @ ( sK12_SY3079 @ SV128 @ SV440 @ SV707 ) ) ) )
= $false )
| ( ( ! [SY2633: $i] : ( hBOOL @ ( hAPP @ SV707 @ SY2633 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8229]) ).
thf(8361,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
| ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8230]) ).
thf(8362,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[8231]) ).
thf(8363,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i,SV1118: $i,SV1127: $i,SV1135: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1135 @ SV1127 @ SV1118 @ SV1088 ) @ SV1027 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SV1127 @ SV1118 @ SV711 ) @ SV444 ) )
= $true )
| ( ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8232]) ).
thf(8364,plain,
! [SV1029: $i,SV1090: $i,SV718: $i,SV142: $i,SV454: $i,SV913: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV913 @ SV454 ) @ SV142 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV718 @ SV454 ) @ SV142 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1090 @ ( tc_fun @ SV1029 @ tc_HOL_Obool ) ) ) @ SV913 ) @ SV718 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8238]) ).
thf(8365,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true )
| ( ( ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8239]) ).
thf(8366,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( ~ ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8240]) ).
thf(8367,plain,
! [SV1031: $i,SV724: $i,SV148: $i,SV460: $i,SV917: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8241]) ).
thf(8368,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i,SV1136: $i,SV1142: $i] :
( ( ! [SY3083: $i] :
( ( ( hAPP @ SY3083 @ ( hAPP @ SV1142 @ SV1136 ) )
!= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SY3083 ) @ SV1142 ) @ SV1136 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8243]) ).
thf(8369,plain,
! [SV1034: $i,SV730: $i,SV154: $i,SV466: $i,SV920: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV1034 @ SV920 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8244]) ).
thf(8370,plain,
! [SV731: $i,SV155: $i,SV1137: $i,SV467: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SV1137 ) @ SV155 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV1137 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8245]) ).
thf(8371,plain,
! [SV155: $i,SV731: $i,SV467: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ ( sK9_SY2674 @ SV731 @ SV155 @ SV467 ) ) @ SV155 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8246]) ).
thf(8372,plain,
! [SV155: $i,SV467: $i,SV731: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ ( sK9_SY2674 @ SV731 @ SV155 @ SV467 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8246]) ).
thf(8373,plain,
! [SV733: $i,SV158: $i,SV470: $i,SV921: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV470 ) @ SV158 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV158 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV921 ) @ SV733 ) @ SV470 ) )
= $false )
| ( ( class_Orderings_Opreorder @ SV921 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8247]) ).
thf(8374,plain,
! [SV161: $i,SV1138: $i,SV473: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SV1138 ) @ SV161 ) )
= $false )
| ( ( SV161
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8248]) ).
thf(8375,plain,
! [SV161: $i,SV473: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ ( sK13_SY2244 @ SV161 @ SV473 ) ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8249]) ).
thf(8376,plain,
! [SV736: $i,SV162: $i,SV924: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8250]) ).
thf(8377,plain,
! [SV924: $i,SV162: $i,SV736: $i,SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8251]) ).
thf(8378,plain,
! [SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1037: $i,SV1095: $i,SV1120: $i,SV1130: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1130 @ SV1120 ) @ SV1095 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SV1130 @ SV1037 ) @ SV1120 ) @ SV927 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8252]) ).
thf(8379,plain,
! [SV480: $i,SV168: $i,SV741: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
| ( SV168 = SV480 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8253]) ).
thf(8380,plain,
! [SV741: $i,SV480: $i,SV168: $i] :
( ( ( ( SV168 != SV480 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8254]) ).
thf(8381,plain,
! [SV744: $i,SV171: $i,SV483: $i] :
( ( ( SV483 = SV171 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8257]) ).
thf(8382,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) ) )
= $false )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8258]) ).
thf(8383,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV174: $i,SV486: $i,SV1038: $i] :
( ( ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
| ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8259]) ).
thf(8384,plain,
! [SV750: $i,SV1041: $i,SV1097: $i,SV179: $i,SV491: $i,SV934: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8265]) ).
thf(8385,plain,
! [SV934: $i,SV1041: $i,SV1097: $i,SV179: $i,SV491: $i,SV750: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8265]) ).
thf(8386,plain,
! [SV182: $i,SV494: $i,SV753: $i,SV936: $i,SV1043: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false )
| ( ( ~ ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8266]) ).
thf(8387,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ( ~ ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8267]) ).
thf(8388,plain,
! [SV756: $i,SV938: $i,SV185: $i,SV497: $i] :
( ( ( SV497 = SV185 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV185 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV938 ) @ SV756 ) @ SV497 ) )
= $false )
| ( ( class_Orderings_Oord @ SV938 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8268]) ).
thf(8389,plain,
! [SV498: $i,SV939: $i,SV186: $i,SV757: $i] :
( ( ( SV757 = SV186 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV186 ) @ SV498 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV939 ) @ SV757 ) @ SV498 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV939 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8269]) ).
thf(8390,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8272]) ).
thf(8391,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8273]) ).
thf(8392,plain,
! [SV507: $i,SV195: $i,SV765: $i,SV947: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8274]) ).
thf(8393,plain,
! [SV770: $i,SV201: $i,SV513: $i,SV950: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV513 ) @ SV201 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV950 ) @ SV770 ) @ SV201 ) )
= $true )
| ( ( SV770 = SV513 )
= $false )
| ( ( class_Orderings_Oord @ SV950 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8276]) ).
thf(8394,plain,
! [SV951: $i,SV514: $i,SV202: $i,SV771: $i] :
( ( ( SV771 = SV202 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV514 @ SV202 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8277]) ).
thf(8395,plain,
! [SV514: $i,SV951: $i,SV202: $i,SV771: $i] :
( ( ( SV771 = SV202 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8278]) ).
thf(8396,plain,
! [SV771: $i,SV951: $i,SV202: $i,SV514: $i] :
( ( ( hBOOL @ ( hAPP @ SV514 @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV951 ) @ SV771 ) @ SV514 ) @ SV202 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8278]) ).
thf(8397,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ( ! [SY2349: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2349 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8280]) ).
thf(8398,plain,
! [SV779: $i,SV956: $i,SV215: $i,SV527: $i] :
( ( ( ! [SY2350: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SY2350 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8281]) ).
thf(8399,plain,
! [SV216: $i,SV528: $i,SV780: $i,SV957: $i,SV1049: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false )
| ( ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8282]) ).
thf(8400,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
| ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8283]) ).
thf(8401,plain,
! [SV219: $i,SV531: $i,SV782: $i,SV958: $i,SV1050: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8285]) ).
thf(8402,plain,
! [SV958: $i,SV1050: $i,SV531: $i,SV219: $i,SV782: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV782 @ SV219 ) @ SV531 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1050 @ SV958 @ SV782 ) @ SV531 ) @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8286]) ).
thf(8403,plain,
! [SV222: $i,SV534: $i,SV785: $i,SV960: $i,SV1052: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8287]) ).
thf(8404,plain,
! [SV960: $i,SV1052: $i,SV222: $i,SV785: $i,SV534: $i] :
( ( ( hBOOL @ ( hAPP @ SV534 @ ( hAPP @ SV785 @ SV222 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ SV1052 @ SV960 @ SV785 ) @ SV534 ) @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8288]) ).
thf(8405,plain,
! [SV787: $i,SV536: $i,SV224: $i,SV962: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV536 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV962 ) @ SV224 ) @ SV787 ) )
= $true )
| ( ( SV787 = SV536 )
= $false )
| ( ( class_Orderings_Oorder @ SV962 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8289]) ).
