%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:01:08 AM UTC 2026
% Result : Theorem 77.29s 15.78s
% Output : CNFRefutation 77.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 70
% Syntax : Number of formulae : 878 ( 627 unt; 0 typ; 0 def)
% Number of atoms : 4208 (2745 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 14561 (1581 ~;1028 |; 21 &;11768 @)
% ( 45 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 531 ( 528 usr; 53 con; 0-7 aty)
% Number of variables : 4323 ( 0 ^;4317 !; 6 ?;4323 :)
% 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_Ocom_OCond,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OLocal,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Com_Ocom_OWhile,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(tp_c_Com_Ocom_Ocom__size,type,
c_Com_Ocom_Ocom__size: $i > $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OINFI,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(tp_c_DSequence_Oempty,type,
c_DSequence_Oempty: $i > $i ).
thf(tp_c_DSequence_Osingle,type,
c_DSequence_Osingle: $i > $i ).
thf(tp_c_DSequence_Ounion,type,
c_DSequence_Ounion: $i > $i ).
thf(tp_c_Divides_Oadjust,type,
c_Divides_Oadjust: $i > $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i ).
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int,type,
c_Divides_Odivmod__int: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__int__rel,type,
c_Divides_Odivmod__int__rel: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(tp_c_Divides_Odivmod__nat__rel,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg,type,
c_Divides_OnegDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OnegDivAlg__rel,type,
c_Divides_OnegDivAlg__rel: $i ).
thf(tp_c_Divides_OnegateSnd,type,
c_Divides_OnegateSnd: $i ).
thf(tp_c_Divides_Opdivmod,type,
c_Divides_Opdivmod: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg,type,
c_Divides_OposDivAlg: $i > $i > $i ).
thf(tp_c_Divides_OposDivAlg__rel,type,
c_Divides_OposDivAlg__rel: $i ).
thf(tp_c_Enum_Oenum__class_Oenum__all,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(tp_c_Enum_Oenum__class_Oenum__ex,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(tp_c_Enum_Oenum__the,type,
c_Enum_Oenum__the: $i > $i > $i ).
thf(tp_c_Enum_On__lists,type,
c_Enum_On__lists: $i > $i > $i > $i ).
thf(tp_c_Enum_Oproduct,type,
c_Enum_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Enum_Osublists,type,
c_Enum_Osublists: $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequivp,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Opart__equivp,type,
c_Equiv__Relations_Opart__equivp: $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: $i > $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(tp_c_Finite__Set_Ofold,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold__image,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofolding,type,
c_Finite__Set_Ofolding: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__idem,type,
c_Finite__Set_Ofolding__idem: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image,type,
c_Finite__Set_Ofolding__image: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__image__simple__idem,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofolding__one__idem,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm,type,
c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofun__left__comm__idem,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(tp_c_FunDef_OTHE__default,type,
c_FunDef_OTHE__default: $i > $i > $i > $i ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_FunDef_Ois__measure,type,
c_FunDef_Ois__measure: $i > $i > $o ).
thf(tp_c_FunDef_Omax__strict,type,
c_FunDef_Omax__strict: $i ).
thf(tp_c_FunDef_Omax__weak,type,
c_FunDef_Omax__weak: $i ).
thf(tp_c_FunDef_Omin__strict,type,
c_FunDef_Omin__strict: $i ).
thf(tp_c_FunDef_Omin__weak,type,
c_FunDef_Omin__weak: $i ).
thf(tp_c_FunDef_Opair__leq,type,
c_FunDef_Opair__leq: $i ).
thf(tp_c_FunDef_Opair__less,type,
c_FunDef_Opair__less: $i ).
thf(tp_c_FunDef_Oreduction__pair,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(tp_c_FunDef_Orp__inv__image,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i ).
thf(tp_c_Fun_Oinj__on,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(tp_c_Fun_Othe__inv__into,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(tp_c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: $i > $i ).
thf(tp_c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
thf(tp_c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tp_c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(tp_c_Groups_Osgn__class_Osgn,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(tp_c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(tp_c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(tp_c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tp_c_HOL_OAll,type,
c_HOL_OAll: $i > $i ).
thf(tp_c_HOL_OEx,type,
c_HOL_OEx: $i > $i ).
thf(tp_c_HOL_OLet,type,
c_HOL_OLet: $i > $i > $i ).
thf(tp_c_HOL_OThe,type,
c_HOL_OThe: $i > $i > $i ).
thf(tp_c_HOL_Obool_Obool__size,type,
c_HOL_Obool_Obool__size: $i > $i ).
thf(tp_c_Hilbert__Choice_OEps,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(tp_c_Hilbert__Choice_Oinv__into,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(tp_c_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_Ohb__bind,type,
c_Lazy__Sequence_Ohb__bind: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__not__seq,type,
c_Lazy__Sequence_Ohb__not__seq: $i > $i ).
thf(tp_c_Lazy__Sequence_Ohb__single,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Ohit__bound,type,
c_Lazy__Sequence_Ohit__bound: $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_OEmpty,type,
c_Lazy__Sequence_Olazy__sequence_OEmpty: $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_OInsert,type,
c_Lazy__Sequence_Olazy__sequence_OInsert: $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size,type,
c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oproduct,type,
c_Lazy__Sequence_Oproduct: $i > $i > $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osingle,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H,type,
c_Lazy__Sequence_Osmall__lazy_H: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy_H__rel,type,
c_Lazy__Sequence_Osmall__lazy_H__rel: $i ).
thf(tp_c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy,type,
c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy: $i > $i > $i ).
thf(tp_c_Lazy__Sequence_Oyield,type,
c_Lazy__Sequence_Oyield: $i > $i ).
thf(tp_c_Lazy__Sequence_Oyieldn,type,
c_Lazy__Sequence_Oyieldn: $i > $i ).
thf(tp_c_List_Oall__interval__int,type,
c_List_Oall__interval__int: $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Oconcat,type,
c_List_Oconcat: $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(tp_c_List_Oembed__list,type,
c_List_Oembed__list: $i > $i ).
thf(tp_c_List_Ofilter,type,
c_List_Ofilter: $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i ).
thf(tp_c_List_Oinsert,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olenlex,type,
c_List_Olenlex: $i > $i > $i ).
thf(tp_c_List_Olex,type,
c_List_Olex: $i > $i > $i ).
thf(tp_c_List_Olexn,type,
c_List_Olexn: $i > $i > $i ).
thf(tp_c_List_Olexord,type,
c_List_Olexord: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__insert__key,type,
c_List_Olinorder__class_Oinsort__insert__key: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__key,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osort__key,type,
c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olinorder__class_Osorted__list__of__set,type,
c_List_Olinorder__class_Osorted__list__of__set: $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_Olist__size,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(tp_c_List_Olist__all,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(tp_c_List_Olist__all2,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex1,type,
c_List_Olist__ex1: $i > $i > $i > $o ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i ).
thf(tp_c_List_Olistrel,type,
c_List_Olistrel: $i > $i > $i ).
thf(tp_c_List_Olistrel1,type,
c_List_Olistrel1: $i > $i > $i ).
thf(tp_c_List_Olistrelp,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(tp_c_List_Olists,type,
c_List_Olists: $i > $i > $i ).
thf(tp_c_List_Olistset,type,
c_List_Olistset: $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i ).
thf(tp_c_List_Omaps,type,
c_List_Omaps: $i > $i > $i > $i > $i ).
thf(tp_c_List_Omeasures,type,
c_List_Omeasures: $i > $i > $i ).
thf(tp_c_List_Omember,type,
c_List_Omember: $i > $i ).
thf(tp_c_List_Omonoid__add__class_Olistsum,type,
c_List_Omonoid__add__class_Olistsum: $i > $i ).
thf(tp_c_List_Onat__list,type,
c_List_Onat__list: $i > $o ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i ).
thf(tp_c_List_Opartition,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(tp_c_List_Oremdups,type,
c_List_Oremdups: $i > $i > $i ).
thf(tp_c_List_Oremove1,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tp_c_List_OremoveAll,type,
c_List_OremoveAll: $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Oreturn__list,type,
c_List_Oreturn__list: $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i ).
thf(tp_c_List_Oset__Cons,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(tp_c_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $i > $i ).
thf(tp_c_List_Otranspose,type,
c_List_Otranspose: $i > $i > $i ).
thf(tp_c_List_Otranspose__rel,type,
c_List_Otranspose__rel: $i > $i ).
thf(tp_c_List_Oupt,type,
c_List_Oupt: $i > $i > $i ).
thf(tp_c_List_Oupto,type,
c_List_Oupto: $i > $i > $i ).
thf(tp_c_List_Oupto__rel,type,
c_List_Oupto__rel: $i ).
thf(tp_c_List_Ozip,type,
c_List_Ozip: $i > $i > $i ).
thf(tp_c_Nat_OSuc,type,
c_Nat_OSuc: $i ).
thf(tp_c_Nat_Ocompow,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(tp_c_Nat_Ofunpow,type,
c_Nat_Ofunpow: $i > $i ).
thf(tp_c_Nat_Onat_Onat__case,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__rec,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__size,type,
c_Nat_Onat_Onat__size: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_ONats,type,
c_Nat_Osemiring__1__class_ONats: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i ).
thf(tp_c_Nat__Numeral_Oneg,type,
c_Nat__Numeral_Oneg: $i ).
thf(tp_c_Nat__Transfer_Ois__nat,type,
c_Nat__Transfer_Ois__nat: $i > $o ).
thf(tp_c_Nat__Transfer_Onat__set,type,
c_Nat__Transfer_Onat__set: $i > $o ).
thf(tp_c_Nat__Transfer_Otransfer__morphism,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(tp_c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(tp_c_New__DSequence_Oneg__bind,type,
c_New__DSequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__decr__bind,type,
c_New__DSequence_Oneg__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Oneg__single,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__bind,type,
c_New__DSequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__decr__bind,type,
c_New__DSequence_Opos__decr__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__empty,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(tp_c_New__DSequence_Opos__not__seq,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(tp_c_New__DSequence_Opos__single,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(tp_c_New__DSequence_Opos__union,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__bind,type,
c_New__Random__Sequence_Oneg__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__decr__bind,type,
c_New__Random__Sequence_Oneg__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__map,type,
c_New__Random__Sequence_Oneg__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Oneg__single,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__bind,type,
c_New__Random__Sequence_Opos__bind: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__decr__bind,type,
c_New__Random__Sequence_Opos__decr__bind: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__empty,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__map,type,
c_New__Random__Sequence_Opos__map: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__not__random__dseq,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__single,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(tp_c_New__Random__Sequence_Opos__union,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_OAbs__Frac,type,
c_Nitpick_OAbs__Frac: $i > $i > $i ).
thf(tp_c_Nitpick_OFrac,type,
c_Nitpick_OFrac: $i ).
thf(tp_c_Nitpick_ORep__Frac,type,
c_Nitpick_ORep__Frac: $i > $i ).
thf(tp_c_Nitpick_Ocard_H,type,
c_Nitpick_Ocard_H: $i > $i > $i ).
thf(tp_c_Nitpick_Odenom,type,
c_Nitpick_Odenom: $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Ofrac,type,
c_Nitpick_Ofrac: $i > $i ).
thf(tp_c_Nitpick_Oint__gcd,type,
c_Nitpick_Oint__gcd: $i ).
thf(tp_c_Nitpick_Oint__lcm,type,
c_Nitpick_Oint__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Oinverse__frac,type,
c_Nitpick_Oinverse__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oless__eq__frac,type,
c_Nitpick_Oless__eq__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Oless__frac,type,
c_Nitpick_Oless__frac: $i > $i > $i > $o ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd__rel,type,
c_Nitpick_Onat__gcd__rel: $i ).
thf(tp_c_Nitpick_Onat__lcm,type,
c_Nitpick_Onat__lcm: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac,type,
c_Nitpick_Onorm__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Onorm__frac__rel,type,
c_Nitpick_Onorm__frac__rel: $i ).
thf(tp_c_Nitpick_Onum,type,
c_Nitpick_Onum: $i > $i ).
thf(tp_c_Nitpick_Onumber__of__frac,type,
c_Nitpick_Onumber__of__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Oof__frac,type,
c_Nitpick_Oof__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oone__frac,type,
c_Nitpick_Oone__frac: $i > $i ).
thf(tp_c_Nitpick_Opair__box_OPairBox,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__case,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__rec,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Opair__box_Opair__box__size,type,
c_Nitpick_Opair__box_Opair__box__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oplus__frac,type,
c_Nitpick_Oplus__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Oprod,type,
c_Nitpick_Oprod: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osetsum_H,type,
c_Nitpick_Osetsum_H: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Otimes__frac,type,
c_Nitpick_Otimes__frac: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ouminus__frac,type,
c_Nitpick_Ouminus__frac: $i > $i > $i ).
thf(tp_c_Nitpick_Ounknown,type,
c_Nitpick_Ounknown: $i > $o ).
thf(tp_c_Nitpick_Owf_H,type,
c_Nitpick_Owf_H: $i > $i > $o ).
thf(tp_c_Nitpick_Ozero__frac,type,
c_Nitpick_Ozero__frac: $i > $i ).
thf(tp_c_Option_Ooption_Ooption__case,type,
c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord_Omax,type,
c_Orderings_Oord_Omax: $i > $i > $i ).
thf(tp_c_Orderings_Oord_Omin,type,
c_Orderings_Oord_Omin: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tp_c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(tp_c_Orderings_Oorder_Omono,type,
c_Orderings_Oorder_Omono: $i > $i > $i > $i > $o ).
thf(tp_c_Orderings_Oorder_Ostrict__mono,type,
c_Orderings_Oorder_Ostrict__mono: $i > $i > $i > $i > $o ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Partial__Function_Oflat__lub,type,
c_Partial__Function_Oflat__lub: $i > $i > $i > $i ).
thf(tp_c_Partial__Function_Ofun__lub,type,
c_Partial__Function_Ofun__lub: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Power_Opower_Opower,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(tp_c_Predicate_ODomainP,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(tp_c_Predicate_OPowp,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(tp_c_Predicate_ORangeP,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Predicate_Oreflp,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(tp_c_Predicate_Osymp,type,
c_Predicate_Osymp: $i > $i > $o ).
thf(tp_c_Predicate_Otransp,type,
c_Predicate_Otransp: $i > $i > $o ).
thf(tp_c_Product__Type_OPair,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(tp_c_Product__Type_OSigma,type,
c_Product__Type_OSigma: $i > $i > $i ).
thf(tp_c_Product__Type_Oapfst,type,
c_Product__Type_Oapfst: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oapsnd,type,
c_Product__Type_Oapsnd: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ocurry,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Ofst,type,
c_Product__Type_Ofst: $i > $i > $i ).
thf(tp_c_Product__Type_Ointernal__split,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Omap__pair,type,
c_Product__Type_Omap__pair: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__case,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__rec,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oprod_Oprod__size,type,
c_Product__Type_Oprod_Oprod__size: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Oscomp,type,
c_Product__Type_Oscomp: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_Osnd,type,
c_Product__Type_Osnd: $i > $i > $i ).
thf(tp_c_Quickcheck_Obeyond,type,
c_Quickcheck_Obeyond: $i > $i > $i ).
thf(tp_c_Random_Oinc__shift,type,
c_Random_Oinc__shift: $i > $i > $i ).
thf(tp_c_Random_Oiterate,type,
c_Random_Oiterate: $i > $i > $i > $i > $i ).
thf(tp_c_Random_Olog,type,
c_Random_Olog: $i > $i > $i ).
thf(tp_c_Random_Ominus__shift,type,
c_Random_Ominus__shift: $i > $i > $i > $i ).
thf(tp_c_Random_Opick,type,
c_Random_Opick: $i > $i > $i ).
thf(tp_c_Random_Orange,type,
c_Random_Orange: $i > $i ).
thf(tp_c_Random_Oselect,type,
c_Random_Oselect: $i > $i > $i ).
thf(tp_c_Random_Oselect__weight,type,
c_Random_Oselect__weight: $i > $i > $i ).
thf(tp_c_Random__Sequence_ORandom,type,
c_Random__Sequence_ORandom: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Obind,type,
c_Random__Sequence_Obind: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Oempty,type,
c_Random__Sequence_Oempty: $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Omap,type,
c_Random__Sequence_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_Random__Sequence_Osingle,type,
c_Random__Sequence_Osingle: $i > $i ).
thf(tp_c_Recdef_Osame__fst,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i ).
thf(tp_c_Relation_OField,type,
c_Relation_OField: $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Relation_Oconverse,type,
c_Relation_Oconverse: $i > $i > $i ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i ).
thf(tp_c_Relation_Oirrefl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_Osym,type,
c_Relation_Osym: $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Otrans,type,
c_Relation_Otrans: $i > $i > $o ).
thf(tp_c_Rings_Odvd__class_Odvd,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
thf(tp_c_Rings_Oinverse__class_Odivide,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
thf(tp_c_SMT_Oz3div,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(tp_c_SMT_Oz3mod,type,
c_SMT_Oz3mod: $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeast,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastAtMost,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastLessThan,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatMost,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThan,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanAtMost,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanLessThan,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OlessThan,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeast,type,
c_SetInterval_Oord__class_OatLeast: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastLessThan,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatMost,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThan,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanAtMost,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanLessThan,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OlessThan,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(tp_c_Set_OBall,type,
c_Set_OBall: $i > $i ).
thf(tp_c_Set_OBex,type,
c_Set_OBex: $i > $i ).
thf(tp_c_Set_OCollect,type,
c_Set_OCollect: $i > $i ).
thf(tp_c_Set_OPow,type,
c_Set_OPow: $i > $i ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i ).
thf(tp_c_Set_Othe__elem,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(tp_c_Set_Ovimage,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(tp_c_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Typedef_Otype__definition,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Ofinite__psubset,type,
c_Wellfounded_Ofinite__psubset: $i > $i ).