thf(8406,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( SV1102 != SV1053 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8290]) ).
thf(8407,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( ~ ( ( SV1102 != SV1053 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8291]) ).
thf(8408,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) ) )
= $false )
| ( ( SV793 = SV544 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8292]) ).
thf(8409,plain,
! [SV793: $i,SV544: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
= $false )
| ( ( SV793 = SV544 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8292]) ).
thf(8410,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
= $true )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8293]) ).
thf(8411,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8297]) ).
thf(8412,plain,
! [SV552: $i,SV801: $i,SV240: $i] :
( ( ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8297]) ).
thf(8413,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( SV552
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8298]) ).
thf(8414,plain,
! [SV247: $i,SV559: $i,SV975: $i,SV807: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) ) )
= $true )
| ( ( ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8299]) ).
thf(8415,plain,
! [SV807: $i,SV247: $i,SV559: $i,SV975: $i] :
( ( ( ~ ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8300]) ).
thf(8416,plain,
! [SV808: $i,SV248: $i,SV560: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8301]) ).
thf(8417,plain,
! [SV1104: $i,SV253: $i,SV565: $i,SV978: $i,SV1057: $i,SV811: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV811 @ SV1057 ) @ SV978 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV565 @ ( tc_fun @ SV253 @ tc_HOL_Obool ) ) ) @ SV1104 ) @ SV811 ) @ SV1057 ) @ SV978 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1104 @ SV1057 ) @ SV978 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8303]) ).
thf(8418,plain,
! [SV568: $i,SV1058: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ SV256 @ SV1058 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV568 ) @ SV1058 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV568 @ tc_HOL_Obool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8306]) ).
thf(8419,plain,
! [SV259: $i,SV571: $i,SV814: $i,SV980: $i,SV1060: $i,SV1106: $i,SV1122: $i,SV1132: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1132 @ SV1122 @ SV1106 @ SV1060 ) @ SV980 )
= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SV1122 @ SV1106 @ SV571 ) @ SV259 ) )
= $false )
| ( ( ! [SY3027: $i] :
( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SY3027 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SY3027 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8307]) ).
thf(8420,plain,
! [SV264: $i,SV819: $i,SV1063: $i,SV1108: $i,SV576: $i,SV983: $i] :
( ( ( SV983 != SV576 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8310]) ).
thf(8421,plain,
! [SV576: $i,SV983: $i,SV1063: $i,SV1108: $i,SV264: $i,SV819: $i] :
( ( ( SV819 != SV264 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8310]) ).
thf(8422,plain,
! [SV268: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP @ SV580 @ ( sK10_SY2454 @ SV268 @ SV580 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8312]) ).
thf(8423,plain,
! [SV268: $i,SV1139: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP @ SV580 @ SV1139 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV580 @ ( c_Hilbert__Choice_OEps @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8313]) ).
thf(8424,plain,
! [SV1065: $i,SV823: $i,SV270: $i,SV582: $i,SV985: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8314]) ).
thf(8425,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8315]) ).
thf(8426,plain,
! [SV986: $i,SV825: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8316]) ).
thf(8427,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ( SV826 = SV585 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8317]) ).
thf(8428,plain,
! [SV273: $i,SV987: $i,SV585: $i,SV826: $i] :
( ( ( SV826 = SV585 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8318]) ).
thf(8429,plain,
! [SV585: $i,SV273: $i,SV826: $i,SV987: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ SV273 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV987 ) @ SV826 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV987 ) @ SV585 ) @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8318]) ).
thf(8430,plain,
! [SV827: $i,SV1066: $i,SV275: $i,SV988: $i,SV1110: $i,SV587: $i] :
( ( ( SV587
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV988 ) @ SV275 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV587 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV827 ) @ SV275 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1110 ) @ SV1066 ) @ SV988 )
= SV827 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8319]) ).
thf(8431,plain,
! [SV828: $i,SV989: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8320]) ).
thf(8432,plain,
! [SV989: $i,SV828: $i,SV276: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8321]) ).
thf(8433,plain,
! [SV281: $i,SV593: $i,SV832: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false )
| ( ( ~ ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8322]) ).
thf(8434,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8323]) ).
thf(8435,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8327]) ).
thf(8436,plain,
! [SV599: $i,SV287: $i] :
( ( ( ! [SY1911: $i,SY1912: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1912 ) @ SY1912 ) ) )
| ( ( hAPP @ SV287 @ SY1911 )
!= ( hAPP @ SV287 @ SY1912 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1911 ) @ SY1912 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8328]) ).
thf(8437,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) ) )
= $false )
| ( ( ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8329]) ).
thf(8438,plain,
! [SV1124: $i,SV836: $i,SV291: $i,SV601: $i] :
( ( ( SV601
= ( c_Hilbert__Choice_OEps @ SV291 @ SV836 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV836 @ SV601 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV836 @ SV1124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8332]) ).
thf(8439,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ( ! [SY2524: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2524 ) @ SV307 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8335]) ).
thf(8440,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV617: $i] :
( ( ( ! [SY2525: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SY2525 ) @ SV307 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8336]) ).
thf(8441,plain,
! [SV314: $i,SV624: $i,SV856: $i,SV1005: $i,SV1073: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8338]) ).
thf(8442,plain,
! [SV1005: $i,SV1073: $i,SV624: $i,SV314: $i,SV856: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV856 @ SV314 ) @ SV624 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV1073 @ SV1005 @ SV856 ) @ SV624 ) @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8339]) ).
thf(8443,plain,
! [SV857: $i,SV315: $i,SV1140: $i,SV625: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1140 ) @ SV315 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV1140 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8340]) ).
thf(8444,plain,
! [SV315: $i,SV857: $i,SV625: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ ( sK11_SY2834 @ SV857 @ SV315 @ SV625 ) ) @ SV315 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8341]) ).
thf(8445,plain,
! [SV315: $i,SV625: $i,SV857: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ ( sK11_SY2834 @ SV857 @ SV315 @ SV625 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8341]) ).
thf(8446,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( SV1112 != SV1074 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8342]) ).
thf(8447,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( ~ ( ( SV1112 != SV1074 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8343]) ).
thf(8448,plain,
! [SV1076: $i,SV1114: $i,SV863: $i,SV322: $i,SV632: $i,SV1009: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8345]) ).
thf(8449,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
| ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8346]) ).
thf(8450,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SV1134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8346]) ).
thf(8451,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8347]) ).
thf(8452,plain,
! [SV113: $i,SV694: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8348]) ).
thf(8453,plain,
! [SV694: $i,SV113: $i,SV426: $i,SV900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8349]) ).
thf(8454,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8353]) ).
thf(8455,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( ( SV903 != SV430 )
| ( SV698 != SV118 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8354]) ).
thf(8456,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8356]) ).
thf(8457,plain,
! [SV706: $i,SV127: $i,SV439: $i] :
( ( ( SV439 != SV127 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8357]) ).
thf(8458,plain,
! [SV127: $i,SV439: $i,SV706: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false )
| ( ( ~ ( ( SV439 != SV127 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8358]) ).
thf(8459,plain,
! [SV1143: $i,SV1141: $i,SV128: $i,SV440: $i,SV707: $i] :
( ( ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ SV1141 ) @ SV1143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV707 @ ( sK7_SY2628 @ SV128 @ SV440 @ SV707 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8359]) ).
thf(8460,plain,
! [SV128: $i,SV440: $i,SV1144: $i,SV707: $i] :
( ( ( hBOOL @ ( hAPP @ SV707 @ SV1144 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV707 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV440 @ SV128 ) @ ( sK8_SY2631 @ SV128 @ SV440 @ SV707 ) ) @ ( sK12_SY3079 @ SV128 @ SV440 @ SV707 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8360]) ).
thf(8461,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) ) )
= $true )
| ( ( ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8361]) ).
thf(8462,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ( ~ ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8362]) ).
thf(8463,plain,
! [SV132: $i,SV444: $i,SV711: $i,SV910: $i,SV1027: $i,SV1088: $i,SV1118: $i,SV1127: $i,SV1135: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1135 @ SV1127 @ SV1118 @ SV1088 ) @ SV1027 )
= ( hAPP @ ( c_Fun_Ocomp @ SV910 @ SV1127 @ SV1118 @ SV711 ) @ SV444 ) )
= $false )
| ( ( ( hAPP @ SV1088 @ ( hAPP @ SV1027 @ SV132 ) )
= ( hAPP @ SV711 @ ( hAPP @ SV444 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8363]) ).
thf(8464,plain,
! [SV146: $i,SV458: $i,SV722: $i,SV915: $i,SV1030: $i,SV1091: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false )
| ( ( ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8365]) ).
thf(8465,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( ~ ( ( SV915 != SV458 )
| ( SV722 != SV146 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8366]) ).
thf(8466,plain,
! [SV1031: $i,SV724: $i,SV148: $i,SV460: $i,SV917: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV460 ) @ SV148 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV917 @ SV724 ) @ SV460 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV1031 @ SV917 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8367]) ).
thf(8467,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i,SV1136: $i,SV1142: $i,SV1145: $i] :
( ( ( ( hAPP @ SV1145 @ ( hAPP @ SV1142 @ SV1136 ) )
!= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SV1145 ) @ SV1142 ) @ SV1136 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8368]) ).
thf(8468,plain,
! [SV1034: $i,SV730: $i,SV154: $i,SV466: $i,SV920: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV466 ) @ SV154 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV154 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV920 @ SV730 ) @ SV466 ) )
= $false )
| ( ( c_Predicate_Otransp @ SV1034 @ SV920 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8369]) ).
thf(8469,plain,
! [SV731: $i,SV155: $i,SV1137: $i,SV467: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ SV1137 ) @ SV155 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV1137 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8370]) ).
thf(8470,plain,
! [SV155: $i,SV731: $i,SV467: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV467 @ ( sK9_SY2674 @ SV731 @ SV155 @ SV467 ) ) @ SV155 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV731 @ SV467 ) @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8371]) ).
thf(8471,plain,
! [SV1138: $i,SV473: $i,SV161: $i] :
( ( ( SV161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ SV1138 ) @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8374]) ).
thf(8472,plain,
! [SV161: $i,SV473: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV473 ) @ ( sK13_SY2244 @ SV161 @ SV473 ) ) @ SV161 ) )
= $true )
| ( ( SV161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8375]) ).
thf(8473,plain,
! [SV736: $i,SV162: $i,SV924: $i,SV474: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8376]) ).
thf(8474,plain,
! [SV924: $i,SV162: $i,SV736: $i,SV474: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV736 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV474 ) @ SV924 ) @ SV162 ) )
= $true )
| ( ( SV924 = SV736 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8377]) ).
thf(8475,plain,
! [SV1120: $i,SV1130: $i,SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1095: $i,SV1037: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SV1130 @ SV1037 ) @ SV1120 ) @ SV927 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1130 @ SV1120 ) @ SV1095 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8378]) ).
thf(8476,plain,
! [SV480: $i,SV168: $i,SV741: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) ) )
= $true )
| ( ( SV168 = SV480 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8379]) ).
thf(8477,plain,
! [SV741: $i,SV480: $i,SV168: $i] :
( ( ( SV168 != SV480 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8380]) ).
thf(8478,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
= $false )
| ( ( SV483 = SV171 )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8381]) ).
thf(8479,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
= $true )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8382]) ).
thf(8480,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV174: $i,SV486: $i,SV1038: $i] :
( ( ( ~ ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8383]) ).
thf(8481,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV1038: $i,SV174: $i,SV486: $i] :
( ( ( ~ ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8383]) ).
thf(8482,plain,
! [SV750: $i,SV1041: $i,SV1097: $i,SV179: $i,SV491: $i,SV934: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV934 @ SV491 ) @ SV179 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8384]) ).
thf(8483,plain,
! [SV934: $i,SV1041: $i,SV1097: $i,SV179: $i,SV491: $i,SV750: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV750 @ SV491 ) @ SV179 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ SV1097 @ ( tc_fun @ SV1041 @ tc_HOL_Obool ) ) ) @ SV934 ) @ SV750 ) @ SV491 ) @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8385]) ).
thf(8484,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ( ! [SY3016: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3016 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3016 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8386]) ).
thf(8485,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV753: $i] :
( ( ( ! [SY3017: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SY3017 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SY3017 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8387]) ).
thf(8486,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8390]) ).
thf(8487,plain,
! [SV764: $i,SV193: $i,SV505: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8390]) ).
thf(8488,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8391]) ).
thf(8489,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
| ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8392]) ).
thf(8490,plain,
! [SV956: $i,SV779: $i,SV215: $i,SV527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ ( sK14_SY2349 @ SV779 @ SV956 @ SV215 @ SV527 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8397]) ).
thf(8491,plain,
! [SV779: $i,SV956: $i,SV1146: $i,SV215: $i,SV527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SV1146 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8398]) ).
thf(8492,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) ) )
= $true )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8399]) ).
thf(8493,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ~ ( ( SV957 != SV528 )
| ( SV780 != SV216 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8400]) ).
thf(8494,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8400]) ).
thf(8495,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( SV1102 = SV1053 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8406]) ).
thf(8496,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( SV1102 != SV1053 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8407]) ).
thf(8497,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
= $true )
| ( ( SV793 = SV544 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8408]) ).
thf(8498,plain,
! [SV793: $i,SV544: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) )
= $true )
| ( ( SV793 = SV544 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8409]) ).
thf(8499,plain,
! [SV544: $i,SV793: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) ) )
= $true )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8410]) ).
thf(8500,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( SV552
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8411]) ).
thf(8501,plain,
! [SV552: $i,SV801: $i,SV240: $i] :
( ( ( SV240
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8412]) ).
thf(8502,plain,
! [SV240: $i,SV801: $i,SV552: $i] :
( ( ( SV552
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( SV240
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8413]) ).
thf(8503,plain,
! [SV247: $i,SV559: $i,SV975: $i,SV807: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
= $false )
| ( ( ! [SY2936: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2936 ) ) @ ( hAPP @ SV247 @ SY2936 ) ) ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8414]) ).
thf(8504,plain,
! [SV807: $i,SV247: $i,SV559: $i,SV975: $i] :
( ( ( ! [SY2937: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SY2937 ) ) @ ( hAPP @ SV247 @ SY2937 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8415]) ).
thf(8505,plain,
! [SV808: $i,SV248: $i,SV560: $i,SV976: $i,SV1056: $i,SV1103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1103 @ SV1056 ) @ SV976 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV560 @ ( tc_fun @ SV248 @ tc_HOL_Obool ) ) ) @ SV808 ) @ SV1103 ) @ SV1056 ) @ SV976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8416]) ).
thf(8506,plain,
! [SV814: $i,SV1106: $i,SV1122: $i,SV1132: $i,SV259: $i,SV571: $i,SV1147: $i,SV980: $i,SV1060: $i] :
( ( ( ( hAPP @ SV1060 @ ( hAPP @ SV980 @ SV1147 ) )
= ( hAPP @ SV571 @ ( hAPP @ SV259 @ SV1147 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV1132 @ SV1122 @ SV1106 @ SV1060 ) @ SV980 )
= ( hAPP @ ( c_Fun_Ocomp @ SV814 @ SV1122 @ SV1106 @ SV571 ) @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8419]) ).