thf(tp_c_Wellfounded_Oless__than,type,
c_Wellfounded_Oless__than: $i ).
thf(tp_c_Wellfounded_Olex__prod,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__ext,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omax__extp,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Omeasure,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(tp_c_Wellfounded_Omin__ext,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(tp_c_Wellfounded_Omlex__prod,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(tp_c_Wellfounded_Opred__nat,type,
c_Wellfounded_Opred__nat: $i ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fFalse,type,
c_fFalse: $i ).
thf(tp_c_fNot,type,
c_fNot: $i ).
thf(tp_c_fTrue,type,
c_fTrue: $i ).
thf(tp_c_fconj,type,
c_fconj: $i ).
thf(tp_c_fdisj,type,
c_fdisj: $i ).
thf(tp_c_fequal,type,
c_fequal: $i ).
thf(tp_c_fimplies,type,
c_fimplies: $i ).
thf(tp_c_member,type,
c_member: $i > $i ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Enum_Oenum,type,
class_Enum_Oenum: $i > $o ).
thf(tp_class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
thf(tp_class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(tp_class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
thf(tp_class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(tp_class_Finite__Set_Ofinite,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tp_class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tp_class_Groups_Oabs__if,type,
class_Groups_Oabs__if: $i > $o ).
thf(tp_class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(tp_class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Olinordered__ab__semigroup__add,type,
class_Groups_Olinordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
thf(tp_class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tp_class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(tp_class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(tp_class_Groups_Osemigroup__add,type,
class_Groups_Osemigroup__add: $i > $o ).
thf(tp_class_Groups_Osgn__if,type,
class_Groups_Osgn__if: $i > $o ).
thf(tp_class_Groups_Ouminus,type,
class_Groups_Ouminus: $i > $o ).
thf(tp_class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
thf(tp_class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__bot,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice__top,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Osemilattice__inf,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(tp_class_Lattices_Osemilattice__sup,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(tp_class_Lazy__Sequence_Osmall__lazy,type,
class_Lazy__Sequence_Osmall__lazy: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_Nat_Osize,type,
class_Nat_Osize: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
thf(tp_class_Orderings_Owellorder,type,
class_Orderings_Owellorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Rings_Ocomm__ring,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(tp_class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(tp_class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
thf(tp_class_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(tp_class_Rings_Odvd,type,
class_Rings_Odvd: $i > $o ).
thf(tp_class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
thf(tp_class_Rings_Oinverse,type,
class_Rings_Oinverse: $i > $o ).
thf(tp_class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tp_class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(tp_class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tp_class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(tp_class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
thf(tp_class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(tp_class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tp_class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(tp_class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(tp_class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
thf(tp_class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
thf(tp_class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
thf(tp_class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
thf(tp_class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
thf(tp_class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(tp_class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY656,type,
sK2_SY656: $i ).
thf(tp_sK3_SY814,type,
sK3_SY814: $i ).
thf(tp_sK4_SY687,type,
sK4_SY687: $i > $i > $i ).
thf(tp_sK5_SY1004,type,
sK5_SY1004: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_SY979,type,
sK6_SY979: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY1000,type,
sK7_SY1000: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY1005,type,
sK8_SY1005: $i > $i > $i > $i > $i > $i ).
thf(tp_tc_Code__Evaluation_Oterm,type,
tc_Code__Evaluation_Oterm: $i ).
thf(tp_tc_Code__Numeral_Ocode__numeral,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_tc_Com_Ostate,type,
tc_Com_Ostate: $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_com,type,
v_com: $i ).
thf(tp_v_fun1,type,
v_fun1: $i > $i > $o ).
thf(tp_v_fun2,type,
v_fun2: $i > $i > $o ).
thf(tp_v_n,type,
v_n: $i ).
thf(16,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(17,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(18,axiom,
! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(19,axiom,
! [V_Q: $i,V_P: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ T_a @ T_b ) @ V_P ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(20,axiom,
! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(542,axiom,
! [V_xs: $i,T_a: $i] :
( ( hAPP @ ( c_List_Orev @ T_a ) @ ( hAPP @ ( c_List_Orev @ T_a ) @ V_xs ) )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
thf(543,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= V_ys_2 )
<=> ( V_xs_2
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).
thf(544,axiom,
! [V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( c_List_Orev @ T_b ) @ V_xs_2 )
= ( hAPP @ ( c_List_Orev @ T_b ) @ V_ys_2 ) )
<=> ( V_xs_2 = V_ys_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
thf(973,axiom,
! [V_us: $i,V_ys: $i,V_zs: $i,V_xs1: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_xs1 )
= V_zs )
=> ( ( V_ys
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs1 ) @ V_us ) )
=> ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_zs ) @ V_us ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(974,axiom,
! [V_x_H: $i,V_x: $i,V_xs: $i,T_a: $i,V_i_H: $i,V_i: $i] :
( ( V_i != V_i_H )
=> ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i_H ) @ V_x_H )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i_H ) @ V_x_H ) ) @ V_i ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).
thf(975,axiom,
! [V_y: $i,V_x: $i,V_i: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_x ) ) @ V_i ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ T_a @ V_xs ) @ V_i ) @ V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).
thf(976,axiom,
! [V_zs_2: $i,V_xs_2: $i,V_ys_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_ys_2 ) @ V_xs_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_zs_2 ) @ V_xs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(977,axiom,
! [V_zs_2: $i,V_ys_2: $i,V_xs_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_ys_2 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_b ) @ V_xs_2 ) @ V_zs_2 ) )
<=> ( V_ys_2 = V_zs_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(978,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/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(979,axiom,
! [V_zs: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ V_ys ) ) @ V_zs )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_xs ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ T_a ) @ V_ys ) @ V_zs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1224,axiom,
! [V_list_H_2: $i,V_a_H_2: $i,V_list_2: $i,V_a_2: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_2 ) @ V_list_2 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_b ) @ V_a_H_2 ) @ V_list_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_list_2 = V_list_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1225,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs )
!= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(1226,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( V_xs
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ T_a ) @ V_x ) @ V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1252,axiom,
! [V_x_2: $i,V_F_2: $i,V_g_2: $i,V_z_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ T_b @ T_c @ V_f_2 @ V_z_2 @ V_g_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1371,axiom,
! [V_x_2: $i,V_na_2: $i,T_b: $i,V_f_2: $i] :
( ( hAPP @ V_f_2 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ V_x_2 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ T_b @ T_b ) @ V_na_2 ) @ V_f_2 ) @ ( hAPP @ V_f_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(1483,axiom,
! [V_r_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ T_c @ T_b ) @ ( hAPP @ ( c_Relation_Oconverse @ T_b @ T_c ) @ V_r_2 ) )
= V_r_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1549,axiom,
! [V_z_2: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_y_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
thf(1682,axiom,
! [V_v_2: $i,V_c_2: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= V_c_2 )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ V_v_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(1685,axiom,
! [T_f: $i,T_e: $i,T_d: $i,T_b: $i,T_c: $i,V_x_H_2: $i,V_g_H_2: $i,V_f_H_2: $i,V_x_2: $i,V_g_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) )
= ( hAPP @ V_f_H_2 @ ( hAPP @ V_g_H_2 @ V_x_H_2 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_b @ T_f @ V_f_H_2 ) @ V_g_H_2 ) @ V_x_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(1686,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).
thf(1687,axiom,
! [V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ! [B_v: $i] :
( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ B_v ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ B_v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(1688,axiom,
! [V_v_2: $i,V_d_2: $i,V_c_2: $i,T_e: $i,V_b_2: $i,V_a_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ V_c_2 ) @ V_d_2 ) )
=> ( ( hAPP @ V_a_2 @ ( hAPP @ V_b_2 @ V_v_2 ) )
= ( hAPP @ V_c_2 @ ( hAPP @ V_d_2 @ V_v_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(1689,axiom,
! [V_x_2: $i,V_g_2: $i,V_f_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ T_c @ T_b @ T_d @ V_f_2 ) @ V_g_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ ( hAPP @ V_g_2 @ V_x_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(1690,axiom,
! [V_h_2: $i,V_g_2: $i,T_e: $i,V_f_2: $i,T_b: $i,T_c: $i,T_d: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_b @ V_f_2 ) @ ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_d @ T_b @ V_g_2 ) @ V_h_2 ) )
= ( hAPP @ ( c_Fun_Ocomp @ T_e @ T_c @ T_b @ ( hAPP @ ( c_Fun_Ocomp @ T_d @ T_c @ T_e @ V_f_2 ) @ V_g_2 ) ) @ V_h_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(1817,axiom,
! [V_T_2: $i,V_S_2: $i,V_R_2: $i,T_e: $i,T_c: $i,T_d: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_d @ T_c ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_d ) @ V_R_2 ) @ V_S_2 ) ) @ V_T_2 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_b @ T_e @ T_c ) @ V_R_2 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ T_e @ T_d @ T_c ) @ V_S_2 ) @ V_T_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1838,axiom,
! [V_x_1: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x_1 )
= V_x_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
thf(1839,axiom,
! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).
thf(1904,axiom,
! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
thf(1925,axiom,
! [V_z_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Finite__Set_Ofun__left__comm__idem @ T_b @ T_c @ V_f_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) )
= ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
thf(2079,axiom,
! [V_y_2: $i,V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( ( hAPP @ V_Rep_2 @ V_x_2 )
= ( hAPP @ V_Rep_2 @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(2080,axiom,
! [V_x_2: $i,V_A_2: $i,V_Abs_2: $i,V_Rep_2: $i,T_c: $i,T_b: $i] :
( ( c_Typedef_Otype__definition @ T_b @ T_c @ V_Rep_2 @ V_Abs_2 @ V_A_2 )
=> ( ( hAPP @ V_Abs_2 @ ( hAPP @ V_Rep_2 @ V_x_2 ) )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(2422,axiom,
! [V_x_2: $i,V_F_2: $i,V_f_2: $i,T_b: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ T_b @ V_f_2 @ V_F_2 )
=> ( ( hAPP @ ( hAPP @ V_f_2 @ V_x_2 ) @ V_x_2 )
= V_x_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(2522,axiom,
! [V_b_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_a_2: $i,V_x_2: $i] :
( ( ( V_x_2 = V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= V_b_2 ) )
& ( ( V_x_2 != V_a_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_a_2 @ V_b_2 ) @ V_x_2 )
= ( hAPP @ V_f_2 @ V_x_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(2523,axiom,
! [T_b: $i,T_c: $i,V_y_2: $i,V_x_2: $i,V_f_2: $i] :
( ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 )
=> ( ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(2524,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2526,axiom,
! [V_y_2: $i,V_f_2: $i,T_c: $i,T_b: $i,V_x_2: $i,V_z_2: $i] :
( ( ( V_z_2 = V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= V_y_2 ) )
& ( ( V_z_2 != V_x_2 )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_z_2 )
= ( hAPP @ V_f_2 @ V_z_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(2527,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ T_c @ T_b @ V_f_2 @ V_x_2 @ V_y_2 ) @ V_x_2 )
= V_y_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(2529,axiom,
! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(2531,axiom,
! [V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ ( hAPP @ V_f_2 @ V_x_2 ) )
= V_f_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(2745,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ V_x_2 )
= ( hAPP @ c_Int_ORep__Integ @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(2960,axiom,
! [V_A_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(2961,axiom,
! [V_A_2: $i,V_y_2: $i,V_x_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ V_A_2 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_y_2 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ T_b ) @ V_x_2 ) @ V_A_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(3382,axiom,
! [V_l_2: $i,V_k_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_k_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_l_2 ) )
<=> ( V_k_2 = V_l_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
thf(3383,axiom,
! [V_y_2: $i,V_x_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Onat__of @ V_x_2 )
= ( hAPP @ c_Code__Numeral_Onat__of @ V_y_2 ) )
<=> ( V_x_2 = V_y_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
thf(3398,axiom,
! [V_m_2: $i,V_na_2: $i] :
( ( ( hAPP @ c_Code__Numeral_Oof__nat @ V_na_2 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ V_m_2 ) )
<=> ( V_na_2 = V_m_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
thf(3564,axiom,
! [V_c_2: $i,T_d: $i,T_c: $i,T_b: $i,V_q_2: $i,V_p_2: $i] :
( ( V_p_2 = V_q_2 )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_p_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ T_b @ T_c @ T_d ) @ V_c_2 ) @ V_q_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(3622,axiom,
! [V_b_H_2: $i,V_a_H_2: $i,V_b_2: $i,V_a_2: $i,T_c: $i,T_b: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_2 ) @ V_b_2 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_b @ T_c ) @ V_a_H_2 ) @ V_b_H_2 ) )
<=> ( ( V_a_2 = V_a_H_2 )
& ( V_b_2 = V_b_H_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(3623,axiom,
! [V_b_H: $i,V_a_H: $i,V_b: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ T_a @ T_b ) @ V_a_H ) @ V_b_H ) )
=> ~ ( ( V_a = V_a_H )
=> ( V_b != V_b_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(5171,axiom,
! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__nat__rec__Suc) ).
thf(5206,axiom,
! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(5207,axiom,
! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(5211,axiom,
! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(5212,axiom,
! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(5213,axiom,
! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(5214,axiom,
! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(5215,axiom,
! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(5216,axiom,
! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(5217,axiom,
! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(5219,axiom,
! [V_y: $i,V_x: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_x )
= ( hAPP @ c_Nat_OSuc @ V_y ) )
=> ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5220,axiom,
! [V_nat_H_2: $i,V_nat_2: $i] :
( ( ( hAPP @ c_Nat_OSuc @ V_nat_2 )
= ( hAPP @ c_Nat_OSuc @ V_nat_H_2 ) )
<=> ( V_nat_2 = V_nat_H_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(5221,axiom,
! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(5222,axiom,
! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(5223,axiom,
! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(5224,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(5225,conjecture,
( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(5226,negated_conjecture,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5225]) ).
thf(5227,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) )
=> ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5226]) ).
thf(5228,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(5229,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(5230,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(5231,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(5232,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(5233,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)],[542]) ).
thf(5234,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)],[543]) ).
thf(5235,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)],[544]) ).
thf(5236,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)],[973]) ).
thf(5237,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)],[974]) ).
thf(5238,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)],[975]) ).
thf(5239,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)],[976]) ).
thf(5240,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)],[977]) ).
thf(5241,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)],[978]) ).
thf(5242,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)],[979]) ).
thf(5243,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)],[1224]) ).
thf(5244,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)],[1225]) ).
thf(5245,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)],[1226]) ).
thf(5246,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)],[1252]) ).
thf(5247,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)],[1371]) ).
thf(5248,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)],[1483]) ).
thf(5249,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)],[1549]) ).
thf(5250,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)],[1682]) ).
thf(5251,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)],[1685]) ).
thf(5252,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)],[1686]) ).
thf(5253,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)],[1687]) ).
thf(5254,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)],[1688]) ).
thf(5255,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)],[1689]) ).
thf(5256,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)],[1690]) ).
thf(5257,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)],[1817]) ).
thf(5258,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)],[1838]) ).
thf(5259,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[1839]) ).
thf(5260,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1904]) ).
thf(5261,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)],[1925]) ).
thf(5262,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)],[2079]) ).
thf(5263,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)],[2080]) ).
thf(5264,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)],[2422]) ).
thf(5265,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)],[2522]) ).
thf(5266,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)],[2523]) ).
thf(5267,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)],[2524]) ).
thf(5268,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)],[2526]) ).
thf(5269,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)],[2527]) ).
thf(5270,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)],[2529]) ).
thf(5271,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)],[2531]) ).
thf(5272,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)],[2745]) ).
thf(5273,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)],[2960]) ).
thf(5274,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)],[2961]) ).
thf(5275,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)],[3382]) ).
thf(5276,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)],[3383]) ).
thf(5277,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)],[3398]) ).
thf(5278,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)],[3564]) ).
thf(5279,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)],[3622]) ).
thf(5280,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)],[3623]) ).
thf(5281,plain,
( ( ! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5171]) ).
thf(5282,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5206]) ).
thf(5283,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5207]) ).
thf(5284,plain,
( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5211]) ).
thf(5285,plain,
( ( ! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5212]) ).
thf(5286,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5213]) ).
thf(5287,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5214]) ).
thf(5288,plain,
( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[5215]) ).
thf(5289,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5216]) ).
thf(5290,plain,
( ( ! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5217]) ).
thf(5291,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)],[5219]) ).
thf(5292,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)],[5220]) ).
thf(5293,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[5221]) ).
thf(5294,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5222]) ).
thf(5295,plain,
( ( ! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5223]) ).
thf(5296,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)],[5224]) ).
thf(5297,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[5227]) ).
thf(5298,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[5227]) ).
thf(5299,plain,
( ( ~ ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5298]) ).
thf(5300,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)],[5296]) ).
thf(5301,plain,
( ( ! [V_s_H: $i,V_n: $i,V_s: $i,V_c: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
=> ( c_Natural_Oevaln @ V_c @ V_s @ ( hAPP @ c_Nat_OSuc @ V_n ) @ V_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[5295]) ).
thf(5302,plain,
( ( ! [V_n: $i] :
( V_n
!= ( hAPP @ c_Nat_OSuc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[5294]) ).
thf(5303,plain,
( ( ! [V_n: $i] :
( ( hAPP @ c_Nat_OSuc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[5293]) ).
thf(5304,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)],[5292]) ).
thf(5305,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)],[5291]) ).
thf(5306,plain,
( ( ! [V_na_2: $i,V_a_2: $i,V_times_2: $i,V_one_2: $i,T_b: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_times_2 @ V_a_2 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ T_b @ V_one_2 @ V_times_2 ) @ V_a_2 ) @ V_na_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5290]) ).
thf(5307,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( c_Nat_Onat_Onat__case @ T_b @ V_f1_2 @ V_f2_2 @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ V_f2_2 @ V_nat_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5289]) ).