thf(8507,plain,
! [SV264: $i,SV819: $i,SV1063: $i,SV1108: $i,SV576: $i,SV983: $i] :
( ( ( SV983 = SV576 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8420]) ).
thf(8508,plain,
! [SV576: $i,SV983: $i,SV1063: $i,SV1108: $i,SV264: $i,SV819: $i] :
( ( ( SV819 = SV264 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV983 ) @ SV819 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1108 @ SV1063 ) @ SV576 ) @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8421]) ).
thf(8509,plain,
! [SV1065: $i,SV823: $i,SV270: $i,SV582: $i,SV985: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV582 ) @ SV270 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV270 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV985 @ SV823 ) @ SV582 ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV1065 @ SV985 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8424]) ).
thf(8510,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8425]) ).
thf(8511,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8426]) ).
thf(8512,plain,
! [SV828: $i,SV989: $i,SV276: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8431]) ).
thf(8513,plain,
! [SV989: $i,SV828: $i,SV276: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV828 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV588 ) @ SV276 ) @ SV989 ) )
= $true )
| ( ( SV989 = SV828 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8432]) ).
thf(8514,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ! [SY3033: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3033 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3033 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3033 ) @ SV281 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8433]) ).
thf(8515,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ! [SY3034: $i] :
~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SY3034 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SY3034 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SY3034 ) @ SV281 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8434]) ).
thf(8516,plain,
! [SV599: $i,SV287: $i] :
( ( ( ! [SY1910: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1910 ) @ SY1910 ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8435]) ).
thf(8517,plain,
! [SV599: $i,SV1148: $i,SV287: $i] :
( ( ( ! [SY3084: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SY3084 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY3084 ) @ SY3084 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SY3084 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY3084 ) @ SY3084 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SY3084 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SY3084 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8436]) ).
thf(8518,plain,
! [SV599: $i,SV287: $i] :
( ( ( ! [SY1913: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1913 ) @ SY1913 ) ) )
= $true )
| ( ( ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8437]) ).
thf(8519,plain,
! [SV307: $i,SV1002: $i,SV850: $i,SV617: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ ( sK15_SY2524 @ SV850 @ SV1002 @ SV307 @ SV617 ) ) @ SV307 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8439]) ).
thf(8520,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV1149: $i,SV617: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SV1149 ) @ SV307 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8440]) ).
thf(8521,plain,
! [SV857: $i,SV315: $i,SV1140: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1140 ) @ SV315 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV1140 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8443]) ).
thf(8522,plain,
! [SV315: $i,SV857: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ ( sK11_SY2834 @ SV857 @ SV315 @ SV625 ) ) @ SV315 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV857 @ SV625 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8444]) ).
thf(8523,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( SV1112 = SV1074 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8446]) ).
thf(8524,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( SV1112 != SV1074 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8447]) ).
thf(8525,plain,
! [SV1076: $i,SV1114: $i,SV863: $i,SV322: $i,SV632: $i,SV1009: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1009 @ SV632 ) @ SV322 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV863 @ SV632 ) @ SV322 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV1114 @ ( tc_fun @ SV1076 @ tc_HOL_Obool ) ) ) @ SV1009 ) @ SV863 ) @ SV632 ) @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8448]) ).
thf(8526,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
| ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8449]) ).
thf(8527,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SV1134 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8450]) ).
thf(8528,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8451]) ).
thf(8529,plain,
! [SV113: $i,SV694: $i,SV426: $i,SV900: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8452]) ).
thf(8530,plain,
! [SV694: $i,SV113: $i,SV426: $i,SV900: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ SV113 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV900 @ tc_HOL_Obool ) ) @ SV426 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV900 ) @ SV694 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV900 ) @ SV694 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8453]) ).
thf(8531,plain,
! [SV118: $i,SV698: $i,SV1024: $i,SV430: $i,SV903: $i] :
( ( ( SV903 != SV430 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8454]) ).
thf(8532,plain,
! [SV430: $i,SV903: $i,SV1024: $i,SV118: $i,SV698: $i] :
( ( ( SV698 != SV118 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8454]) ).
thf(8533,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( SV903 != SV430 )
= $true )
| ( ( SV698 != SV118 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8455]) ).
thf(8534,plain,
! [SV706: $i,SV127: $i,SV439: $i] :
( ( ( SV439 = SV127 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8457]) ).
thf(8535,plain,
! [SV706: $i,SV127: $i,SV439: $i] :
( ( ( SV439 != SV127 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8458]) ).
thf(8536,plain,
! [SV131: $i,SV443: $i,SV710: $i,SV909: $i,SV1026: $i,SV1087: $i,SV1117: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false )
| ( ( ~ ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8461]) ).
thf(8537,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ( ~ ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8462]) ).
thf(8538,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8464]) ).
thf(8539,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( ( SV915 != SV458 )
| ( SV722 != SV146 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8465]) ).
thf(8540,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i,SV1136: $i,SV1142: $i,SV1145: $i] :
( ( ( ( hAPP @ SV1145 @ ( hAPP @ SV1142 @ SV1136 ) )
!= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SV1145 ) @ SV1142 ) @ SV1136 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8467]) ).
thf(8541,plain,
! [SV1120: $i,SV1130: $i,SV165: $i,SV477: $i,SV739: $i,SV927: $i,SV1095: $i,SV1037: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1037 @ SV1095 ) @ SV927 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV739 @ SV477 @ SV165 @ SV1130 @ SV1037 ) @ SV1120 ) @ SV927 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1130 @ SV1120 ) @ SV1095 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8475]) ).
thf(8542,plain,
! [SV480: $i,SV168: $i,SV741: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
= $false )
| ( ( SV168 = SV480 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8476]) ).
thf(8543,plain,
! [SV741: $i,SV480: $i,SV168: $i] :
( ( ( SV168 = SV480 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV168 ) @ SV480 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV741 ) @ SV480 ) @ SV168 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8477]) ).
thf(8544,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) ) )
= $false )
| ( ( SV483 = SV171 )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8478]) ).
thf(8545,plain,
! [SV483: $i,SV171: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
= $false )
| ( ( SV483 = SV171 )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8478]) ).
thf(8546,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
= $true )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8479]) ).
thf(8547,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV174: $i,SV486: $i,SV1038: $i] :
( ( ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
| ( SV486 = SV174 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8480]) ).
thf(8548,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV1038: $i,SV174: $i,SV486: $i] :
( ( ( ( SV486 != SV174 )
| ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8481]) ).
thf(8549,plain,
! [SV182: $i,SV936: $i,SV1043: $i,SV494: $i,SV753: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8484]) ).
thf(8550,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV1150: $i,SV753: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8485]) ).
thf(8551,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8486]) ).
thf(8552,plain,
! [SV764: $i,SV193: $i,SV505: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8487]) ).
thf(8553,plain,
! [SV505: $i,SV193: $i,SV764: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8488]) ).
thf(8554,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8489]) ).
thf(8555,plain,
! [SV765: $i,SV947: $i,SV195: $i,SV507: $i] :
( ( ( ~ ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8489]) ).
thf(8556,plain,
! [SV956: $i,SV779: $i,SV215: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ ( sK14_SY2349 @ SV779 @ SV956 @ SV215 @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8490]) ).
thf(8557,plain,
! [SV779: $i,SV956: $i,SV1146: $i,SV215: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV527 @ SV215 ) @ SV1146 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ SV956 @ SV779 @ SV527 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8491]) ).
thf(8558,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
= $false )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8492]) ).
thf(8559,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( ( SV957 != SV528 )
| ( SV780 != SV216 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8493]) ).
thf(8560,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( ( SV957 != SV216 )
| ( SV780 != SV528 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8494]) ).
thf(8561,plain,
! [SV230: $i,SV542: $i,SV791: $i,SV965: $i,SV1053: $i,SV1102: $i] :
( ( ( SV1102 = SV1053 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV965 @ SV791 @ SV542 @ SV1053 @ SV230 ) @ SV1102 )
= ( hAPP @ SV542 @ SV1102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8496]) ).
thf(8562,plain,
! [SV793: $i,SV544: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV544 ) @ SV793 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV232 @ tc_HOL_Obool ) ) @ SV793 ) @ SV544 ) )
= $false )
| ( ( SV793 = SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8499]) ).
thf(8563,plain,
! [SV552: $i,SV801: $i,SV240: $i] :
( ( ( SV240
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( SV552
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) @ SV552 ) @ SV240 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV801 @ tc_HOL_Obool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8502]) ).
thf(8564,plain,
! [SV807: $i,SV247: $i,SV1151: $i,SV559: $i,SV975: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ SV1151 ) ) @ ( hAPP @ SV247 @ SV1151 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
= $false )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8503]) ).
thf(8565,plain,
! [SV247: $i,SV807: $i,SV559: $i,SV975: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV975 ) @ ( hAPP @ SV559 @ ( sK17_SY2937 @ SV807 @ SV247 @ SV559 @ SV975 ) ) ) @ ( hAPP @ SV247 @ ( sK17_SY2937 @ SV807 @ SV247 @ SV559 @ SV975 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV807 @ SV975 ) ) @ SV559 ) @ SV247 ) )
= $true )
| ( ( class_Orderings_Oord @ SV975 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8504]) ).
thf(8566,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8510]) ).
thf(8567,plain,
! [SV986: $i,SV825: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8510]) ).
thf(8568,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8511]) ).
thf(8569,plain,
! [SV986: $i,SV825: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8511]) ).
thf(8570,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8514]) ).
thf(8571,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8515]) ).
thf(8572,plain,
! [SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK19_SY1910 @ SV599 @ SV287 ) ) @ ( sK19_SY1910 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8516]) ).
thf(8573,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[8517]) ).
thf(8574,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) ) )
= $true )
| ( ( ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8518]) ).
thf(8575,plain,
! [SV307: $i,SV1002: $i,SV850: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ ( sK15_SY2524 @ SV850 @ SV1002 @ SV307 @ SV617 ) ) @ SV307 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8519]) ).
thf(8576,plain,
! [SV850: $i,SV1002: $i,SV307: $i,SV1149: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV617 @ SV1149 ) @ SV307 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ SV1002 @ SV850 @ SV617 ) @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8520]) ).
thf(8577,plain,
! [SV319: $i,SV629: $i,SV860: $i,SV1007: $i,SV1074: $i,SV1112: $i] :
( ( ( SV1112 = SV1074 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1007 @ SV860 @ SV629 @ SV1074 @ SV319 ) @ SV1112 )
= ( hAPP @ SV629 @ SV1112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8524]) ).
thf(8578,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) ) )
= $true )
| ( ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8526]) ).
thf(8579,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV1126 )
!= ( hAPP @ SV110 @ SV1134 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8527]) ).
thf(8580,plain,
! [SV423: $i,SV110: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8528]) ).
thf(8581,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8528]) ).
thf(8582,plain,
! [SV118: $i,SV698: $i,SV1024: $i,SV430: $i,SV903: $i] :
( ( ( SV903 = SV430 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8531]) ).
thf(8583,plain,
! [SV430: $i,SV903: $i,SV1024: $i,SV118: $i,SV698: $i] :
( ( ( SV698 = SV118 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8532]) ).
thf(8584,plain,
! [SV1024: $i,SV118: $i,SV698: $i,SV430: $i,SV903: $i] :
( ( ( SV903 = SV430 )
= $false )
| ( ( SV698 != SV118 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8533]) ).
thf(8585,plain,
! [SV706: $i,SV127: $i,SV439: $i] :
( ( ( SV439 = SV127 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ SV706 @ tc_HOL_Obool ) ) @ SV439 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8535]) ).
thf(8586,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ( ! [SY2877: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2877 ) @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8536]) ).
thf(8587,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV443: $i,SV909: $i] :
( ( ( ! [SY2878: $i] :
~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SY2878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SY2878 ) @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8537]) ).
thf(8588,plain,
! [SV146: $i,SV722: $i,SV1030: $i,SV1091: $i,SV458: $i,SV915: $i] :
( ( ( SV915 != SV458 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8538]) ).
thf(8589,plain,
! [SV458: $i,SV915: $i,SV1030: $i,SV1091: $i,SV146: $i,SV722: $i] :
( ( ( SV722 != SV146 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8538]) ).
thf(8590,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( SV915 != SV458 )
= $true )
| ( ( SV722 != SV146 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8539]) ).
thf(8591,plain,
! [SV153: $i,SV465: $i,SV729: $i,SV919: $i,SV1033: $i,SV1092: $i,SV1119: $i,SV1129: $i,SV1136: $i,SV1142: $i,SV1145: $i] :
( ( ( ( hAPP @ SV1145 @ ( hAPP @ SV1142 @ SV1136 ) )
= ( hAPP @ SV1129 @ ( hAPP @ SV1119 @ SV1092 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV1033 @ SV919 @ SV729 @ SV1145 ) @ SV1142 ) @ SV1136 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV465 @ SV919 @ SV153 @ SV1129 ) @ SV1119 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8540]) ).
thf(8592,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
= $true )
| ( ( SV483 = SV171 )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8544]) ).
thf(8593,plain,
! [SV483: $i,SV171: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) )
= $true )
| ( ( SV483 = SV171 )
= $false )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8545]) ).
thf(8594,plain,
! [SV171: $i,SV483: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) ) )
= $true )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8546]) ).
thf(8595,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV174: $i,SV486: $i,SV1038: $i] :
( ( ( ( hAPP @ SV1038 @ SV486 )
!= ( hAPP @ SV1038 @ SV174 ) )
= $true )
| ( ( SV486 = SV174 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8547]) ).
thf(8596,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV1038: $i,SV174: $i,SV486: $i] :
( ( ( SV486 != SV174 )
= $true )
| ( ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8548]) ).
thf(8597,plain,
! [SV182: $i,SV936: $i,SV1043: $i,SV494: $i,SV753: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8549]) ).
thf(8598,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV1150: $i,SV753: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8550]) ).
thf(8599,plain,
! [SV764: $i,SV193: $i,SV505: $i,SV946: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ SV505 ) @ SV193 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV946 ) @ SV764 ) @ SV193 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV946 @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV946 ) @ SV764 ) @ SV505 ) ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8553]) ).
thf(8600,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
| ( SV507 = SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8554]) ).
thf(8601,plain,
! [SV765: $i,SV947: $i,SV195: $i,SV507: $i] :
( ( ( ( SV507 != SV195 )
| ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8555]) ).
thf(8602,plain,
! [SV1049: $i,SV780: $i,SV216: $i,SV528: $i,SV957: $i] :
( ( ( SV957 != SV528 )
= $false )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8558]) ).
thf(8603,plain,
! [SV1049: $i,SV528: $i,SV957: $i,SV216: $i,SV780: $i] :
( ( ( SV780 != SV216 )
= $false )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8558]) ).
thf(8604,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( SV957 != SV528 )
= $true )
| ( ( SV780 != SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8559]) ).