thf(5308,plain,
( ( ! [V_n: $i,V_s: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[5288]) ).
thf(5309,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t )
=> ( V_t = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[5287]) ).
thf(5310,plain,
( ( ! [V_s2: $i,V_c1: $i,V_s1: $i,V_n: $i,V_s0: $i,V_c0: $i] :
( ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 )
=> ( ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5286]) ).
thf(5311,plain,
( ( ! [V_a6_2: $i,V_a3_2: $i,V_a2_2: $i,V_a5_2: $i,V_a1_2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_a1_2 @ V_a5_2 ) @ V_a2_2 @ V_a3_2 @ V_a6_2 )
<=> ? [B_s1: $i] :
( ( c_Natural_Oevaln @ V_a1_2 @ V_a2_2 @ V_a3_2 @ B_s1 )
& ( c_Natural_Oevaln @ V_a5_2 @ B_s1 @ V_a3_2 @ V_a6_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5285]) ).
thf(5312,plain,
( ( ! [V_a2: $i,V_a1: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_a1 @ V_a2 @ V_a1 ) )
= $true ),
inference(copy,[status(thm)],[5284]) ).
thf(5313,plain,
( ( ! [V_t: $i,V_n: $i,V_s: $i,V_c2: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t )
=> ~ ! [B_s1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ B_s1 )
=> ~ ( c_Natural_Oevaln @ V_c2 @ B_s1 @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[5283]) ).
thf(5314,plain,
( ( ! [V_nat_2: $i,V_f2_2: $i,V_f1_2: $i,T_b: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ ( hAPP @ c_Nat_OSuc @ V_nat_2 ) )
= ( hAPP @ ( hAPP @ V_f2_2 @ V_nat_2 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_f1_2 @ V_f2_2 ) @ V_nat_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5282]) ).
thf(5315,plain,
( ( ! [V_na_2: $i,V_h_2: $i,V_c_2: $i,T_b: $i,V_f_2: $i] :
( ! [B_n: $i] :
( ( hAPP @ V_f_2 @ B_n )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ T_b @ V_c_2 @ V_h_2 ) @ B_n ) )
=> ( ( hAPP @ V_f_2 @ ( hAPP @ c_Nat_OSuc @ V_na_2 ) )
= ( hAPP @ ( hAPP @ V_h_2 @ V_na_2 ) @ ( hAPP @ V_f_2 @ V_na_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5281]) ).
thf(5316,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)],[5280]) ).
thf(5317,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)],[5279]) ).
thf(5318,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)],[5278]) ).
thf(5319,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)],[5277]) ).
thf(5320,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)],[5276]) ).
thf(5321,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)],[5275]) ).
thf(5322,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)],[5274]) ).
thf(5323,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)],[5273]) ).
thf(5324,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)],[5272]) ).
thf(5325,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)],[5271]) ).
thf(5326,plain,
( ( ! [V_y_2: $i,V_x_2: $i,V_f_2: $i,T_c: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ T_b @ T_c @ V_f_2 @ V_x_2 @ V_y_2 )
= V_f_2 )
<=> ( ( hAPP @ V_f_2 @ V_x_2 )
= V_y_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5270]) ).
thf(5327,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)],[5269]) ).
thf(5328,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)],[5268]) ).
thf(5329,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)],[5267]) ).
thf(5330,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)],[5266]) ).
thf(5331,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)],[5265]) ).
thf(5332,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)],[5264]) ).
thf(5333,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)],[5263]) ).
thf(5334,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)],[5262]) ).
thf(5335,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)],[5261]) ).
thf(5336,plain,
( ( ! [V_P_2: $i,T_b: $i] :
( ( hAPP @ ( c_Set_OCollect @ T_b ) @ V_P_2 )
= V_P_2 ) )
= $true ),
inference(copy,[status(thm)],[5260]) ).
thf(5337,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[5259]) ).
thf(5338,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)],[5258]) ).
thf(5339,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)],[5257]) ).
thf(5340,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)],[5256]) ).
thf(5341,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)],[5255]) ).
thf(5342,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)],[5254]) ).
thf(5343,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)],[5253]) ).
thf(5344,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)],[5252]) ).
thf(5345,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)],[5251]) ).
thf(5346,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)],[5250]) ).
thf(5347,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)],[5249]) ).
thf(5348,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)],[5248]) ).
thf(5349,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)],[5247]) ).
thf(5350,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)],[5246]) ).
thf(5351,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)],[5245]) ).
thf(5352,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)],[5244]) ).
thf(5353,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)],[5243]) ).
thf(5354,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)],[5242]) ).
thf(5355,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)],[5241]) ).
thf(5356,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)],[5240]) ).
thf(5357,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)],[5239]) ).
thf(5358,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)],[5238]) ).
thf(5359,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)],[5237]) ).
thf(5360,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)],[5236]) ).
thf(5361,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)],[5235]) ).
thf(5362,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)],[5234]) ).
thf(5363,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)],[5233]) ).
thf(5364,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[5232]) ).
thf(5365,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)],[5231]) ).
thf(5366,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_d: $i,T_b: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ T_c @ T_b @ T_d ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ V_P_2 @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5230]) ).
thf(5367,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ V_Q_2 ) ) )
= $true ),
inference(copy,[status(thm)],[5229]) ).
thf(5368,plain,
( ( ! [V_R_2: $i,V_Q_2: $i,V_P_2: $i,T_b: $i,T_d: $i,T_c: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ T_c @ T_d @ T_b ) @ V_P_2 ) @ V_Q_2 ) @ V_R_2 )
= ( hAPP @ ( hAPP @ V_P_2 @ V_R_2 ) @ ( hAPP @ V_Q_2 @ V_R_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5228]) ).
thf(5369,plain,
( ( ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ ( hAPP @ c_Nat_OSuc @ v_n ) @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5297]) ).
thf(5370,plain,
( ( ~ ! [B_Z: $i,B_s: $i] :
( ( v_fun1 @ B_Z @ B_s )
=> ! [B_s_H: $i] :
( ( c_Natural_Oevaln @ v_com @ B_s @ v_n @ B_s_H )
=> ( v_fun2 @ B_Z @ B_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[5299]) ).
thf(5371,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)],[5345]) ).
thf(5372,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)],[5330]) ).
thf(5373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5313]) ).
thf(5374,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)],[5342]) ).
thf(5375,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)],[5347]) ).
thf(5376,plain,
( ( ! [SX0: $i] :
( ( hAPP @ c_Nat_OSuc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5303]) ).
thf(5377,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_fun1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SX1 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SX2 )
| ( v_fun2 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5369]) ).
thf(5378,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)],[5324]) ).
thf(5379,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)],[5332]) ).
thf(5380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( v_fun1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SX1 @ v_n @ SX2 )
| ( v_fun2 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5370]) ).
thf(5381,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)],[5326]) ).
thf(5382,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)],[5317]) ).
thf(5383,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)],[5334]) ).
thf(5384,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)],[5321]) ).
thf(5385,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)],[5359]) ).
thf(5386,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( c_Natural_Oevaln @ SX5 @ SX4 @ SX3 @ SX2 )
| ~ ( c_Natural_Oevaln @ SX1 @ SX2 @ SX3 @ SX0 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX5 @ SX1 ) @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5310]) ).
thf(5387,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)],[5304]) ).
thf(5388,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)],[5316]) ).
thf(5389,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)],[5320]) ).
thf(5390,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX2 ) @ SX1 ) @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[5352]) ).
thf(5391,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)],[5328]) ).
thf(5392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ( hAPP @ SX1 @ SX2 )
= ( hAPP @ SX0 @ SX2 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5300]) ).
thf(5393,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX2
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SX1 ) @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5351]) ).
thf(5394,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)],[5343]) ).
thf(5395,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_Natural_Oevaln @ SX3 @ SX2 @ SX1 @ SX0 )
| ( c_Natural_Oevaln @ SX3 @ SX2 @ ( hAPP @ c_Nat_OSuc @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5301]) ).
thf(5396,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)],[5335]) ).
thf(5397,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)],[5318]) ).
thf(5398,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)],[5360]) ).
thf(5399,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SX2 @ SX1 @ SX0 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5309]) ).
thf(5400,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)],[5346]) ).
thf(5401,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)],[5355]) ).
thf(5402,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)],[5333]) ).
thf(5403,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)],[5357]) ).
thf(5404,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)],[5331]) ).
thf(5405,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)],[5361]) ).
thf(5406,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SX4 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SX3 @ SX2 @ SX1 ) @ SX5 ) )
| ( ( hAPP @ SX4 @ ( hAPP @ c_Nat_OSuc @ SX0 ) )
= ( hAPP @ ( hAPP @ SX1 @ SX0 ) @ ( hAPP @ SX4 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5315]) ).
thf(5407,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SX4 @ SX2 @ SX1 @ SX5 )
| ~ ( c_Natural_Oevaln @ SX3 @ SX5 @ SX1 @ SX0 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SX4 @ SX3 ) @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5311]) ).
thf(5408,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)],[5356]) ).
thf(5409,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SX1 )
!= ( hAPP @ c_Nat_OSuc @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5305]) ).
thf(5410,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)],[5319]) ).
thf(5411,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)],[5362]) ).
thf(5412,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)],[5329]) ).
thf(5413,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)],[5353]) ).
thf(5414,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)],[5350]) ).
thf(5415,plain,
( ( ! [SX0: $i] :
( SX0
!= ( hAPP @ c_Nat_OSuc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5302]) ).
thf(5416,plain,
! [SV1: $i] :
( ( ! [SY321: $i,SY322: $i,SY323: $i,SY324: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY324 @ SY323 @ SY322 ) @ SY321 ) @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ ( hAPP @ SY322 @ SY321 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY324 @ SY323 @ SY322 ) @ SY321 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5306]) ).
thf(5417,plain,
! [SV2: $i] :
( ( ! [SY325: $i,SY326: $i,SY327: $i] :
( ( c_Nat_Onat_Onat__case @ SY327 @ SY326 @ SY325 @ ( hAPP @ c_Nat_OSuc @ SV2 ) )
= ( hAPP @ SY325 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5307]) ).
thf(5418,plain,
! [SV3: $i] :
( ( ! [SY328: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY328 @ SV3 @ SY328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5308]) ).
thf(5419,plain,
! [SV4: $i] :
( ( ! [SY329: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY329 @ SV4 @ SY329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5312]) ).
thf(5420,plain,
! [SV5: $i] :
( ( ! [SY330: $i,SY331: $i,SY332: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY332 @ SY331 @ SY330 ) @ ( hAPP @ c_Nat_OSuc @ SV5 ) )
= ( hAPP @ ( hAPP @ SY330 @ SV5 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY332 @ SY331 @ SY330 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5314]) ).
thf(5421,plain,
! [SV6: $i] :
( ( ! [SY333: $i,SY334: $i,SY335: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY335 ) @ SY334 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY335 ) @ SY333 ) @ SV6 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY335 ) @ SY333 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY335 ) @ SY334 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5322]) ).
thf(5422,plain,
! [SV7: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY337 ) @ SY336 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY337 ) @ SY336 ) @ SV7 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY337 ) @ SY336 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5323]) ).
thf(5423,plain,
! [SV8: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i] :
( ( c_Fun_Ofun__upd @ SY340 @ SY339 @ SY338 @ SV8 @ ( hAPP @ SY338 @ SV8 ) )
= SY338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5325]) ).
thf(5424,plain,
! [SV9: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i,SY344: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY344 @ SY343 @ SY342 @ SY341 @ SV9 ) @ SY341 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5327]) ).
thf(5425,plain,
! [SV10: $i] :
( ( ! [SY345: $i] :
( ( hAPP @ ( c_Set_OCollect @ SY345 ) @ SV10 )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5336]) ).
thf(5426,plain,
! [SV11: $i] :
( ( ! [SY346: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY346 ) @ SV11 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5337]) ).
thf(5427,plain,
! [SV12: $i] :
( ( ! [SY347: $i] :
( ( hAPP @ ( c_Fun_Oid @ SY347 ) @ SV12 )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5338]) ).
thf(5428,plain,
! [SV13: $i] :
( ( ! [SY348: $i,SY349: $i,SY350: $i,SY351: $i,SY352: $i,SY353: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY353 @ SY352 @ SY351 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY353 @ SY350 @ SY352 ) @ SY349 ) @ SY348 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY353 @ SY350 @ SY351 ) @ SY349 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY350 @ SY352 @ SY351 ) @ SY348 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5339]) ).
thf(5429,plain,
! [SV14: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i,SY358: $i,SY359: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY359 @ SY358 @ SY357 @ SY356 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY355 @ SY359 @ SY357 @ SY354 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY355 @ SY358 @ SY357 @ ( hAPP @ ( c_Fun_Ocomp @ SY359 @ SY358 @ SY355 @ SY356 ) @ SY354 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5340]) ).
thf(5430,plain,
! [SV15: $i] :
( ( ! [SY360: $i,SY361: $i,SY362: $i,SY363: $i,SY364: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY364 @ SY363 @ SY362 @ SY361 ) @ SY360 ) @ SV15 )
= ( hAPP @ SY361 @ ( hAPP @ SY360 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5341]) ).
thf(5431,plain,
! [SV16: $i] :
( ( ! [SY365: $i,SY366: $i,SY367: $i,SY368: $i,SY369: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY369 @ SY368 @ SY367 @ SY366 ) @ SY365 ) @ SV16 )
= ( hAPP @ SY366 @ ( hAPP @ SY365 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5344]) ).
thf(5432,plain,
! [SV17: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY371 @ SY370 ) @ ( hAPP @ ( c_Relation_Oconverse @ SY370 @ SY371 ) @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5348]) ).
thf(5433,plain,
! [SV18: $i] :
( ( ! [SY372: $i,SY373: $i,SY374: $i] :
( ( hAPP @ SY374 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY373 @ SY373 ) @ SY372 ) @ SY374 ) @ SV18 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY373 @ SY373 ) @ SY372 ) @ SY374 ) @ ( hAPP @ SY374 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5349]) ).
thf(5434,plain,
! [SV19: $i] :
( ( ! [SY375: $i,SY376: $i,SY377: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY377 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY377 ) @ SY376 ) @ SY375 ) ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY377 ) @ SY376 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY377 ) @ SY375 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5354]) ).
thf(5435,plain,
! [SV20: $i] :
( ( ! [SY378: $i,SY379: $i,SY380: $i,SY381: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY381 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY381 @ SY380 ) @ SY379 ) @ SY378 ) ) @ SY379 ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY381 @ SY380 ) @ SY379 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5358]) ).
thf(5436,plain,
! [SV21: $i] :
( ( ! [SY382: $i] :
( ( hAPP @ ( c_List_Orev @ SY382 ) @ ( hAPP @ ( c_List_Orev @ SY382 ) @ SV21 ) )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5437,plain,
! [SV22: $i] :
( ( ! [SY383: $i] :
( ( hAPP @ ( c_COMBI @ SY383 ) @ SV22 )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5364]) ).
thf(5438,plain,
! [SV23: $i] :
( ( ! [SY384: $i,SY385: $i,SY386: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY386 @ SY385 ) @ SY384 ) @ SV23 )
= SY384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(5439,plain,
! [SV24: $i] :
( ( ! [SY387: $i,SY388: $i,SY389: $i,SY390: $i,SY391: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY391 @ SY390 @ SY389 ) @ SY388 ) @ SY387 ) @ SV24 )
= ( hAPP @ SY388 @ ( hAPP @ SY387 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5366]) ).
thf(5440,plain,
! [SV25: $i] :
( ( ! [SY392: $i,SY393: $i,SY394: $i,SY395: $i,SY396: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY396 @ SY395 @ SY394 ) @ SY393 ) @ SY392 ) @ SV25 )
= ( hAPP @ ( hAPP @ SY393 @ SV25 ) @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5367]) ).
thf(5441,plain,
! [SV26: $i] :
( ( ! [SY397: $i,SY398: $i,SY399: $i,SY400: $i,SY401: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY401 @ SY400 @ SY399 ) @ SY398 ) @ SY397 ) @ SV26 )
= ( hAPP @ ( hAPP @ SY398 @ SV26 ) @ ( hAPP @ SY397 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5368]) ).
thf(5442,plain,
! [SV27: $i] :
( ( ! [SY402: $i,SY403: $i,SY404: $i,SY405: $i,SY406: $i,SY407: $i,SY408: $i,SY409: $i,SY410: $i,SY411: $i] :
( ( ( hAPP @ SY411 @ ( hAPP @ SY410 @ SY409 ) )
!= ( hAPP @ SY408 @ ( hAPP @ SY407 @ SY406 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY405 @ SY404 @ SY403 @ SY411 ) @ SY410 ) @ SY409 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY402 @ SY404 @ SV27 @ SY408 ) @ SY407 ) @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5371]) ).
thf(5443,plain,
! [SV28: $i] :
( ( ! [SY412: $i,SY413: $i,SY414: $i,SY415: $i] :
( ( ( hAPP @ SY415 @ SY414 )
!= SY413 )
| ( ( c_Fun_Ofun__upd @ SY412 @ SV28 @ SY415 @ SY414 @ SY413 )
= SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5372]) ).
thf(5444,plain,
! [SV29: $i] :
( ( ! [SY416: $i,SY417: $i,SY418: $i,SY419: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY419 @ SY418 ) @ SY417 @ SY416 @ SV29 )
| ~ ! [SY420: $i] :
( ~ ( c_Natural_Oevaln @ SY419 @ SY417 @ SY416 @ SY420 )
| ~ ( c_Natural_Oevaln @ SY418 @ SY420 @ SY416 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5373]) ).