thf(8605,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( SV957 != SV216 )
= $true )
| ( ( SV780 != SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8560]) ).
thf(8606,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8566]) ).
thf(8607,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8568]) ).
thf(8608,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8570]) ).
thf(8609,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8571]) ).
thf(8610,plain,
! [SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK19_SY1910 @ SV599 @ SV287 ) ) @ ( sK19_SY1910 @ SV599 @ SV287 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8572]) ).
thf(8611,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8573]) ).
thf(8612,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( ~ ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8574]) ).
thf(8613,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
= $false )
| ( ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8578]) ).
thf(8614,plain,
! [SV423: $i,SV1134: $i,SV1126: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV1126 )
= ( hAPP @ SV110 @ SV1134 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV1126 ) @ SV1134 ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8579]) ).
thf(8615,plain,
! [SV423: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8580]) ).
thf(8616,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8581]) ).
thf(8617,plain,
! [SV1024: $i,SV430: $i,SV903: $i,SV118: $i,SV698: $i] :
( ( ( SV698 = SV118 )
= $false )
| ( ( SV903 = SV430 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV903 ) @ SV698 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV1024 ) @ SV430 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8584]) ).
thf(8618,plain,
! [SV710: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV443: $i,SV909: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[8586]) ).
thf(8619,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV1155: $i,SV443: $i,SV909: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[8587]) ).
thf(8620,plain,
! [SV146: $i,SV722: $i,SV1030: $i,SV1091: $i,SV458: $i,SV915: $i] :
( ( ( SV915 = SV458 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8588]) ).
thf(8621,plain,
! [SV458: $i,SV915: $i,SV1030: $i,SV1091: $i,SV146: $i,SV722: $i] :
( ( ( SV722 = SV146 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8589]) ).
thf(8622,plain,
! [SV1030: $i,SV1091: $i,SV146: $i,SV722: $i,SV458: $i,SV915: $i] :
( ( ( SV915 = SV458 )
= $false )
| ( ( SV722 != SV146 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8590]) ).
thf(8623,plain,
! [SV483: $i,SV171: $i,SV744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV171 ) @ SV483 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ SV744 ) @ SV483 ) @ SV171 ) )
= $false )
| ( ( SV483 = SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV744 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8594]) ).
thf(8624,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV174: $i,SV486: $i,SV1038: $i] :
( ( ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) )
= $false )
| ( ( SV486 = SV174 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8595]) ).
thf(8625,plain,
! [SV745: $i,SV929: $i,SV1096: $i,SV1121: $i,SV1038: $i,SV174: $i,SV486: $i] :
( ( ( SV486 = SV174 )
= $false )
| ( ( ( hAPP @ SV1038 @ SV486 )
= ( hAPP @ SV1038 @ SV174 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV1121 @ SV1096 @ SV1038 @ SV929 @ SV745 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8596]) ).
thf(8626,plain,
! [SV182: $i,SV936: $i,SV1043: $i,SV494: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8597]) ).
thf(8627,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV1150: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) )
| ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8598]) ).
thf(8628,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( SV507 = SV195 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8600]) ).
thf(8629,plain,
! [SV765: $i,SV947: $i,SV195: $i,SV507: $i] :
( ( ( SV507 != SV195 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8601]) ).
thf(8630,plain,
! [SV1049: $i,SV780: $i,SV216: $i,SV528: $i,SV957: $i] :
( ( ( SV957 = SV528 )
= $true )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8602]) ).
thf(8631,plain,
! [SV1049: $i,SV528: $i,SV957: $i,SV216: $i,SV780: $i] :
( ( ( SV780 = SV216 )
= $true )
| ( ( ~ ( ( SV957 != SV216 )
| ( SV780 != SV528 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8603]) ).
thf(8632,plain,
! [SV1049: $i,SV216: $i,SV780: $i,SV528: $i,SV957: $i] :
( ( ( SV957 = SV528 )
= $false )
| ( ( SV780 != SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8604]) ).
thf(8633,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( SV957 = SV216 )
= $false )
| ( ( SV780 != SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8605]) ).
thf(8634,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8606]) ).
thf(8635,plain,
! [SV825: $i,SV986: $i,SV272: $i,SV584: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV986 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV584 ) @ SV272 ) @ SV825 ) )
= $true )
| ( ( SV986 = SV825 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8607]) ).
thf(8636,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
!= SV281 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8608]) ).
thf(8637,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ~ ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8609]) ).
thf(8638,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1152: $i,SV993: $i,SV1067: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8609]) ).
thf(8639,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8611]) ).
thf(8640,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) ) ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8611]) ).
thf(8641,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( ! [SY1914: $i,SY1915: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1915 ) @ SY1915 ) ) )
| ( ( hAPP @ SV287 @ SY1914 )
!= ( hAPP @ SV287 @ SY1915 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY1914 ) @ SY1915 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8612]) ).
thf(8642,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8615]) ).
thf(8643,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8616]) ).
thf(8644,plain,
! [SV423: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8616]) ).
thf(8645,plain,
! [SV710: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8618]) ).
thf(8646,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV1155: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8619]) ).
thf(8647,plain,
! [SV1030: $i,SV1091: $i,SV458: $i,SV915: $i,SV146: $i,SV722: $i] :
( ( ( SV722 = SV146 )
= $false )
| ( ( SV915 = SV458 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV915 ) @ SV722 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV1091 @ SV1030 ) @ SV458 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8622]) ).
thf(8648,plain,
! [SV182: $i,SV936: $i,SV1043: $i,SV494: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) @ SV182 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8626]) ).
thf(8649,plain,
! [SV182: $i,SV494: $i,SV1043: $i,SV753: $i,SV936: $i] :
( ( ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8626]) ).
thf(8650,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV1150: $i,SV753: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) ) )
= $true )
| ( ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8627]) ).
thf(8651,plain,
! [SV195: $i,SV507: $i,SV765: $i,SV947: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
= $false )
| ( ( SV507 = SV195 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8628]) ).
thf(8652,plain,
! [SV765: $i,SV947: $i,SV195: $i,SV507: $i] :
( ( ( SV507 = SV195 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV507 )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ SV947 ) @ SV765 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8629]) ).
thf(8653,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( ( SV957 != SV216 )
| ( SV780 != SV528 ) )
= $false )
| ( ( SV957 = SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8630]) ).
thf(8654,plain,
! [SV1049: $i,SV528: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( ( SV957 != SV216 )
| ( SV780 != SV528 ) )
= $false )
| ( ( SV780 = SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8631]) ).
thf(8655,plain,
! [SV1049: $i,SV528: $i,SV957: $i,SV216: $i,SV780: $i] :
( ( ( SV780 = SV216 )
= $false )
| ( ( SV957 = SV528 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8632]) ).
thf(8656,plain,
! [SV1049: $i,SV216: $i,SV957: $i,SV528: $i,SV780: $i] :
( ( ( SV780 = SV528 )
= $false )
| ( ( SV957 = SV216 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8633]) ).
thf(8657,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
!= SV281 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8636]) ).
thf(8658,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8637]) ).
thf(8659,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1152: $i,SV993: $i,SV1067: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8638]) ).
thf(8660,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8639]) ).
thf(8661,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8640]) ).
thf(8662,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ! [SY3085: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ SY3085 ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY3085 ) @ SY3085 ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ SY3085 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SY3085 ) @ SY3085 ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ SY3085 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ SY3085 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8641]) ).
thf(8663,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
!= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8642]) ).
thf(8664,plain,
! [SV423: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8642]) ).
thf(8665,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $false )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8643]) ).