thf(5445,plain,
! [SV30: $i] :
( ( ! [SY421: $i,SY422: $i,SY423: $i,SY424: $i,SY425: $i,SY426: $i,SY427: $i,SY428: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY428 @ SY427 @ SY426 @ SY425 ) @ SY424 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY423 @ SY427 @ SY426 @ SY422 ) @ SY421 ) )
| ( ( hAPP @ SY425 @ ( hAPP @ SY424 @ SV30 ) )
= ( hAPP @ SY422 @ ( hAPP @ SY421 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5374]) ).
thf(5446,plain,
! [SV31: $i] :
( ( ! [SY429: $i,SY430: $i,SY431: $i,SY432: $i,SY433: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY433 @ SY432 @ SY431 )
| ( ( hAPP @ ( hAPP @ SY431 @ SY430 ) @ ( hAPP @ ( hAPP @ SY431 @ SY429 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SY431 @ SY429 ) @ ( hAPP @ ( hAPP @ SY431 @ SY430 ) @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5375]) ).
thf(5447,plain,
! [SV32: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV32 )
!= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5376]) ).
thf(5448,plain,
! [SV33: $i] :
( ( ! [SY434: $i] :
( ~ ( v_fun1 @ SV33 @ SY434 )
| ! [SY435: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SY434 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY435 )
| ( v_fun2 @ SV33 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(5449,plain,
! [SV34: $i] :
( ( ! [SY436: $i] :
~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SY436 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
| ( SY436 = SV34 ) )
| ~ ( ( SY436 != SV34 )
| ( ( hAPP @ c_Int_ORep__Integ @ SY436 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5378]) ).
thf(5450,plain,
! [SV35: $i] :
( ( ! [SY437: $i,SY438: $i,SY439: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY439 @ SY438 @ SY437 )
| ( ( hAPP @ ( hAPP @ SY438 @ SV35 ) @ SV35 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5379]) ).
thf(5451,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( v_fun1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SX1 @ v_n @ SX2 )
| ( v_fun2 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5380]) ).
thf(5452,plain,
! [SV36: $i] :
( ( ! [SY440: $i,SY441: $i,SY442: $i,SY443: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY443 @ SY442 @ SY441 @ SY440 @ SV36 )
!= SY441 )
| ( ( hAPP @ SY441 @ SY440 )
= SV36 ) )
| ~ ( ( ( hAPP @ SY441 @ SY440 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SY443 @ SY442 @ SY441 @ SY440 @ SV36 )
= SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5381]) ).
thf(5453,plain,
! [SV37: $i] :
( ( ! [SY444: $i,SY445: $i,SY446: $i,SY447: $i,SY448: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY448 @ SY447 ) @ SY446 ) @ SY445 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY448 @ SY447 ) @ SY444 ) @ SV37 ) )
| ~ ( ( SY446 != SY444 )
| ( SY445 != SV37 ) ) )
| ~ ( ~ ~ ( ( SY446 != SY444 )
| ( SY445 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY448 @ SY447 ) @ SY446 ) @ SY445 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY448 @ SY447 ) @ SY444 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(5454,plain,
! [SV38: $i] :
( ( ! [SY449: $i,SY450: $i,SY451: $i,SY452: $i,SY453: $i,SY454: $i] :
( ~ ( c_Typedef_Otype__definition @ SY454 @ SY453 @ SY452 @ SY451 @ SY450 )
| ~ ( ~ ( ( ( hAPP @ SY452 @ SY449 )
!= ( hAPP @ SY452 @ SV38 ) )
| ( SY449 = SV38 ) )
| ~ ( ( SY449 != SV38 )
| ( ( hAPP @ SY452 @ SY449 )
= ( hAPP @ SY452 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5383]) ).
thf(5455,plain,
! [SV39: $i] :
( ( ! [SY455: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY455 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
| ( SY455 = SV39 ) )
| ~ ( ( SY455 != SV39 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY455 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5384]) ).
thf(5456,plain,
! [SV40: $i] :
( ( ! [SY456: $i,SY457: $i,SY458: $i,SY459: $i,SY460: $i] :
( ~ ( ( SY460 != SY459 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY458 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY458 @ SY457 ) @ SY460 ) @ SY456 ) ) @ SY459 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY458 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY458 @ SY457 ) @ SY459 ) @ SV40 ) ) @ SY460 ) @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5385]) ).
thf(5457,plain,
! [SV41: $i] :
( ( ! [SY461: $i,SY462: $i,SY463: $i,SY464: $i,SY465: $i] :
( ~ ( c_Natural_Oevaln @ SY465 @ SY464 @ SY463 @ SY462 )
| ~ ( c_Natural_Oevaln @ SY461 @ SY462 @ SY463 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY465 @ SY461 ) @ SY464 @ SY463 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5386]) ).
thf(5458,plain,
! [SV42: $i] :
( ( ! [SY466: $i] :
~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SY466 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SY466 = SV42 ) )
| ~ ( ( SY466 != SV42 )
| ( ( hAPP @ c_Nat_OSuc @ SY466 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5387]) ).
thf(5459,plain,
! [SV43: $i] :
( ( ! [SY467: $i,SY468: $i,SY469: $i,SY470: $i,SY471: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY471 @ SY470 ) @ SY469 ) @ SY468 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY471 @ SY470 ) @ SY467 ) @ SV43 ) )
| ~ ( ( SY469 != SY467 )
| ( SY468 != SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5388]) ).
thf(5460,plain,
! [SV44: $i] :
( ( ! [SY472: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SY472 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SY472 = SV44 ) )
| ~ ( ( SY472 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SY472 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5389]) ).
thf(5461,plain,
! [SV45: $i] :
( ( ! [SY473: $i,SY474: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY474 ) @ SY473 ) @ SV45 )
!= SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5390]) ).
thf(5462,plain,
! [SV46: $i] :
( ( ! [SY475: $i,SY476: $i,SY477: $i,SY478: $i,SY479: $i] :
~ ( ~ ( ( SY479 != SY478 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY477 @ SY476 @ SY475 @ SY478 @ SV46 ) @ SY479 )
= SV46 ) )
| ~ ( ~ ( ( SY479 != SY478 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY477 @ SY476 @ SY475 @ SY478 @ SV46 ) @ SY479 )
= ( hAPP @ SY475 @ SY479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5391]) ).
thf(5463,plain,
! [SV47: $i] :
( ( ! [SY480: $i] :
( ~ ! [SY481: $i] :
( ( hAPP @ SY480 @ SY481 )
= ( hAPP @ SV47 @ SY481 ) )
| ( SY480 = SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5392]) ).
thf(5464,plain,
! [SV48: $i] :
( ( ! [SY482: $i,SY483: $i] :
( SY483
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY482 ) @ SV48 ) @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5393]) ).
thf(5465,plain,
! [SV49: $i] :
( ( ! [SY484: $i,SY485: $i,SY486: $i,SY487: $i,SY488: $i,SY489: $i,SY490: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY490 @ SY489 @ SY488 @ SY487 ) @ SY486 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY485 @ SY489 @ SY488 @ SY484 ) @ SV49 ) )
| ! [SY491: $i] :
( ( hAPP @ SY487 @ ( hAPP @ SY486 @ SY491 ) )
= ( hAPP @ SY484 @ ( hAPP @ SV49 @ SY491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5394]) ).
thf(5466,plain,
! [SV50: $i] :
( ( ! [SY492: $i,SY493: $i,SY494: $i] :
( ~ ( c_Natural_Oevaln @ SY494 @ SY493 @ SY492 @ SV50 )
| ( c_Natural_Oevaln @ SY494 @ SY493 @ ( hAPP @ c_Nat_OSuc @ SY492 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5395]) ).
thf(5467,plain,
! [SV51: $i] :
( ( ! [SY495: $i,SY496: $i,SY497: $i,SY498: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY498 @ SY497 @ SY496 )
| ( ( hAPP @ ( hAPP @ SY496 @ SY495 ) @ ( hAPP @ ( hAPP @ SY496 @ SY495 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SY496 @ SY495 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5396]) ).
thf(5468,plain,
! [SV52: $i] :
( ( ! [SY499: $i,SY500: $i,SY501: $i,SY502: $i,SY503: $i] :
( ( SY503 != SY502 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY501 @ SY500 @ SY499 ) @ SV52 ) @ SY503 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY501 @ SY500 @ SY499 ) @ SV52 ) @ SY502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(5469,plain,
! [SV53: $i] :
( ( ! [SY504: $i,SY505: $i,SY506: $i,SY507: $i,SY508: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY508 ) @ SY507 ) @ SY506 )
!= SY505 )
| ( SY504
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY508 ) @ SY506 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY508 ) @ SY507 ) @ SY504 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY508 ) @ SY505 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5398]) ).
thf(5470,plain,
! [SV54: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY510 @ SY509 @ SV54 )
| ( SV54 = SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(5471,plain,
! [SV55: $i] :
( ( ! [SY511: $i,SY512: $i,SY513: $i,SY514: $i,SY515: $i,SY516: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY516 @ SY515 @ SY514 @ SY513 ) @ SY512 )
!= SY511 )
| ( ( hAPP @ SY513 @ ( hAPP @ SY512 @ SV55 ) )
= ( hAPP @ SY511 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5400]) ).
thf(5472,plain,
! [SV56: $i] :
( ( ! [SY517: $i,SY518: $i,SY519: $i,SY520: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY519 ) @ SY518 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY517 ) @ SV56 ) )
| ~ ! [SY521: $i] :
~ ( ~ ( ( SY519
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY517 ) @ SY521 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY521 ) @ SY518 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY519 ) @ SY521 )
!= SY517 )
| ( SY518
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY521 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY522: $i] :
~ ( ~ ( ( SY519
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY517 ) @ SY522 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY522 ) @ SY518 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY519 ) @ SY522 )
!= SY517 )
| ( SY518
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY522 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY519 ) @ SY518 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY520 ) @ SY517 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5401]) ).
thf(5473,plain,
! [SV57: $i] :
( ( ! [SY523: $i,SY524: $i,SY525: $i,SY526: $i,SY527: $i] :
( ~ ( c_Typedef_Otype__definition @ SY527 @ SY526 @ SY525 @ SY524 @ SY523 )
| ( ( hAPP @ SY524 @ ( hAPP @ SY525 @ SV57 ) )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5402]) ).
thf(5474,plain,
! [SV58: $i] :
( ( ! [SY528: $i,SY529: $i,SY530: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY530 ) @ SY529 ) @ SY528 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY530 ) @ SV58 ) @ SY528 ) )
| ( SY529 = SV58 ) )
| ~ ( ( SY529 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY530 ) @ SY529 ) @ SY528 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY530 ) @ SV58 ) @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5403]) ).
thf(5475,plain,
! [SV59: $i] :
( ( ! [SY531: $i,SY532: $i,SY533: $i,SY534: $i,SY535: $i] :
~ ( ~ ( ( SY535 != SY534 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY533 @ SY532 @ SY531 @ SY534 @ SV59 ) @ SY535 )
= SV59 ) )
| ~ ( ~ ( ( SY535 != SY534 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY533 @ SY532 @ SY531 @ SY534 @ SV59 ) @ SY535 )
= ( hAPP @ SY531 @ SY535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5404]) ).
thf(5476,plain,
! [SV60: $i] :
( ( ! [SY536: $i,SY537: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY537 ) @ SY536 )
!= ( hAPP @ ( c_List_Orev @ SY537 ) @ SV60 ) )
| ( SY536 = SV60 ) )
| ~ ( ( SY536 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SY537 ) @ SY536 )
= ( hAPP @ ( c_List_Orev @ SY537 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5405]) ).
thf(5477,plain,
! [SV61: $i] :
( ( ! [SY538: $i,SY539: $i,SY540: $i,SY541: $i] :
( ~ ! [SX5: $i] :
( ( hAPP @ SY541 @ SX5 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY540 @ SY539 @ SY538 ) @ SX5 ) )
| ( ( hAPP @ SY541 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SY538 @ SV61 ) @ ( hAPP @ SY541 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5406]) ).
thf(5478,plain,
! [SV62: $i] :
( ( ! [SY543: $i,SY544: $i,SY545: $i,SY546: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY546 @ SY545 ) @ SY544 @ SY543 @ SV62 )
| ~ ! [SY547: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY546 @ SY544 @ SY543 @ SY547 )
| ~ ( c_Natural_Oevaln @ SY545 @ SY547 @ SY543 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY548: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY546 @ SY544 @ SY543 @ SY548 )
| ~ ( c_Natural_Oevaln @ SY545 @ SY548 @ SY543 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY546 @ SY545 ) @ SY544 @ SY543 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5407]) ).
thf(5479,plain,
! [SV63: $i] :
( ( ! [SY549: $i,SY550: $i,SY551: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY551 ) @ SY550 ) @ SY549 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY551 ) @ SY550 ) @ SV63 ) )
| ( SY549 = SV63 ) )
| ~ ( ( SY549 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY551 ) @ SY550 ) @ SY549 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY551 ) @ SY550 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5408]) ).
thf(5480,plain,
! [SV64: $i] :
( ( ! [SY552: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SY552 )
!= ( hAPP @ c_Nat_OSuc @ SV64 ) )
| ( SY552 = SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5409]) ).
thf(5481,plain,
! [SV65: $i] :
( ( ! [SY553: $i] :
~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY553 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
| ( SY553 = SV65 ) )
| ~ ( ( SY553 != SV65 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SY553 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5410]) ).
thf(5482,plain,
! [SV66: $i] :
( ( ! [SY554: $i,SY555: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY555 ) @ SY554 )
!= SV66 )
| ( SY554
= ( hAPP @ ( c_List_Orev @ SY555 ) @ SV66 ) ) )
| ~ ( ( SY554
!= ( hAPP @ ( c_List_Orev @ SY555 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SY555 ) @ SY554 )
= SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5411]) ).
thf(5483,plain,
! [SV67: $i] :
( ( ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i,SY560: $i] :
( ~ ( ( SY560 != SY559 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY558 @ SY557 @ SY556 @ SY559 @ SV67 ) @ SY560 )
= ( hAPP @ SY556 @ SY560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(5484,plain,
! [SV68: $i] :
( ( ! [SY561: $i,SY562: $i,SY563: $i,SY564: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY564 ) @ SY563 ) @ SY562 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY564 ) @ SY561 ) @ SV68 ) )
| ~ ( ( SY563 != SY561 )
| ( SY562 != SV68 ) ) )
| ~ ( ~ ~ ( ( SY563 != SY561 )
| ( SY562 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY564 ) @ SY563 ) @ SY562 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY564 ) @ SY561 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5413]) ).
thf(5485,plain,
! [SV69: $i] :
( ( ! [SY565: $i,SY566: $i,SY567: $i,SY568: $i,SY569: $i,SY570: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY570 @ SY569 @ SY568 @ SY567 @ SY566 @ SY565 )
| ( ( hAPP @ ( hAPP @ SY568 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5414]) ).
thf(5486,plain,
! [SV70: $i] :
( ( SV70
!= ( hAPP @ c_Nat_OSuc @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5415]) ).
thf(5487,plain,
! [SV1: $i,SV71: $i] :
( ( ! [SY571: $i,SY572: $i,SY573: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY573 @ SY572 @ SY571 ) @ SV71 ) @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ ( hAPP @ SY571 @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY573 @ SY572 @ SY571 ) @ SV71 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5416]) ).
thf(5488,plain,
! [SV2: $i,SV72: $i] :
( ( ! [SY574: $i,SY575: $i] :
( ( c_Nat_Onat_Onat__case @ SY575 @ SY574 @ SV72 @ ( hAPP @ c_Nat_OSuc @ SV2 ) )
= ( hAPP @ SV72 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5417]) ).
thf(5489,plain,
! [SV3: $i,SV73: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV73 @ SV3 @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5418]) ).
thf(5490,plain,
! [SV4: $i,SV74: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV74 @ SV4 @ SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5419]) ).
thf(5491,plain,
! [SV5: $i,SV75: $i] :
( ( ! [SY576: $i,SY577: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY577 @ SY576 @ SV75 ) @ ( hAPP @ c_Nat_OSuc @ SV5 ) )
= ( hAPP @ ( hAPP @ SV75 @ SV5 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY577 @ SY576 @ SV75 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5420]) ).
thf(5492,plain,
! [SV6: $i,SV76: $i] :
( ( ! [SY578: $i,SY579: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY579 ) @ SY578 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY579 ) @ SV76 ) @ SV6 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY579 ) @ SV76 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY579 ) @ SY578 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5421]) ).
thf(5493,plain,
! [SV7: $i,SV77: $i] :
( ( ! [SY580: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY580 ) @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY580 ) @ SV77 ) @ SV7 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY580 ) @ SV77 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5422]) ).
thf(5494,plain,
! [SV8: $i,SV78: $i] :
( ( ! [SY581: $i,SY582: $i] :
( ( c_Fun_Ofun__upd @ SY582 @ SY581 @ SV78 @ SV8 @ ( hAPP @ SV78 @ SV8 ) )
= SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5423]) ).
thf(5495,plain,
! [SV9: $i,SV79: $i] :
( ( ! [SY583: $i,SY584: $i,SY585: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY585 @ SY584 @ SY583 @ SV79 @ SV9 ) @ SV79 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5496,plain,
! [SV10: $i,SV80: $i] :
( ( ( hAPP @ ( c_Set_OCollect @ SV80 ) @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5497,plain,
! [SV11: $i,SV81: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV81 ) @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(5498,plain,
! [SV12: $i,SV82: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV82 ) @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5427]) ).
thf(5499,plain,
! [SV13: $i,SV83: $i] :
( ( ! [SY586: $i,SY587: $i,SY588: $i,SY589: $i,SY590: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY590 @ SY589 @ SY588 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY590 @ SY587 @ SY589 ) @ SY586 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY590 @ SY587 @ SY588 ) @ SY586 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY587 @ SY589 @ SY588 ) @ SV83 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5428]) ).