thf(8666,plain,
! [SV710: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) @ SV131 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8645]) ).
thf(8667,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV1155: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8646]) ).
thf(8668,plain,
! [SV182: $i,SV936: $i,SV1043: $i,SV494: $i,SV753: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) @ SV182 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8648]) ).
thf(8669,plain,
! [SV182: $i,SV494: $i,SV1043: $i,SV753: $i,SV936: $i] :
( ( ( SV936
= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ ( sK16_SY3016 @ SV494 @ SV1043 @ SV936 @ SV182 @ SV753 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8649]) ).
thf(8670,plain,
! [SV494: $i,SV1043: $i,SV936: $i,SV182: $i,SV1150: $i,SV753: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) )
= $false )
| ( ( SV936
!= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8650]) ).
thf(8671,plain,
! [SV780: $i,SV1049: $i,SV528: $i,SV216: $i,SV957: $i] :
( ( ( SV957 != SV216 )
= $false )
| ( ( SV957 = SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8653]) ).
thf(8672,plain,
! [SV216: $i,SV1049: $i,SV957: $i,SV528: $i,SV780: $i] :
( ( ( SV780 != SV528 )
= $false )
| ( ( SV957 = SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8653]) ).
thf(8673,plain,
! [SV528: $i,SV1049: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( SV957 != SV216 )
= $false )
| ( ( SV780 = SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8654]) ).
thf(8674,plain,
! [SV957: $i,SV1049: $i,SV216: $i,SV528: $i,SV780: $i] :
( ( ( SV780 != SV528 )
= $false )
| ( ( SV780 = SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8654]) ).
thf(8675,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8657]) ).
thf(8676,plain,
! [SV993: $i,SV593: $i,SV832: $i,SV281: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
!= SV281 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8657]) ).
thf(8677,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( SV993
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8658]) ).
thf(8678,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1152: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
!= SV593 )
= $true )
| ( ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8659]) ).
thf(8679,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8660]) ).
thf(8680,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8661]) ).
thf(8681,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[8662]) ).
thf(8682,plain,
! [SV423: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) )
= ( hAPP @ SV110 @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ ( sK2_SY1378 @ SV423 @ SV110 ) ) @ ( sK6_SY3073 @ SV423 @ SV110 ) ) )
= $true )
| ( ( c_Equiv__Relations_Oequivp @ SV423 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8663]) ).
thf(8683,plain,
! [SV710: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8666]) ).
thf(8684,plain,
! [SV909: $i,SV443: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV710: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) @ SV131 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8666]) ).
thf(8685,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV1155: $i,SV443: $i,SV909: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8667]) ).
thf(8686,plain,
! [SV182: $i,SV1150: $i,SV494: $i,SV1043: $i,SV753: $i,SV936: $i] :
( ( ( SV936
= ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV1150 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV753 @ tc_HOL_Obool ) ) @ SV1150 ) @ SV182 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ SV1043 @ tc_HOL_Obool ) ) @ SV936 ) @ ( hAPP @ ( c_Set_Oimage @ SV753 @ SV1043 @ SV494 ) @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8670]) ).
thf(8687,plain,
! [SV780: $i,SV1049: $i,SV528: $i,SV216: $i,SV957: $i] :
( ( ( SV957 = SV216 )
= $true )
| ( ( SV957 = SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8671]) ).
thf(8688,plain,
! [SV216: $i,SV1049: $i,SV957: $i,SV528: $i,SV780: $i] :
( ( ( SV780 = SV528 )
= $true )
| ( ( SV957 = SV528 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8672]) ).
thf(8689,plain,
! [SV528: $i,SV1049: $i,SV780: $i,SV216: $i,SV957: $i] :
( ( ( SV957 = SV216 )
= $true )
| ( ( SV780 = SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8673]) ).
thf(8690,plain,
! [SV957: $i,SV1049: $i,SV216: $i,SV528: $i,SV780: $i] :
( ( ( SV780 = SV528 )
= $true )
| ( ( SV780 = SV216 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV957 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV780 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV528 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV1049 ) @ SV216 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1049 @ tc_HOL_Obool ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8674]) ).
thf(8691,plain,
! [SV832: $i,SV281: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8675]) ).
thf(8692,plain,
! [SV993: $i,SV593: $i,SV832: $i,SV281: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8676]) ).
thf(8693,plain,
! [SV281: $i,SV832: $i,SV1152: $i,SV593: $i,SV1067: $i,SV993: $i] :
( ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
!= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8677]) ).
thf(8694,plain,
! [SV281: $i,SV832: $i,SV593: $i,SV1152: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
= SV593 )
= $false )
| ( ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8678]) ).
thf(8695,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8679]) ).
thf(8696,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8680]) ).
thf(8697,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8681]) ).
thf(8698,plain,
! [SV710: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV443: $i,SV909: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8683]) ).
thf(8699,plain,
! [SV909: $i,SV443: $i,SV131: $i,SV1117: $i,SV1087: $i,SV1026: $i,SV710: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ ( sK20_SY2877 @ SV1026 @ SV1087 @ SV1117 @ SV131 @ SV710 @ SV443 @ SV909 ) ) @ SV131 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8684]) ).
thf(8700,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV131: $i,SV710: $i,SV1155: $i,SV443: $i,SV909: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8685]) ).
thf(8701,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) )
= $false )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8691]) ).
thf(8702,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
| ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8692]) ).
thf(8703,plain,
! [SV593: $i,SV993: $i,SV281: $i,SV832: $i,SV1152: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV832 )
= SV281 )
= $false )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV1152 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8693]) ).
thf(8704,plain,
! [SV593: $i,SV993: $i,SV281: $i,SV1152: $i,SV1067: $i,SV832: $i] :
( ( ( SV832
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV1152 ) @ SV281 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV1152 )
= SV593 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8694]) ).
thf(8705,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8695]) ).
thf(8706,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
| ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8696]) ).
thf(8707,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8697]) ).
thf(8708,plain,
! [SV1026: $i,SV1087: $i,SV1117: $i,SV443: $i,SV909: $i,SV131: $i,SV1155: $i,SV710: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV710 @ SV1155 ) @ SV131 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV909 @ SV443 ) @ SV1155 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV1117 @ SV1087 @ SV1026 @ SV909 @ SV710 ) @ SV443 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8700]) ).
thf(8709,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
= $false )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8701]) ).
thf(8710,plain,
! [SV993: $i,SV593: $i,SV281: $i,SV1067: $i,SV832: $i] :
( ( ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) )
= $false )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8701]) ).
thf(8711,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
!= SV593 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8702]) ).
thf(8712,plain,
! [SV993: $i,SV593: $i,SV281: $i,SV1067: $i,SV832: $i] :
( ( ( SV832
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8702]) ).
thf(8713,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8705]) ).
thf(8714,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8705]) ).
thf(8715,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8706]) ).
thf(8716,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8707]) ).
thf(8717,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
= SV593 )
= $true )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8709]) ).
thf(8718,plain,
! [SV993: $i,SV593: $i,SV281: $i,SV1067: $i,SV832: $i] :
( ( ( SV832
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) )
= $true )
| ( ( SV993
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8710]) ).
thf(8719,plain,
! [SV593: $i,SV832: $i,SV281: $i,SV993: $i,SV1067: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) )
= SV593 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8711]) ).
thf(8720,plain,
! [SV993: $i,SV593: $i,SV281: $i,SV1067: $i,SV832: $i] :
( ( ( SV832
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV281 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ ( sK18_SY3033 @ SV281 @ SV832 @ SV593 @ SV1067 @ SV993 ) ) @ SV832 )
= SV281 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV993 ) @ SV832 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV1067 ) @ SV593 ) @ SV281 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8712]) ).