thf(5500,plain,
! [SV14: $i,SV84: $i] :
( ( ! [SY591: $i,SY592: $i,SY593: $i,SY594: $i,SY595: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY595 @ SY594 @ SY593 @ SY592 ) @ ( hAPP @ ( c_Fun_Ocomp @ SY591 @ SY595 @ SY593 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SY591 @ SY594 @ SY593 @ ( hAPP @ ( c_Fun_Ocomp @ SY595 @ SY594 @ SY591 @ SY592 ) @ SV84 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5429]) ).
thf(5501,plain,
! [SV15: $i,SV85: $i] :
( ( ! [SY596: $i,SY597: $i,SY598: $i,SY599: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY599 @ SY598 @ SY597 @ SY596 ) @ SV85 ) @ SV15 )
= ( hAPP @ SY596 @ ( hAPP @ SV85 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5430]) ).
thf(5502,plain,
! [SV16: $i,SV86: $i] :
( ( ! [SY600: $i,SY601: $i,SY602: $i,SY603: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY603 @ SY602 @ SY601 @ SY600 ) @ SV86 ) @ SV16 )
= ( hAPP @ SY600 @ ( hAPP @ SV86 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(5503,plain,
! [SV17: $i,SV87: $i] :
( ( ! [SY604: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ SY604 @ SV87 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV87 @ SY604 ) @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5432]) ).
thf(5504,plain,
! [SV18: $i,SV88: $i] :
( ( ! [SY605: $i,SY606: $i] :
( ( hAPP @ SY606 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY605 @ SY605 ) @ SV88 ) @ SY606 ) @ SV18 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SY605 @ SY605 ) @ SV88 ) @ SY606 ) @ ( hAPP @ SY606 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5433]) ).
thf(5505,plain,
! [SV19: $i,SV89: $i] :
( ( ! [SY607: $i,SY608: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY608 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY608 ) @ SY607 ) @ SV89 ) ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY608 ) @ SY607 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY608 ) @ SV89 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5434]) ).
thf(5506,plain,
! [SV20: $i,SV90: $i] :
( ( ! [SY609: $i,SY610: $i,SY611: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY611 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY611 @ SY610 ) @ SY609 ) @ SV90 ) ) @ SY609 ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY611 @ SY610 ) @ SY609 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5435]) ).
thf(5507,plain,
! [SV21: $i,SV91: $i] :
( ( ( hAPP @ ( c_List_Orev @ SV91 ) @ ( hAPP @ ( c_List_Orev @ SV91 ) @ SV21 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5436]) ).
thf(5508,plain,
! [SV22: $i,SV92: $i] :
( ( ( hAPP @ ( c_COMBI @ SV92 ) @ SV22 )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5437]) ).
thf(5509,plain,
! [SV23: $i,SV93: $i] :
( ( ! [SY612: $i,SY613: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY613 @ SY612 ) @ SV93 ) @ SV23 )
= SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5438]) ).
thf(5510,plain,
! [SV24: $i,SV94: $i] :
( ( ! [SY614: $i,SY615: $i,SY616: $i,SY617: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY617 @ SY616 @ SY615 ) @ SY614 ) @ SV94 ) @ SV24 )
= ( hAPP @ SY614 @ ( hAPP @ SV94 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5439]) ).
thf(5511,plain,
! [SV25: $i,SV95: $i] :
( ( ! [SY618: $i,SY619: $i,SY620: $i,SY621: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY621 @ SY620 @ SY619 ) @ SY618 ) @ SV95 ) @ SV25 )
= ( hAPP @ ( hAPP @ SY618 @ SV25 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(5512,plain,
! [SV26: $i,SV96: $i] :
( ( ! [SY622: $i,SY623: $i,SY624: $i,SY625: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY625 @ SY624 @ SY623 ) @ SY622 ) @ SV96 ) @ SV26 )
= ( hAPP @ ( hAPP @ SY622 @ SV26 ) @ ( hAPP @ SV96 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(5513,plain,
! [SV27: $i,SV97: $i] :
( ( ! [SY626: $i,SY627: $i,SY628: $i,SY629: $i,SY630: $i,SY631: $i,SY632: $i,SY633: $i,SY634: $i] :
( ( ( hAPP @ SY634 @ ( hAPP @ SY633 @ SY632 ) )
!= ( hAPP @ SY631 @ ( hAPP @ SY630 @ SY629 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY628 @ SY627 @ SY626 @ SY634 ) @ SY633 ) @ SY632 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SY627 @ SV27 @ SY631 ) @ SY630 ) @ SY629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5442]) ).
thf(5514,plain,
! [SV28: $i,SV98: $i] :
( ( ! [SY635: $i,SY636: $i,SY637: $i] :
( ( ( hAPP @ SY637 @ SY636 )
!= SY635 )
| ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SY637 @ SY636 @ SY635 )
= SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5443]) ).
thf(5515,plain,
! [SV29: $i,SV99: $i] :
( ( ! [SY638: $i,SY639: $i,SY640: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY640 @ SY639 ) @ SY638 @ SV99 @ SV29 )
| ~ ! [SY641: $i] :
( ~ ( c_Natural_Oevaln @ SY640 @ SY638 @ SV99 @ SY641 )
| ~ ( c_Natural_Oevaln @ SY639 @ SY641 @ SV99 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5444]) ).
thf(5516,plain,
! [SV30: $i,SV100: $i] :
( ( ! [SY642: $i,SY643: $i,SY644: $i,SY645: $i,SY646: $i,SY647: $i,SY648: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY648 @ SY647 @ SY646 @ SY645 ) @ SY644 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY643 @ SY647 @ SY646 @ SY642 ) @ SV100 ) )
| ( ( hAPP @ SY645 @ ( hAPP @ SY644 @ SV30 ) )
= ( hAPP @ SY642 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5445]) ).
thf(5517,plain,
! [SV31: $i,SV101: $i] :
( ( ! [SY649: $i,SY650: $i,SY651: $i,SY652: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY652 @ SY651 @ SY650 )
| ( ( hAPP @ ( hAPP @ SY650 @ SY649 ) @ ( hAPP @ ( hAPP @ SY650 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SY650 @ SV101 ) @ ( hAPP @ ( hAPP @ SY650 @ SY649 ) @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5446]) ).
thf(5518,plain,
! [SV32: $i] :
( ( ( hAPP @ c_Nat_OSuc @ SV32 )
= SV32 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5519,plain,
! [SV102: $i,SV33: $i] :
( ( ~ ( v_fun1 @ SV33 @ SV102 )
| ! [SY653: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY653 )
| ( v_fun2 @ SV33 @ SY653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5448]) ).
thf(5520,plain,
! [SV34: $i,SV103: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
| ( SV103 = SV34 ) )
| ~ ( ( SV103 != SV34 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5449]) ).
thf(5521,plain,
! [SV35: $i,SV104: $i] :
( ( ! [SY654: $i,SY655: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY655 @ SY654 @ SV104 )
| ( ( hAPP @ ( hAPP @ SY654 @ SV35 ) @ SV35 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5450]) ).
thf(5522,plain,
( ( ! [SY656: $i] :
( ~ ( v_fun1 @ sK1_SX0 @ SY656 )
| ! [SY657: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SY656 @ v_n @ SY657 )
| ( v_fun2 @ sK1_SX0 @ SY657 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5451]) ).
thf(5523,plain,
! [SV36: $i,SV105: $i] :
( ( ! [SY658: $i,SY659: $i,SY660: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY660 @ SY659 @ SY658 @ SV105 @ SV36 )
!= SY658 )
| ( ( hAPP @ SY658 @ SV105 )
= SV36 ) )
| ~ ( ( ( hAPP @ SY658 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SY660 @ SY659 @ SY658 @ SV105 @ SV36 )
= SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5452]) ).
thf(5524,plain,
! [SV37: $i,SV106: $i] :
( ( ! [SY661: $i,SY662: $i,SY663: $i,SY664: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY664 @ SY663 ) @ SY662 ) @ SY661 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY664 @ SY663 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SY662 != SV106 )
| ( SY661 != SV37 ) ) )
| ~ ( ~ ~ ( ( SY662 != SV106 )
| ( SY661 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY664 @ SY663 ) @ SY662 ) @ SY661 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY664 @ SY663 ) @ SV106 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5453]) ).
thf(5525,plain,
! [SV38: $i,SV107: $i] :
( ( ! [SY665: $i,SY666: $i,SY667: $i,SY668: $i,SY669: $i] :
( ~ ( c_Typedef_Otype__definition @ SY669 @ SY668 @ SY667 @ SY666 @ SY665 )
| ~ ( ~ ( ( ( hAPP @ SY667 @ SV107 )
!= ( hAPP @ SY667 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SY667 @ SV107 )
= ( hAPP @ SY667 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5454]) ).
thf(5526,plain,
! [SV39: $i,SV108: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
| ( SV108 = SV39 ) )
| ~ ( ( SV108 != SV39 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5455]) ).
thf(5527,plain,
! [SV40: $i,SV109: $i] :
( ( ! [SY670: $i,SY671: $i,SY672: $i,SY673: $i] :
( ~ ( ( SY673 != SY672 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY671 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY671 @ SY670 ) @ SY673 ) @ SV109 ) ) @ SY672 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY671 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY671 @ SY670 ) @ SY672 ) @ SV40 ) ) @ SY673 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5456]) ).
thf(5528,plain,
! [SV41: $i,SV110: $i] :
( ( ! [SY674: $i,SY675: $i,SY676: $i,SY677: $i] :
( ~ ( c_Natural_Oevaln @ SY677 @ SY676 @ SY675 @ SY674 )
| ~ ( c_Natural_Oevaln @ SV110 @ SY674 @ SY675 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY677 @ SV110 ) @ SY676 @ SY675 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5457]) ).
thf(5529,plain,
! [SV42: $i,SV111: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SV111 = SV42 ) )
| ~ ( ( SV111 != SV42 )
| ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5458]) ).
thf(5530,plain,
! [SV43: $i,SV112: $i] :
( ( ! [SY678: $i,SY679: $i,SY680: $i,SY681: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY681 @ SY680 ) @ SY679 ) @ SY678 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY681 @ SY680 ) @ SV112 ) @ SV43 ) )
| ~ ( ( SY679 != SV112 )
| ( SY678 != SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5459]) ).
thf(5531,plain,
! [SV44: $i,SV113: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV113 = SV44 ) )
| ~ ( ( SV113 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5460]) ).
thf(5532,plain,
! [SV45: $i,SV114: $i] :
( ( ! [SY682: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY682 ) @ SV114 ) @ SV45 )
!= SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5461]) ).
thf(5533,plain,
! [SV46: $i,SV115: $i] :
( ( ! [SY683: $i,SY684: $i,SY685: $i,SY686: $i] :
~ ( ~ ( ( SY686 != SY685 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY684 @ SY683 @ SV115 @ SY685 @ SV46 ) @ SY686 )
= SV46 ) )
| ~ ( ~ ( ( SY686 != SY685 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY684 @ SY683 @ SV115 @ SY685 @ SV46 ) @ SY686 )
= ( hAPP @ SV115 @ SY686 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5462]) ).
thf(5534,plain,
! [SV47: $i,SV116: $i] :
( ( ~ ! [SY687: $i] :
( ( hAPP @ SV116 @ SY687 )
= ( hAPP @ SV47 @ SY687 ) )
| ( SV116 = SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5535,plain,
! [SV48: $i,SV117: $i] :
( ( ! [SY688: $i] :
( SY688
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV117 ) @ SV48 ) @ SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5464]) ).
thf(5536,plain,
! [SV49: $i,SV118: $i] :
( ( ! [SY689: $i,SY690: $i,SY691: $i,SY692: $i,SY693: $i,SY694: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY694 @ SY693 @ SY692 @ SY691 ) @ SY690 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY689 @ SY693 @ SY692 @ SV118 ) @ SV49 ) )
| ! [SY695: $i] :
( ( hAPP @ SY691 @ ( hAPP @ SY690 @ SY695 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY695 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5465]) ).
thf(5537,plain,
! [SV50: $i,SV119: $i] :
( ( ! [SY696: $i,SY697: $i] :
( ~ ( c_Natural_Oevaln @ SY697 @ SY696 @ SV119 @ SV50 )
| ( c_Natural_Oevaln @ SY697 @ SY696 @ ( hAPP @ c_Nat_OSuc @ SV119 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5466]) ).
thf(5538,plain,
! [SV51: $i,SV120: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY700 @ SY699 @ SY698 )
| ( ( hAPP @ ( hAPP @ SY698 @ SV120 ) @ ( hAPP @ ( hAPP @ SY698 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SY698 @ SV120 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5467]) ).
thf(5539,plain,
! [SV52: $i,SV121: $i] :
( ( ! [SY701: $i,SY702: $i,SY703: $i,SY704: $i] :
( ( SY704 != SY703 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY702 @ SY701 @ SV121 ) @ SV52 ) @ SY704 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY702 @ SY701 @ SV121 ) @ SV52 ) @ SY703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5468]) ).
thf(5540,plain,
! [SV53: $i,SV122: $i] :
( ( ! [SY705: $i,SY706: $i,SY707: $i,SY708: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY708 ) @ SY707 ) @ SY706 )
!= SY705 )
| ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY708 ) @ SY706 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY708 ) @ SY707 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY708 ) @ SY705 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(5541,plain,
! [SV54: $i,SV123: $i] :
( ( ! [SY709: $i] :
( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY709 @ SV123 @ SV54 )
| ( SV54 = SY709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(5542,plain,
! [SV55: $i,SV124: $i] :
( ( ! [SY710: $i,SY711: $i,SY712: $i,SY713: $i,SY714: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY714 @ SY713 @ SY712 @ SY711 ) @ SY710 )
!= SV124 )
| ( ( hAPP @ SY711 @ ( hAPP @ SY710 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5471]) ).
thf(5543,plain,
! [SV56: $i,SV125: $i] :
( ( ! [SY715: $i,SY716: $i,SY717: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY716 ) @ SY715 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY718: $i] :
~ ( ~ ( ( SY716
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SV125 ) @ SY718 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY718 ) @ SY715 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY716 ) @ SY718 )
!= SV125 )
| ( SY715
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY718 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY719: $i] :
~ ( ~ ( ( SY716
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SV125 ) @ SY719 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY719 ) @ SY715 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY716 ) @ SY719 )
!= SV125 )
| ( SY715
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY719 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SY716 ) @ SY715 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY717 ) @ SV125 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5472]) ).
thf(5544,plain,
! [SV57: $i,SV126: $i] :
( ( ! [SY720: $i,SY721: $i,SY722: $i,SY723: $i] :
( ~ ( c_Typedef_Otype__definition @ SY723 @ SY722 @ SY721 @ SY720 @ SV126 )
| ( ( hAPP @ SY720 @ ( hAPP @ SY721 @ SV57 ) )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5473]) ).
thf(5545,plain,
! [SV58: $i,SV127: $i] :
( ( ! [SY724: $i,SY725: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY725 ) @ SY724 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY725 ) @ SV58 ) @ SV127 ) )
| ( SY724 = SV58 ) )
| ~ ( ( SY724 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY725 ) @ SY724 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY725 ) @ SV58 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(5546,plain,
! [SV59: $i,SV128: $i] :
( ( ! [SY726: $i,SY727: $i,SY728: $i,SY729: $i] :
~ ( ~ ( ( SY729 != SY728 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY727 @ SY726 @ SV128 @ SY728 @ SV59 ) @ SY729 )
= SV59 ) )
| ~ ( ~ ( ( SY729 != SY728 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY727 @ SY726 @ SV128 @ SY728 @ SV59 ) @ SY729 )
= ( hAPP @ SV128 @ SY729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5475]) ).
thf(5547,plain,
! [SV60: $i,SV129: $i] :
( ( ! [SY730: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY730 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SY730 ) @ SV60 ) )
| ( SV129 = SV60 ) )
| ~ ( ( SV129 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SY730 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SY730 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(5548,plain,
! [SV61: $i,SV130: $i] :
( ( ! [SY731: $i,SY732: $i,SY733: $i] :
( ~ ! [SY734: $i] :
( ( hAPP @ SY733 @ SY734 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY732 @ SY731 @ SV130 ) @ SY734 ) )
| ( ( hAPP @ SY733 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SY733 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(5549,plain,
! [SV62: $i,SV131: $i] :
( ( ! [SY735: $i,SY736: $i,SY737: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY737 @ SY736 ) @ SY735 @ SV131 @ SV62 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY737 @ SY735 @ SV131 @ SY738 )
| ~ ( c_Natural_Oevaln @ SY736 @ SY738 @ SV131 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY737 @ SY735 @ SV131 @ SY739 )
| ~ ( c_Natural_Oevaln @ SY736 @ SY739 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY737 @ SY736 ) @ SY735 @ SV131 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5478]) ).
thf(5550,plain,
! [SV63: $i,SV132: $i] :
( ( ! [SY740: $i,SY741: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY741 ) @ SY740 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY741 ) @ SY740 ) @ SV63 ) )
| ( SV132 = SV63 ) )
| ~ ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY741 ) @ SY740 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY741 ) @ SY740 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5479]) ).
thf(5551,plain,
! [SV64: $i,SV133: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV133 )
!= ( hAPP @ c_Nat_OSuc @ SV64 ) )
| ( SV133 = SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5480]) ).
thf(5552,plain,
! [SV65: $i,SV134: $i] :
( ( ~ ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
| ( SV134 = SV65 ) )
| ~ ( ( SV134 != SV65 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5481]) ).
thf(5553,plain,
! [SV66: $i,SV135: $i] :
( ( ! [SY742: $i] :
~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SY742 ) @ SV135 )
!= SV66 )
| ( SV135
= ( hAPP @ ( c_List_Orev @ SY742 ) @ SV66 ) ) )
| ~ ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SY742 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SY742 ) @ SV135 )
= SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5482]) ).
thf(5554,plain,
! [SV67: $i,SV136: $i] :
( ( ! [SY743: $i,SY744: $i,SY745: $i,SY746: $i] :
( ~ ( ( SY746 != SY745 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY744 @ SY743 @ SV136 @ SY745 @ SV67 ) @ SY746 )
= ( hAPP @ SV136 @ SY746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5483]) ).
thf(5555,plain,
! [SV68: $i,SV137: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY749 ) @ SY748 ) @ SY747 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY749 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SY748 != SV137 )
| ( SY747 != SV68 ) ) )
| ~ ( ~ ~ ( ( SY748 != SV137 )
| ( SY747 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY749 ) @ SY748 ) @ SY747 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY749 ) @ SV137 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5484]) ).
thf(5556,plain,
! [SV69: $i,SV138: $i] :
( ( ! [SY750: $i,SY751: $i,SY752: $i,SY753: $i,SY754: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY754 @ SY753 @ SY752 @ SY751 @ SY750 @ SV138 )
| ( ( hAPP @ ( hAPP @ SY752 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5485]) ).
thf(5557,plain,
! [SV70: $i] :
( ( SV70
= ( hAPP @ c_Nat_OSuc @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(5558,plain,
! [SV1: $i,SV71: $i,SV139: $i] :
( ( ! [SY755: $i,SY756: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY756 @ SY755 @ SV139 ) @ SV71 ) @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ ( hAPP @ SV139 @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY756 @ SY755 @ SV139 ) @ SV71 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(5559,plain,
! [SV2: $i,SV72: $i,SV140: $i] :
( ( ! [SY757: $i] :
( ( c_Nat_Onat_Onat__case @ SY757 @ SV140 @ SV72 @ ( hAPP @ c_Nat_OSuc @ SV2 ) )
= ( hAPP @ SV72 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5488]) ).
thf(5560,plain,
! [SV5: $i,SV75: $i,SV141: $i] :
( ( ! [SY758: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY758 @ SV141 @ SV75 ) @ ( hAPP @ c_Nat_OSuc @ SV5 ) )
= ( hAPP @ ( hAPP @ SV75 @ SV5 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY758 @ SV141 @ SV75 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5491]) ).
thf(5561,plain,
! [SV6: $i,SV76: $i,SV142: $i] :
( ( ! [SY759: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY759 ) @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY759 ) @ SV76 ) @ SV6 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY759 ) @ SV76 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SY759 ) @ SV142 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5562,plain,
! [SV7: $i,SV77: $i,SV143: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV143 ) @ SV77 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV143 ) @ SV77 ) @ SV7 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV143 ) @ SV77 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(5563,plain,
! [SV8: $i,SV78: $i,SV144: $i] :
( ( ! [SY760: $i] :
( ( c_Fun_Ofun__upd @ SY760 @ SV144 @ SV78 @ SV8 @ ( hAPP @ SV78 @ SV8 ) )
= SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(5564,plain,
! [SV9: $i,SV79: $i,SV145: $i] :
( ( ! [SY761: $i,SY762: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY762 @ SY761 @ SV145 @ SV79 @ SV9 ) @ SV79 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5495]) ).
thf(5565,plain,
! [SV13: $i,SV83: $i,SV146: $i] :
( ( ! [SY763: $i,SY764: $i,SY765: $i,SY766: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY766 @ SY765 @ SY764 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY766 @ SY763 @ SY765 ) @ SV146 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY766 @ SY763 @ SY764 ) @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY763 @ SY765 @ SY764 ) @ SV83 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(5566,plain,
! [SV14: $i,SV84: $i,SV147: $i] :
( ( ! [SY767: $i,SY768: $i,SY769: $i,SY770: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY770 @ SY769 @ SY768 @ SY767 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY770 @ SY768 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY769 @ SY768 @ ( hAPP @ ( c_Fun_Ocomp @ SY770 @ SY769 @ SV147 @ SY767 ) @ SV84 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(5567,plain,
! [SV15: $i,SV85: $i,SV148: $i] :
( ( ! [SY771: $i,SY772: $i,SY773: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY773 @ SY772 @ SY771 @ SV148 ) @ SV85 ) @ SV15 )
= ( hAPP @ SV148 @ ( hAPP @ SV85 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(5568,plain,
! [SV16: $i,SV86: $i,SV149: $i] :
( ( ! [SY774: $i,SY775: $i,SY776: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY776 @ SY775 @ SY774 @ SV149 ) @ SV86 ) @ SV16 )
= ( hAPP @ SV149 @ ( hAPP @ SV86 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(5569,plain,
! [SV17: $i,SV87: $i,SV150: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ SV150 @ SV87 ) @ ( hAPP @ ( c_Relation_Oconverse @ SV87 @ SV150 ) @ SV17 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5570,plain,
! [SV18: $i,SV88: $i,SV151: $i] :
( ( ! [SY777: $i] :
( ( hAPP @ SY777 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV151 @ SV151 ) @ SV88 ) @ SY777 ) @ SV18 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV151 @ SV151 ) @ SV88 ) @ SY777 ) @ ( hAPP @ SY777 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5504]) ).
thf(5571,plain,
! [SV19: $i,SV89: $i,SV152: $i] :
( ( ! [SY778: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY778 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY778 ) @ SV152 ) @ SV89 ) ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY778 ) @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY778 ) @ SV89 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5505]) ).
thf(5572,plain,
! [SV20: $i,SV90: $i,SV153: $i] :
( ( ! [SY779: $i,SY780: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY780 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY780 @ SY779 ) @ SV153 ) @ SV90 ) ) @ SV153 ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY780 @ SY779 ) @ SV153 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5573,plain,
! [SV23: $i,SV93: $i,SV154: $i] :
( ( ! [SY781: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ SY781 @ SV154 ) @ SV93 ) @ SV23 )
= SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5509]) ).
thf(5574,plain,
! [SV24: $i,SV94: $i,SV155: $i] :
( ( ! [SY782: $i,SY783: $i,SY784: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY784 @ SY783 @ SY782 ) @ SV155 ) @ SV94 ) @ SV24 )
= ( hAPP @ SV155 @ ( hAPP @ SV94 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5510]) ).
thf(5575,plain,
! [SV25: $i,SV95: $i,SV156: $i] :
( ( ! [SY785: $i,SY786: $i,SY787: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY787 @ SY786 @ SY785 ) @ SV156 ) @ SV95 ) @ SV25 )
= ( hAPP @ ( hAPP @ SV156 @ SV25 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5576,plain,
! [SV26: $i,SV96: $i,SV157: $i] :
( ( ! [SY788: $i,SY789: $i,SY790: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY790 @ SY789 @ SY788 ) @ SV157 ) @ SV96 ) @ SV26 )
= ( hAPP @ ( hAPP @ SV157 @ SV26 ) @ ( hAPP @ SV96 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5512]) ).
thf(5577,plain,
! [SV27: $i,SV97: $i,SV158: $i] :
( ( ! [SY791: $i,SY792: $i,SY793: $i,SY794: $i,SY795: $i,SY796: $i,SY797: $i,SY798: $i] :
( ( ( hAPP @ SY798 @ ( hAPP @ SY797 @ SY796 ) )
!= ( hAPP @ SY795 @ ( hAPP @ SY794 @ SY793 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY792 @ SY791 @ SV158 @ SY798 ) @ SY797 ) @ SY796 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SY791 @ SV27 @ SY795 ) @ SY794 ) @ SY793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(5578,plain,
! [SV28: $i,SV98: $i,SV159: $i] :
( ( ! [SY799: $i,SY800: $i] :
( ( ( hAPP @ SY800 @ SY799 )
!= SV159 )
| ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SY800 @ SY799 @ SV159 )
= SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(5579,plain,
! [SV29: $i,SV99: $i,SV160: $i] :
( ( ! [SY801: $i,SY802: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY802 @ SY801 ) @ SV160 @ SV99 @ SV29 )
| ~ ! [SY803: $i] :
( ~ ( c_Natural_Oevaln @ SY802 @ SV160 @ SV99 @ SY803 )
| ~ ( c_Natural_Oevaln @ SY801 @ SY803 @ SV99 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5515]) ).
thf(5580,plain,
! [SV30: $i,SV100: $i,SV161: $i] :
( ( ! [SY804: $i,SY805: $i,SY806: $i,SY807: $i,SY808: $i,SY809: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY809 @ SY808 @ SY807 @ SY806 ) @ SY805 )
!= ( hAPP @ ( c_Fun_Ocomp @ SY804 @ SY808 @ SY807 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SY806 @ ( hAPP @ SY805 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5516]) ).
thf(5581,plain,
! [SV31: $i,SV101: $i,SV162: $i] :
( ( ! [SY810: $i,SY811: $i,SY812: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY812 @ SY811 @ SY810 )
| ( ( hAPP @ ( hAPP @ SY810 @ SV162 ) @ ( hAPP @ ( hAPP @ SY810 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SY810 @ SV101 ) @ ( hAPP @ ( hAPP @ SY810 @ SV162 ) @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(5582,plain,
! [SV102: $i,SV33: $i] :
( ( ( ~ ( v_fun1 @ SV33 @ SV102 ) )
= $true )
| ( ( ! [SY653: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY653 )
| ( v_fun2 @ SV33 @ SY653 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5519]) ).
thf(5583,plain,
! [SV34: $i,SV103: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
| ( SV103 = SV34 ) )
| ~ ( ( SV103 != SV34 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5520]) ).
thf(5584,plain,
! [SV35: $i,SV104: $i,SV163: $i] :
( ( ! [SY813: $i] :
( ~ ( c_Finite__Set_Ofolding__one__idem @ SY813 @ SV163 @ SV104 )
| ( ( hAPP @ ( hAPP @ SV163 @ SV35 ) @ SV35 )
= SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(5585,plain,
( ( ~ ( v_fun1 @ sK1_SX0 @ sK2_SY656 )
| ! [SY814: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ sK2_SY656 @ v_n @ SY814 )
| ( v_fun2 @ sK1_SX0 @ SY814 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5522]) ).
thf(5586,plain,
! [SV36: $i,SV105: $i,SV164: $i] :
( ( ! [SY815: $i,SY816: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY816 @ SY815 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) )
| ~ ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SY816 @ SY815 @ SV164 @ SV105 @ SV36 )
= SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5587,plain,
! [SV37: $i,SV106: $i,SV165: $i] :
( ( ! [SY817: $i,SY818: $i,SY819: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY819 @ SY818 ) @ SY817 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY819 @ SY818 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SY817 != SV106 )
| ( SV165 != SV37 ) ) )
| ~ ( ~ ~ ( ( SY817 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY819 @ SY818 ) @ SY817 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY819 @ SY818 ) @ SV106 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5588,plain,
! [SV38: $i,SV107: $i,SV166: $i] :
( ( ! [SY820: $i,SY821: $i,SY822: $i,SY823: $i] :
( ~ ( c_Typedef_Otype__definition @ SY823 @ SY822 @ SY821 @ SY820 @ SV166 )
| ~ ( ~ ( ( ( hAPP @ SY821 @ SV107 )
!= ( hAPP @ SY821 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SY821 @ SV107 )
= ( hAPP @ SY821 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5589,plain,
! [SV39: $i,SV108: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
| ( SV108 = SV39 ) )
| ~ ( ( SV108 != SV39 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5590,plain,
! [SV40: $i,SV109: $i,SV167: $i] :
( ( ! [SY824: $i,SY825: $i,SY826: $i] :
( ~ ( ( SY826 != SY825 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY824 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY824 @ SV167 ) @ SY826 ) @ SV109 ) ) @ SY825 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY824 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY824 @ SV167 ) @ SY825 ) @ SV40 ) ) @ SY826 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(5591,plain,
! [SV41: $i,SV110: $i,SV168: $i] :
( ( ! [SY827: $i,SY828: $i,SY829: $i] :
( ~ ( c_Natural_Oevaln @ SY829 @ SY828 @ SY827 @ SV168 )
| ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SY827 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY829 @ SV110 ) @ SY828 @ SY827 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(5592,plain,
! [SV42: $i,SV111: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SV111 = SV42 ) )
| ~ ( ( SV111 != SV42 )
| ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5529]) ).
thf(5593,plain,
! [SV43: $i,SV112: $i,SV169: $i] :
( ( ! [SY830: $i,SY831: $i,SY832: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY832 @ SY831 ) @ SY830 ) @ SV169 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY832 @ SY831 ) @ SV112 ) @ SV43 ) )
| ~ ( ( SY830 != SV112 )
| ( SV169 != SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(5594,plain,
! [SV44: $i,SV113: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV113 = SV44 ) )
| ~ ( ( SV113 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5595,plain,
! [SV45: $i,SV114: $i,SV170: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV170 ) @ SV114 ) @ SV45 )
!= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5532]) ).
thf(5596,plain,
! [SV46: $i,SV115: $i,SV171: $i] :
( ( ! [SY833: $i,SY834: $i,SY835: $i] :
~ ( ~ ( ( SY835 != SY834 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY833 @ SV171 @ SV115 @ SY834 @ SV46 ) @ SY835 )
= SV46 ) )
| ~ ( ~ ( ( SY835 != SY834 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY833 @ SV171 @ SV115 @ SY834 @ SV46 ) @ SY835 )
= ( hAPP @ SV115 @ SY835 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5597,plain,
! [SV47: $i,SV116: $i] :
( ( ( ~ ! [SY687: $i] :
( ( hAPP @ SV116 @ SY687 )
= ( hAPP @ SV47 @ SY687 ) ) )
= $true )
| ( ( SV116 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5534]) ).
thf(5598,plain,
! [SV48: $i,SV117: $i,SV172: $i] :
( ( SV172
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV117 ) @ SV48 ) @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5599,plain,
! [SV49: $i,SV118: $i,SV173: $i] :
( ( ! [SY836: $i,SY837: $i,SY838: $i,SY839: $i,SY840: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY840 @ SY839 @ SY838 @ SY837 ) @ SY836 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SY839 @ SY838 @ SV118 ) @ SV49 ) )
| ! [SY695: $i] :
( ( hAPP @ SY837 @ ( hAPP @ SY836 @ SY695 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY695 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5600,plain,
! [SV50: $i,SV119: $i,SV174: $i] :
( ( ! [SY842: $i] :
( ~ ( c_Natural_Oevaln @ SY842 @ SV174 @ SV119 @ SV50 )
| ( c_Natural_Oevaln @ SY842 @ SV174 @ ( hAPP @ c_Nat_OSuc @ SV119 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5601,plain,
! [SV51: $i,SV120: $i,SV175: $i] :
( ( ! [SY843: $i,SY844: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY844 @ SY843 @ SV175 )
| ( ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5602,plain,
! [SV52: $i,SV121: $i,SV176: $i] :
( ( ! [SY845: $i,SY846: $i,SY847: $i] :
( ( SY847 != SY846 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY845 @ SV176 @ SV121 ) @ SV52 ) @ SY847 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SY845 @ SV176 @ SV121 ) @ SV52 ) @ SY846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(5603,plain,
! [SV53: $i,SV122: $i,SV177: $i] :
( ( ! [SY848: $i,SY849: $i,SY850: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY850 ) @ SY849 ) @ SY848 )
!= SV177 )
| ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY850 ) @ SY848 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY850 ) @ SY849 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY850 ) @ SV177 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5604,plain,
! [SV54: $i,SV123: $i,SV178: $i] :
( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV178 @ SV123 @ SV54 )
| ( SV54 = SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5541]) ).
thf(5605,plain,
! [SV55: $i,SV124: $i,SV179: $i] :
( ( ! [SY851: $i,SY852: $i,SY853: $i,SY854: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY854 @ SY853 @ SY852 @ SY851 ) @ SV179 )
!= SV124 )
| ( ( hAPP @ SY851 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5542]) ).
thf(5606,plain,
! [SV56: $i,SV125: $i,SV180: $i] :
( ( ! [SY855: $i,SY856: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY855 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY857: $i] :
~ ( ~ ( ( SY855
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SV125 ) @ SY857 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY857 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY855 ) @ SY857 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY857 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY858: $i] :
~ ( ~ ( ( SY855
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SV125 ) @ SY858 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY858 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY855 ) @ SY858 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY858 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SY855 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY856 ) @ SV125 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(5607,plain,
! [SV57: $i,SV126: $i,SV181: $i] :
( ( ! [SY859: $i,SY860: $i,SY861: $i] :
( ~ ( c_Typedef_Otype__definition @ SY861 @ SY860 @ SY859 @ SV181 @ SV126 )
| ( ( hAPP @ SV181 @ ( hAPP @ SY859 @ SV57 ) )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(5608,plain,
! [SV58: $i,SV127: $i,SV182: $i] :
( ( ! [SY862: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY862 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY862 ) @ SV58 ) @ SV127 ) )
| ( SV182 = SV58 ) )
| ~ ( ( SV182 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY862 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY862 ) @ SV58 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(5609,plain,
! [SV59: $i,SV128: $i,SV183: $i] :
( ( ! [SY863: $i,SY864: $i,SY865: $i] :
~ ( ~ ( ( SY865 != SY864 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY863 @ SV183 @ SV128 @ SY864 @ SV59 ) @ SY865 )
= SV59 ) )
| ~ ( ~ ( ( SY865 != SY864 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY863 @ SV183 @ SV128 @ SY864 @ SV59 ) @ SY865 )
= ( hAPP @ SV128 @ SY865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5610,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
| ( SV129 = SV60 ) )
| ~ ( ( SV129 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(5611,plain,
! [SV61: $i,SV130: $i,SV185: $i] :
( ( ! [SY866: $i,SY867: $i] :
( ~ ! [SY868: $i] :
( ( hAPP @ SY867 @ SY868 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SY866 @ SV185 @ SV130 ) @ SY868 ) )
| ( ( hAPP @ SY867 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SY867 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(5612,plain,
! [SV62: $i,SV131: $i,SV186: $i] :
( ( ! [SY869: $i,SY870: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY870 @ SY869 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY871: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY870 @ SV186 @ SV131 @ SY871 )
| ~ ( c_Natural_Oevaln @ SY869 @ SY871 @ SV131 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY872: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY870 @ SV186 @ SV131 @ SY872 )
| ~ ( c_Natural_Oevaln @ SY869 @ SY872 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY870 @ SY869 ) @ SV186 @ SV131 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(5613,plain,
! [SV63: $i,SV132: $i,SV187: $i] :
( ( ! [SY873: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY873 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY873 ) @ SV187 ) @ SV63 ) )
| ( SV132 = SV63 ) )
| ~ ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY873 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY873 ) @ SV187 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(5614,plain,
! [SV64: $i,SV133: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV133 )
!= ( hAPP @ c_Nat_OSuc @ SV64 ) )
= $true )
| ( ( SV133 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5615,plain,
! [SV65: $i,SV134: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
| ( SV134 = SV65 ) )
| ~ ( ( SV134 != SV65 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5552]) ).