thf(8721,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8713]) ).
thf(8722,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ SV1148 )
= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8714]) ).
thf(8723,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8715]) ).
thf(8724,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8716]) ).
thf(8725,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8716]) ).
thf(8726,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8721]) ).
thf(8727,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8723]) ).
thf(8728,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8724]) ).
thf(8729,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8725]) ).
thf(8730,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8726]) ).
thf(8731,plain,
! [SV599: $i,SV1148: $i,SV1153: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[8726]) ).
thf(8732,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8727]) ).
thf(8733,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8728]) ).
thf(8734,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8729]) ).
thf(8735,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8730]) ).
thf(8736,plain,
! [SV599: $i,SV1148: $i,SV1153: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[8731]) ).
thf(8737,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8732]) ).
thf(8738,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8733]) ).
thf(8739,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8733]) ).
thf(8740,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8734]) ).
thf(8741,plain,
! [SV599: $i,SV1148: $i,SV1153: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
= $false )
| ( ( ( hAPP @ SV287 @ SV1148 )
!= ( hAPP @ SV287 @ SV1153 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8737]) ).
thf(8742,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8738]) ).
thf(8743,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8740]) ).
thf(8744,plain,
! [SV599: $i,SV1153: $i,SV1148: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ SV1148 )
= ( hAPP @ SV287 @ SV1153 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1148 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1153 ) @ SV1153 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1148 ) @ SV1153 ) )
= $true )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8741]) ).
thf(8745,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8742]) ).
thf(8746,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8743]) ).
thf(8747,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8745]) ).
thf(8748,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8745]) ).
thf(8749,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $true )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8746]) ).
thf(8750,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8747]) ).
thf(8751,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8748]) ).
thf(8752,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8749]) ).
thf(8753,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8750]) ).
thf(8754,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8752]) ).
thf(8755,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8753]) ).
thf(8756,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8753]) ).
thf(8757,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8754]) ).
thf(8758,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8755]) ).
thf(8759,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8756]) ).
thf(8760,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8757]) ).
thf(8761,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8757]) ).
thf(8762,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8760]) ).
thf(8763,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
| ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8762]) ).
thf(8764,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8763]) ).
thf(8765,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
!= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8763]) ).
thf(8766,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8764]) ).
thf(8767,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8765]) ).
thf(8768,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8766]) ).
thf(8769,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8768]) ).
thf(8770,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[8768]) ).
thf(8771,plain,
! [SV1154: $i,SV599: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8769]) ).
thf(8772,plain,
! [SV599: $i,SV1154: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) ) )
= $false )
| ( ( ( hAPP @ SV287 @ ( sK21_SY1914 @ SV599 @ SV1154 @ SV287 ) )
= ( hAPP @ SV287 @ ( sK22_SY3085 @ SV1154 @ SV599 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV287 @ SV1154 ) @ SV1154 ) )
= $false )
| ( ( c_Equiv__Relations_Opart__equivp @ SV599 @ SV287 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[8770]) ).
thf(8773,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5579,8772,8771,8767,8761,8759,8758,8751,8744,8739,8736,8735,8722,8720,8719,8718,8717,8708,8704,8703,8699,8698,8690,8689,8688,8687,8686,8682,8669,8668,8665,8664,8656,8655,8652,8651,8647,8644,8635,8634,8625,8624,8623,8621,8620,8617,8614,8613,8610,8599,8593,8592,8591,8585,8583,8582,8577,8576,8575,8569,8567,8565,8564,8563,8562,8561,8557,8556,8552,8551,8543,8542,8541,8534,8530,8529,8525,8523,8522,8521,8513,8512,8509,8508,8507,8506,8505,8501,8500,8498,8497,8495,8483,8482,8474,8473,8472,8471,8470,8469,8468,8466,8463,8460,8459,8456,8445,8442,8441,8438,8430,8429,8428,8427,8423,8422,8418,8417,8405,8404,8403,8402,8401,8396,8395,8394,8393,8389,8388,8373,8372,8364,8355,8352,8351,8350,8344,8337,8334,8333,8331,8330,8326,8325,8324,8311,8309,8308,8305,8304,8302,8296,8295,8294,8284,8279,8275,8271,8270,8264,8263,8262,8261,8260,8256,8255,8242,8237,8236,8235,8234,8233,8215,8214,8209,8204,8203,8202,8198,8197,8196,8195,8194,8193,8191,8179,8178,8170,8169,8163,8162,8159,8154,8150,8149,8145,8144,8139,8138,8135,8134,8132,8121,8120,8115,8114,8109,8108,8107,8103,8102,8101,8098,8090,8085,8084,8081,8076,8070,8069,8066,8063,8061,8058,8048,8047,8046,8037,8036,8029,8016,8015,8012,8007,8006,7998,7997,7976,7972,7966,7965,7961,7960,7959,7950,7943,7942,7936,7925,7920,7919,7913,7908,7898,7894,7880,7874,7872,7865,7860,7841,7831,7830,7829,7827,7826,7823,7822,7813,7783,7751,7746,7737,7735,7725,7711,7710,7706,7645,7636,7630,7626,7625,7614,7607,7606,7605,7604,7603,7602,7600,7598,7596,7583,7581,7579,7570,7565,7555,7540,7529,7524,7510,7497,7487,7476,7475,7474,7465,7437,7426,7414,7403,7400,7384,7370,7368,7366,7361,7359,7355,7354,7353,7347,7340,7322,7308,7303,7300,7294,7278,7241,7238,7232,7231,7217,7195,7189,7174,7163,7162,7161,7142,7134,7133,7117,7115,7114,7113,7112,7110,7109,7108,7104,7103,7101,7099,7098,7097,7096,7095,7094,7093,7091,7085,7084,7083,7082,7081,7080,7079,7078,7076,7038,6853,6836,6834,6832,6831,6828,6827,6826,6825,6824,6823,6822,6821,6811,6810,6805,6802,6797,6796,6795,6794,6792,6791,6790,6789,6788,6786,6753,6751,6578,6546,6545,6542,6538,6537,6536,6534,6533,6531,6524,6523,6522,6519,6518,6515,6507,6486,6485,6484,6481,6475,6471,6247,6235,6218,6202,6182,6175,6160,6155,6148,5911,5902,5901,5900,5899,5898,5897,5896,5895,5894,5893,5892,5891,5890,5889,5888,5887,5886,5885,5870]) ).
thf(8774,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[8773]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW365+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n002.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 16:57:42 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 177.55/35.94 .....................................
% 177.55/35.94
% 177.55/35.94 No.of.Axioms: 344
% 177.55/35.94
% 177.55/35.94 Length.of.Defs: 0
% 177.55/35.94
% 177.55/35.94 Contains.Choice.Funs: false
% 177.55/35.94 ...................................................................................................................................................................................................................................................
% 177.55/35.94
% 177.55/35.94 ********************************
% 177.55/35.94 * All subproblems solved! *
% 177.55/35.94 ********************************
% 177.55/35.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:344,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:288,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8773,loop_count:0,foatp_calls:1,translation:fof_full)
% 177.55/35.94
% 177.55/35.94 %**** Beginning of derivation protocol ****
% 177.55/35.94 % SZS output start CNFRefutation
% See solution above
% 177.55/35.97
% 177.55/35.97 %**** End of derivation protocol ****
% 177.55/35.97 %**** no. of clauses in derivation: 3888 ****
% 177.55/35.97 %**** clause counter: 8773 ****
% 177.55/35.97
% 177.55/35.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:344,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:288,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8773,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------