thf(5616,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
!= SV66 )
| ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) ) )
| ~ ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5553]) ).
thf(5617,plain,
! [SV67: $i,SV136: $i,SV189: $i] :
( ( ! [SY874: $i,SY875: $i,SY876: $i] :
( ~ ( ( SY876 != SY875 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SY874 @ SV189 @ SV136 @ SY875 @ SV67 ) @ SY876 )
= ( hAPP @ SV136 @ SY876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5618,plain,
! [SV68: $i,SV137: $i,SV190: $i] :
( ( ! [SY877: $i,SY878: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY878 ) @ SY877 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY878 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SY877 != SV137 )
| ( SV190 != SV68 ) ) )
| ~ ( ~ ~ ( ( SY877 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY878 ) @ SY877 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY878 ) @ SV137 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(5619,plain,
! [SV69: $i,SV138: $i,SV191: $i] :
( ( ! [SY879: $i,SY880: $i,SY881: $i,SY882: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY882 @ SY881 @ SY880 @ SY879 @ SV191 @ SV138 )
| ( ( hAPP @ ( hAPP @ SY880 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(5620,plain,
! [SV1: $i,SV71: $i,SV139: $i,SV192: $i] :
( ( ! [SY883: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY883 @ SV192 @ SV139 ) @ SV71 ) @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ ( hAPP @ SV139 @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SY883 @ SV192 @ SV139 ) @ SV71 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5558]) ).
thf(5621,plain,
! [SV2: $i,SV72: $i,SV140: $i,SV193: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV193 @ SV140 @ SV72 @ ( hAPP @ c_Nat_OSuc @ SV2 ) )
= ( hAPP @ SV72 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5559]) ).
thf(5622,plain,
! [SV5: $i,SV75: $i,SV141: $i,SV194: $i] :
( ( ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV194 @ SV141 @ SV75 ) @ ( hAPP @ c_Nat_OSuc @ SV5 ) )
= ( hAPP @ ( hAPP @ SV75 @ SV5 ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV194 @ SV141 @ SV75 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5623,plain,
! [SV6: $i,SV76: $i,SV142: $i,SV195: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV195 ) @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV195 ) @ SV76 ) @ SV6 ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV195 ) @ SV76 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ SV195 ) @ SV142 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5624,plain,
! [SV8: $i,SV78: $i,SV144: $i,SV196: $i] :
( ( ( c_Fun_Ofun__upd @ SV196 @ SV144 @ SV78 @ SV8 @ ( hAPP @ SV78 @ SV8 ) )
= SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5563]) ).
thf(5625,plain,
! [SV9: $i,SV79: $i,SV145: $i,SV197: $i] :
( ( ! [SY884: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY884 @ SV197 @ SV145 @ SV79 @ SV9 ) @ SV79 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5564]) ).
thf(5626,plain,
! [SV13: $i,SV83: $i,SV146: $i,SV198: $i] :
( ( ! [SY885: $i,SY886: $i,SY887: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY887 @ SY886 @ SY885 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY887 @ SV198 @ SY886 ) @ SV146 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY887 @ SV198 @ SY885 ) @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV198 @ SY886 @ SY885 ) @ SV83 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5627,plain,
! [SV14: $i,SV84: $i,SV147: $i,SV199: $i] :
( ( ! [SY888: $i,SY889: $i,SY890: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY890 @ SY889 @ SY888 @ SV199 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY890 @ SY888 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY889 @ SY888 @ ( hAPP @ ( c_Fun_Ocomp @ SY890 @ SY889 @ SV147 @ SV199 ) @ SV84 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(5628,plain,
! [SV15: $i,SV85: $i,SV148: $i,SV200: $i] :
( ( ! [SY891: $i,SY892: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY892 @ SY891 @ SV200 @ SV148 ) @ SV85 ) @ SV15 )
= ( hAPP @ SV148 @ ( hAPP @ SV85 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5629,plain,
! [SV16: $i,SV86: $i,SV149: $i,SV201: $i] :
( ( ! [SY893: $i,SY894: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY894 @ SY893 @ SV201 @ SV149 ) @ SV86 ) @ SV16 )
= ( hAPP @ SV149 @ ( hAPP @ SV86 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5568]) ).
thf(5630,plain,
! [SV18: $i,SV88: $i,SV151: $i,SV202: $i] :
( ( ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV151 @ SV151 ) @ SV88 ) @ SV202 ) @ SV18 ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ SV151 @ SV151 ) @ SV88 ) @ SV202 ) @ ( hAPP @ SV202 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(5631,plain,
! [SV19: $i,SV89: $i,SV152: $i,SV203: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV203 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV203 ) @ SV152 ) @ SV89 ) ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV203 ) @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV203 ) @ SV89 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5632,plain,
! [SV20: $i,SV90: $i,SV153: $i,SV204: $i] :
( ( ! [SY895: $i] :
( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY895 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY895 @ SV204 ) @ SV153 ) @ SV90 ) ) @ SV153 ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SY895 @ SV204 ) @ SV153 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5633,plain,
! [SV23: $i,SV93: $i,SV154: $i,SV205: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBK @ SV205 @ SV154 ) @ SV93 ) @ SV23 )
= SV93 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5573]) ).
thf(5634,plain,
! [SV24: $i,SV94: $i,SV155: $i,SV206: $i] :
( ( ! [SY896: $i,SY897: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY897 @ SY896 @ SV206 ) @ SV155 ) @ SV94 ) @ SV24 )
= ( hAPP @ SV155 @ ( hAPP @ SV94 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5635,plain,
! [SV25: $i,SV95: $i,SV156: $i,SV207: $i] :
( ( ! [SY898: $i,SY899: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY899 @ SY898 @ SV207 ) @ SV156 ) @ SV95 ) @ SV25 )
= ( hAPP @ ( hAPP @ SV156 @ SV25 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5636,plain,
! [SV26: $i,SV96: $i,SV157: $i,SV208: $i] :
( ( ! [SY900: $i,SY901: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY901 @ SY900 @ SV208 ) @ SV157 ) @ SV96 ) @ SV26 )
= ( hAPP @ ( hAPP @ SV157 @ SV26 ) @ ( hAPP @ SV96 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(5637,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i] :
( ( ! [SY902: $i,SY903: $i,SY904: $i,SY905: $i,SY906: $i,SY907: $i,SY908: $i] :
( ( ( hAPP @ SY908 @ ( hAPP @ SY907 @ SY906 ) )
!= ( hAPP @ SY905 @ ( hAPP @ SY904 @ SY903 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY902 @ SV209 @ SV158 @ SY908 ) @ SY907 ) @ SY906 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SY905 ) @ SY904 ) @ SY903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(5638,plain,
! [SV28: $i,SV98: $i,SV159: $i,SV210: $i] :
( ( ! [SY909: $i] :
( ( ( hAPP @ SY909 @ SV210 )
!= SV159 )
| ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SY909 @ SV210 @ SV159 )
= SY909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(5639,plain,
! [SV29: $i,SV99: $i,SV160: $i,SV211: $i] :
( ( ! [SY910: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY910 @ SV211 ) @ SV160 @ SV99 @ SV29 )
| ~ ! [SY911: $i] :
( ~ ( c_Natural_Oevaln @ SY910 @ SV160 @ SV99 @ SY911 )
| ~ ( c_Natural_Oevaln @ SV211 @ SY911 @ SV99 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5579]) ).
thf(5640,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i] :
( ( ! [SY912: $i,SY913: $i,SY914: $i,SY915: $i,SY916: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY916 @ SY915 @ SY914 @ SY913 ) @ SY912 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SY915 @ SY914 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SY913 @ ( hAPP @ SY912 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5580]) ).
thf(5641,plain,
! [SV31: $i,SV101: $i,SV162: $i,SV213: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY918 @ SY917 @ SV213 )
| ( ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5581]) ).
thf(5642,plain,
! [SV102: $i,SV33: $i] :
( ( ( v_fun1 @ SV33 @ SV102 )
= $false )
| ( ( ! [SY653: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SY653 )
| ( v_fun2 @ SV33 @ SY653 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(5643,plain,
! [SV34: $i,SV103: $i] :
( ( ~ ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
| ( SV103 = SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5583]) ).
thf(5644,plain,
! [SV34: $i,SV103: $i] :
( ( ~ ( ( SV103 != SV34 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5583]) ).
thf(5645,plain,
! [SV35: $i,SV104: $i,SV163: $i,SV214: $i] :
( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV214 @ SV163 @ SV104 )
| ( ( hAPP @ ( hAPP @ SV163 @ SV35 ) @ SV35 )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(5646,plain,
( ( ~ ( v_fun1 @ sK1_SX0 @ sK2_SY656 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5585]) ).
thf(5647,plain,
( ( ! [SY814: $i] :
( ~ ( c_Natural_Oevaln @ v_com @ sK2_SY656 @ v_n @ SY814 )
| ( v_fun2 @ sK1_SX0 @ SY814 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5585]) ).
thf(5648,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i] :
( ( ! [SY919: $i] :
~ ( ~ ( ( ( c_Fun_Ofun__upd @ SY919 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) )
| ~ ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SY919 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(5649,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i] :
( ( ! [SY920: $i,SY921: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY921 @ SY920 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY921 @ SY920 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
| ~ ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY921 @ SY920 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY921 @ SY920 ) @ SV106 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(5650,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i] :
( ( ! [SY922: $i,SY923: $i,SY924: $i] :
( ~ ( c_Typedef_Otype__definition @ SY924 @ SY923 @ SY922 @ SV217 @ SV166 )
| ~ ( ~ ( ( ( hAPP @ SY922 @ SV107 )
!= ( hAPP @ SY922 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SY922 @ SV107 )
= ( hAPP @ SY922 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(5651,plain,
! [SV39: $i,SV108: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
| ( SV108 = SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5589]) ).
thf(5652,plain,
! [SV39: $i,SV108: $i] :
( ( ~ ( ( SV108 != SV39 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5589]) ).
thf(5653,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ~ ( ( SY926 != SY925 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SY926 ) @ SV109 ) ) @ SY925 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SY925 ) @ SV40 ) ) @ SY926 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(5654,plain,
! [SV41: $i,SV110: $i,SV168: $i,SV219: $i] :
( ( ! [SY927: $i,SY928: $i] :
( ~ ( c_Natural_Oevaln @ SY928 @ SY927 @ SV219 @ SV168 )
| ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY928 @ SV110 ) @ SY927 @ SV219 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(5655,plain,
! [SV42: $i,SV111: $i] :
( ( ~ ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SV111 = SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5592]) ).
thf(5656,plain,
! [SV42: $i,SV111: $i] :
( ( ~ ( ( SV111 != SV42 )
| ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5592]) ).
thf(5657,plain,
! [SV43: $i,SV112: $i,SV169: $i,SV220: $i] :
( ( ! [SY929: $i,SY930: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY930 @ SY929 ) @ SV220 ) @ SV169 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY930 @ SY929 ) @ SV112 ) @ SV43 ) )
| ~ ( ( SV220 != SV112 )
| ( SV169 != SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(5658,plain,
! [SV44: $i,SV113: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV113 = SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5594]) ).
thf(5659,plain,
! [SV44: $i,SV113: $i] :
( ( ~ ( ( SV113 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5594]) ).
thf(5660,plain,
! [SV45: $i,SV114: $i,SV170: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV170 ) @ SV114 ) @ SV45 )
= SV45 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5661,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i] :
( ( ! [SY931: $i,SY932: $i] :
~ ( ~ ( ( SY932 != SY931 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SY931 @ SV46 ) @ SY932 )
= SV46 ) )
| ~ ( ~ ( ( SY932 != SY931 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SY931 @ SV46 ) @ SY932 )
= ( hAPP @ SV115 @ SY932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(5662,plain,
! [SV47: $i,SV116: $i] :
( ( ( ! [SY687: $i] :
( ( hAPP @ SV116 @ SY687 )
= ( hAPP @ SV47 @ SY687 ) ) )
= $false )
| ( ( SV116 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5597]) ).
thf(5663,plain,
! [SV48: $i,SV117: $i,SV172: $i] :
( ( SV172
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV117 ) @ SV48 ) @ SV172 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5664,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i] :
( ( ! [SY933: $i,SY934: $i,SY935: $i,SY936: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY936 @ SY935 @ SY934 @ SY933 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SY935 @ SY934 @ SV118 ) @ SV49 ) )
| ! [SY937: $i] :
( ( hAPP @ SY933 @ ( hAPP @ SV222 @ SY937 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY937 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5599]) ).
thf(5665,plain,
! [SV50: $i,SV119: $i,SV174: $i,SV223: $i] :
( ( ~ ( c_Natural_Oevaln @ SV223 @ SV174 @ SV119 @ SV50 )
| ( c_Natural_Oevaln @ SV223 @ SV174 @ ( hAPP @ c_Nat_OSuc @ SV119 ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5600]) ).
thf(5666,plain,
! [SV51: $i,SV120: $i,SV175: $i,SV224: $i] :
( ( ! [SY938: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SY938 @ SV224 @ SV175 )
| ( ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5667,plain,
! [SV52: $i,SV121: $i,SV176: $i,SV225: $i] :
( ( ! [SY939: $i,SY940: $i] :
( ( SY940 != SY939 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SY940 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SY939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(5668,plain,
! [SV53: $i,SV122: $i,SV177: $i,SV226: $i] :
( ( ! [SY941: $i,SY942: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY942 ) @ SY941 ) @ SV226 )
!= SV177 )
| ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY942 ) @ SV226 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY942 ) @ SY941 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY942 ) @ SV177 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(5669,plain,
! [SV54: $i,SV123: $i,SV178: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV178 @ SV123 @ SV54 ) )
= $true )
| ( ( SV54 = SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5604]) ).
thf(5670,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY945 @ SY944 @ SY943 @ SV227 ) @ SV179 )
!= SV124 )
| ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(5671,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i] :
( ( ! [SY946: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY947: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV125 ) @ SY947 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SY947 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV228 ) @ SY947 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SY947 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY948: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV125 ) @ SY948 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SY948 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV228 ) @ SY948 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SY948 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY946 ) @ SV125 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(5672,plain,
! [SV57: $i,SV126: $i,SV181: $i,SV229: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ~ ( c_Typedef_Otype__definition @ SY950 @ SY949 @ SV229 @ SV181 @ SV126 )
| ( ( hAPP @ SV181 @ ( hAPP @ SV229 @ SV57 ) )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(5673,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
| ( SV182 = SV58 ) )
| ~ ( ( SV182 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5608]) ).
thf(5674,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i] :
( ( ! [SY951: $i,SY952: $i] :
~ ( ~ ( ( SY952 != SY951 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SY951 @ SV59 ) @ SY952 )
= SV59 ) )
| ~ ( ~ ( ( SY952 != SY951 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SY951 @ SV59 ) @ SY952 )
= ( hAPP @ SV128 @ SY952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5609]) ).
thf(5675,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
| ( SV129 = SV60 ) )
| ~ ( ( SV129 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(5676,plain,
! [SV61: $i,SV130: $i,SV185: $i,SV232: $i] :
( ( ! [SY953: $i] :
( ~ ! [SY954: $i] :
( ( hAPP @ SY953 @ SY954 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV232 @ SV185 @ SV130 ) @ SY954 ) )
| ( ( hAPP @ SY953 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SY953 @ SV61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(5677,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i] :
( ( ! [SY955: $i] :
~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY955 @ SV233 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY956: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY955 @ SV186 @ SV131 @ SY956 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY956 @ SV131 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY957: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SY955 @ SV186 @ SV131 @ SY957 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY957 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY955 @ SV233 ) @ SV186 @ SV131 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(5678,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
| ( SV132 = SV63 ) )
| ~ ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5613]) ).
thf(5679,plain,
! [SV64: $i,SV133: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV133 )
= ( hAPP @ c_Nat_OSuc @ SV64 ) )
= $false )
| ( ( SV133 = SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5614]) ).
thf(5680,plain,
! [SV65: $i,SV134: $i] :
( ( ~ ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
| ( SV134 = SV65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5615]) ).
thf(5681,plain,
! [SV65: $i,SV134: $i] :
( ( ~ ( ( SV134 != SV65 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5615]) ).
thf(5682,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
!= SV66 )
| ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) ) )
| ~ ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(5683,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i] :
( ( ! [SY958: $i,SY959: $i] :
( ~ ( ( SY959 != SY958 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SY958 @ SV67 ) @ SY959 )
= ( hAPP @ SV136 @ SY959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5617]) ).
thf(5684,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i] :
( ( ! [SY960: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY960 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY960 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
| ~ ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY960 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SY960 ) @ SV137 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5618]) ).
thf(5685,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i] :
( ( ! [SY961: $i,SY962: $i,SY963: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY963 @ SY962 @ SY961 @ SV237 @ SV191 @ SV138 )
| ( ( hAPP @ ( hAPP @ SY961 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5619]) ).
thf(5686,plain,
! [SV1: $i,SV71: $i,SV139: $i,SV192: $i,SV238: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV238 @ SV192 @ SV139 ) @ SV71 ) @ ( hAPP @ c_Nat_OSuc @ SV1 ) )
= ( hAPP @ ( hAPP @ SV139 @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ SV238 @ SV192 @ SV139 ) @ SV71 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5620]) ).
thf(5687,plain,
! [SV9: $i,SV79: $i,SV145: $i,SV197: $i,SV239: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV239 @ SV197 @ SV145 @ SV79 @ SV9 ) @ SV79 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5625]) ).
thf(5688,plain,
! [SV13: $i,SV83: $i,SV146: $i,SV198: $i,SV240: $i] :
( ( ! [SY964: $i,SY965: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY965 @ SY964 @ SV240 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY965 @ SV198 @ SY964 ) @ SV146 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY965 @ SV198 @ SV240 ) @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV198 @ SY964 @ SV240 ) @ SV83 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5626]) ).
thf(5689,plain,
! [SV14: $i,SV84: $i,SV147: $i,SV199: $i,SV241: $i] :
( ( ! [SY966: $i,SY967: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY967 @ SY966 @ SV241 @ SV199 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY967 @ SV241 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY966 @ SV241 @ ( hAPP @ ( c_Fun_Ocomp @ SY967 @ SY966 @ SV147 @ SV199 ) @ SV84 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5627]) ).
thf(5690,plain,
! [SV15: $i,SV85: $i,SV148: $i,SV200: $i,SV242: $i] :
( ( ! [SY968: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY968 @ SV242 @ SV200 @ SV148 ) @ SV85 ) @ SV15 )
= ( hAPP @ SV148 @ ( hAPP @ SV85 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5628]) ).
thf(5691,plain,
! [SV16: $i,SV86: $i,SV149: $i,SV201: $i,SV243: $i] :
( ( ! [SY969: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SY969 @ SV243 @ SV201 @ SV149 ) @ SV86 ) @ SV16 )
= ( hAPP @ SV149 @ ( hAPP @ SV86 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(5692,plain,
! [SV20: $i,SV90: $i,SV153: $i,SV204: $i,SV244: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV244 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV244 @ SV204 ) @ SV153 ) @ SV90 ) ) @ SV153 ) @ SV20 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV244 @ SV204 ) @ SV153 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(5693,plain,
! [SV24: $i,SV94: $i,SV155: $i,SV206: $i,SV245: $i] :
( ( ! [SY970: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SY970 @ SV245 @ SV206 ) @ SV155 ) @ SV94 ) @ SV24 )
= ( hAPP @ SV155 @ ( hAPP @ SV94 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(5694,plain,
! [SV25: $i,SV95: $i,SV156: $i,SV207: $i,SV246: $i] :
( ( ! [SY971: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SY971 @ SV246 @ SV207 ) @ SV156 ) @ SV95 ) @ SV25 )
= ( hAPP @ ( hAPP @ SV156 @ SV25 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5635]) ).
thf(5695,plain,
! [SV26: $i,SV96: $i,SV157: $i,SV208: $i,SV247: $i] :
( ( ! [SY972: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SY972 @ SV247 @ SV208 ) @ SV157 ) @ SV96 ) @ SV26 )
= ( hAPP @ ( hAPP @ SV157 @ SV26 ) @ ( hAPP @ SV96 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(5696,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i] :
( ( ! [SY973: $i,SY974: $i,SY975: $i,SY976: $i,SY977: $i,SY978: $i] :
( ( ( hAPP @ SY978 @ ( hAPP @ SY977 @ SY976 ) )
!= ( hAPP @ SY975 @ ( hAPP @ SY974 @ SY973 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY978 ) @ SY977 ) @ SY976 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SY975 ) @ SY974 ) @ SY973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(5697,plain,
! [SV28: $i,SV98: $i,SV159: $i,SV210: $i,SV249: $i] :
( ( ( ( hAPP @ SV249 @ SV210 )
!= SV159 )
| ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SV249 @ SV210 @ SV159 )
= SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(5698,plain,
! [SV29: $i,SV99: $i,SV160: $i,SV211: $i,SV250: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
| ~ ! [SY979: $i] :
( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ SY979 )
| ~ ( c_Natural_Oevaln @ SV211 @ SY979 @ SV99 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(5699,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i] :
( ( ! [SY980: $i,SY981: $i,SY982: $i,SY983: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY983 @ SY982 @ SY981 @ SY980 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SY982 @ SY981 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SY980 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(5700,plain,
! [SV31: $i,SV101: $i,SV162: $i,SV213: $i,SV252: $i] :
( ( ! [SY984: $i] :
( ~ ( c_Finite__Set_Ofun__left__comm @ SY984 @ SV252 @ SV213 )
| ( ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5641]) ).
thf(5701,plain,
! [SV33: $i,SV253: $i,SV102: $i] :
( ( ( ~ ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV253 )
| ( v_fun2 @ SV33 @ SV253 ) )
= $true )
| ( ( v_fun1 @ SV33 @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(5702,plain,
! [SV34: $i,SV103: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
| ( SV103 = SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5643]) ).
thf(5703,plain,
! [SV34: $i,SV103: $i] :
( ( ( SV103 != SV34 )
| ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5644]) ).
thf(5704,plain,
! [SV35: $i,SV104: $i,SV163: $i,SV214: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__one__idem @ SV214 @ SV163 @ SV104 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV163 @ SV35 ) @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5645]) ).
thf(5705,plain,
( ( v_fun1 @ sK1_SX0 @ sK2_SY656 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5646]) ).
thf(5706,plain,
( ( ~ ( c_Natural_Oevaln @ v_com @ sK2_SY656 @ v_n @ sK3_SY814 )
| ( v_fun2 @ sK1_SX0 @ sK3_SY814 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5647]) ).
thf(5707,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ~ ( ~ ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) )
| ~ ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(5708,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i] :
( ( ! [SY985: $i] :
~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY985 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY985 @ SV255 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
| ~ ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY985 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY985 @ SV255 ) @ SV106 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(5709,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i,SV256: $i] :
( ( ! [SY986: $i,SY987: $i] :
( ~ ( c_Typedef_Otype__definition @ SY987 @ SY986 @ SV256 @ SV217 @ SV166 )
| ~ ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(5710,plain,
! [SV39: $i,SV108: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
| ( SV108 = SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5651]) ).
thf(5711,plain,
! [SV39: $i,SV108: $i] :
( ( ( SV108 != SV39 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5652]) ).
thf(5712,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i,SV257: $i] :
( ( ! [SY988: $i] :
( ~ ( ( SY988 != SV257 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SY988 ) @ SV109 ) ) @ SV257 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV257 ) @ SV40 ) ) @ SY988 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5653]) ).
thf(5713,plain,
! [SV41: $i,SV110: $i,SV168: $i,SV219: $i,SV258: $i] :
( ( ! [SY989: $i] :
( ~ ( c_Natural_Oevaln @ SY989 @ SV258 @ SV219 @ SV168 )
| ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY989 @ SV110 ) @ SV258 @ SV219 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(5714,plain,
! [SV42: $i,SV111: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
| ( SV111 = SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5655]) ).
thf(5715,plain,
! [SV42: $i,SV111: $i] :
( ( ( SV111 != SV42 )
| ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5656]) ).
thf(5716,plain,
! [SV43: $i,SV112: $i,SV169: $i,SV220: $i,SV259: $i] :
( ( ! [SY990: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY990 @ SV259 ) @ SV220 ) @ SV169 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SY990 @ SV259 ) @ SV112 ) @ SV43 ) )
| ~ ( ( SV220 != SV112 )
| ( SV169 != SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(5717,plain,
! [SV44: $i,SV113: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
| ( SV113 = SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5658]) ).
thf(5718,plain,
! [SV44: $i,SV113: $i] :
( ( ( SV113 != SV44 )
| ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5659]) ).
thf(5719,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i] :
( ( ! [SY991: $i] :
~ ( ~ ( ( SY991 != SV260 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SY991 )
= SV46 ) )
| ~ ( ~ ( ( SY991 != SV260 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SY991 )
= ( hAPP @ SV115 @ SY991 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5661]) ).
thf(5720,plain,
! [SV47: $i,SV116: $i] :
( ( ( ( hAPP @ SV116 @ ( sK4_SY687 @ SV47 @ SV116 ) )
= ( hAPP @ SV47 @ ( sK4_SY687 @ SV47 @ SV116 ) ) )
= $false )
| ( ( SV116 = SV47 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5662]) ).
thf(5721,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i] :
( ( ! [SY992: $i,SY993: $i,SY994: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY994 @ SY993 @ SY992 @ SV261 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SY993 @ SY992 @ SV118 ) @ SV49 ) )
| ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5664]) ).
thf(5722,plain,
! [SV50: $i,SV119: $i,SV174: $i,SV223: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV223 @ SV174 @ SV119 @ SV50 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV223 @ SV174 @ ( hAPP @ c_Nat_OSuc @ SV119 ) @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5665]) ).
thf(5723,plain,
! [SV51: $i,SV120: $i,SV175: $i,SV224: $i,SV262: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV262 @ SV224 @ SV175 )
| ( ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5724,plain,
! [SV52: $i,SV121: $i,SV176: $i,SV225: $i,SV263: $i] :
( ( ! [SY996: $i] :
( ( SY996 != SV263 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SY996 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5725,plain,
! [SV53: $i,SV122: $i,SV177: $i,SV226: $i,SV264: $i] :
( ( ! [SY997: $i] :
( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY997 ) @ SV264 ) @ SV226 )
!= SV177 )
| ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY997 ) @ SV226 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY997 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SY997 ) @ SV177 ) @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(5726,plain,
! [SV54: $i,SV123: $i,SV178: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV178 @ SV123 @ SV54 )
= $false )
| ( ( SV54 = SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(5727,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i,SV265: $i] :
( ( ! [SY998: $i,SY999: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY999 @ SY998 @ SV265 @ SV227 ) @ SV179 )
!= SV124 )
| ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5728,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5671]) ).
thf(5729,plain,
! [SV57: $i,SV126: $i,SV181: $i,SV229: $i,SV267: $i] :
( ( ! [SY1002: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1002 @ SV267 @ SV229 @ SV181 @ SV126 )
| ( ( hAPP @ SV181 @ ( hAPP @ SV229 @ SV57 ) )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5672]) ).
thf(5730,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
| ( SV182 = SV58 ) )
| ~ ( ( SV182 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5673]) ).
thf(5731,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i] :
( ( ! [SY1003: $i] :
~ ( ~ ( ( SY1003 != SV268 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SY1003 )
= SV59 ) )
| ~ ( ~ ( ( SY1003 != SV268 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SY1003 )
= ( hAPP @ SV128 @ SY1003 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5674]) ).
thf(5732,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
| ( SV129 = SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5675]) ).
thf(5733,plain,
! [SV184: $i,SV60: $i,SV129: $i] :
( ( ~ ( ( SV129 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5675]) ).
thf(5734,plain,
! [SV61: $i,SV130: $i,SV185: $i,SV232: $i,SV269: $i] :
( ( ~ ! [SY1004: $i] :
( ( hAPP @ SV269 @ SY1004 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV232 @ SV185 @ SV130 ) @ SY1004 ) )
| ( ( hAPP @ SV269 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SV269 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5676]) ).
thf(5735,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ~ ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5677]) ).
thf(5736,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
| ( SV132 = SV63 ) )
| ~ ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5678]) ).
thf(5737,plain,
! [SV65: $i,SV134: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
| ( SV134 = SV65 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5680]) ).
thf(5738,plain,
! [SV65: $i,SV134: $i] :
( ( ( SV134 != SV65 )
| ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5681]) ).
thf(5739,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ~ ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
!= SV66 )
| ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5740,plain,
! [SV66: $i,SV188: $i,SV135: $i] :
( ( ~ ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5741,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i,SV271: $i] :
( ( ! [SY1007: $i] :
( ~ ( ( SY1007 != SV271 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SV271 @ SV67 ) @ SY1007 )
= ( hAPP @ SV136 @ SY1007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(5742,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
| ~ ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(5743,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i,SV273: $i] :
( ( ! [SY1008: $i,SY1009: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1009 @ SY1008 @ SV273 @ SV237 @ SV191 @ SV138 )
| ( ( hAPP @ ( hAPP @ SV273 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(5744,plain,
! [SV13: $i,SV83: $i,SV146: $i,SV198: $i,SV240: $i,SV274: $i] :
( ( ! [SY1010: $i] :
( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1010 @ SV274 @ SV240 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1010 @ SV198 @ SV274 ) @ SV146 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SY1010 @ SV198 @ SV240 ) @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV198 @ SV274 @ SV240 ) @ SV83 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(5745,plain,
! [SV14: $i,SV84: $i,SV147: $i,SV199: $i,SV241: $i,SV275: $i] :
( ( ! [SY1011: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SY1011 @ SV275 @ SV241 @ SV199 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SY1011 @ SV241 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SV275 @ SV241 @ ( hAPP @ ( c_Fun_Ocomp @ SY1011 @ SV275 @ SV147 @ SV199 ) @ SV84 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(5746,plain,
! [SV15: $i,SV85: $i,SV148: $i,SV200: $i,SV242: $i,SV276: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV276 @ SV242 @ SV200 @ SV148 ) @ SV85 ) @ SV15 )
= ( hAPP @ SV148 @ ( hAPP @ SV85 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(5747,plain,
! [SV16: $i,SV86: $i,SV149: $i,SV201: $i,SV243: $i,SV277: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV277 @ SV243 @ SV201 @ SV149 ) @ SV86 ) @ SV16 )
= ( hAPP @ SV149 @ ( hAPP @ SV86 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5691]) ).
thf(5748,plain,
! [SV24: $i,SV94: $i,SV155: $i,SV206: $i,SV245: $i,SV278: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ SV278 @ SV245 @ SV206 ) @ SV155 ) @ SV94 ) @ SV24 )
= ( hAPP @ SV155 @ ( hAPP @ SV94 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(5749,plain,
! [SV25: $i,SV95: $i,SV156: $i,SV207: $i,SV246: $i,SV279: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ SV279 @ SV246 @ SV207 ) @ SV156 ) @ SV95 ) @ SV25 )
= ( hAPP @ ( hAPP @ SV156 @ SV25 ) @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5694]) ).
thf(5750,plain,
! [SV26: $i,SV96: $i,SV157: $i,SV208: $i,SV247: $i,SV280: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ SV280 @ SV247 @ SV208 ) @ SV157 ) @ SV96 ) @ SV26 )
= ( hAPP @ ( hAPP @ SV157 @ SV26 ) @ ( hAPP @ SV96 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5695]) ).
thf(5751,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i] :
( ( ! [SY1012: $i,SY1013: $i,SY1014: $i,SY1015: $i,SY1016: $i] :
( ( ( hAPP @ SY1016 @ ( hAPP @ SY1015 @ SY1014 ) )
!= ( hAPP @ SY1013 @ ( hAPP @ SY1012 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY1016 ) @ SY1015 ) @ SY1014 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SY1013 ) @ SY1012 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5696]) ).
thf(5752,plain,
! [SV28: $i,SV98: $i,SV159: $i,SV210: $i,SV249: $i] :
( ( ( ( hAPP @ SV249 @ SV210 )
!= SV159 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SV249 @ SV210 @ SV159 )
= SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5697]) ).
thf(5753,plain,
! [SV29: $i,SV99: $i,SV160: $i,SV211: $i,SV250: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 ) )
= $true )
| ( ( ~ ! [SY979: $i] :
( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ SY979 )
| ~ ( c_Natural_Oevaln @ SV211 @ SY979 @ SV99 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5698]) ).
thf(5754,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i] :
( ( ! [SY1017: $i,SY1018: $i,SY1019: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1019 @ SY1018 @ SY1017 @ SV282 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SY1018 @ SY1017 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(5755,plain,
! [SV31: $i,SV101: $i,SV162: $i,SV213: $i,SV252: $i,SV283: $i] :
( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV283 @ SV252 @ SV213 )
| ( ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(5756,plain,
! [SV33: $i,SV253: $i,SV102: $i] :
( ( ( ~ ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV253 ) )
= $true )
| ( ( v_fun2 @ SV33 @ SV253 )
= $true )
| ( ( v_fun1 @ SV33 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5701]) ).
thf(5757,plain,
! [SV34: $i,SV103: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
!= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
= $true )
| ( ( SV103 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5702]) ).
thf(5758,plain,
! [SV34: $i,SV103: $i] :
( ( ( SV103 != SV34 )
= $true )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(5759,plain,
! [SV35: $i,SV104: $i,SV163: $i,SV214: $i] :
( ( ( c_Finite__Set_Ofolding__one__idem @ SV214 @ SV163 @ SV104 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV163 @ SV35 ) @ SV35 )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(5760,plain,
( ( ~ ( c_Natural_Oevaln @ v_com @ sK2_SY656 @ v_n @ sK3_SY814 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5706]) ).
thf(5761,plain,
( ( v_fun2 @ sK1_SX0 @ sK3_SY814 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5706]) ).
thf(5762,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) )
| ~ ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(5763,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ~ ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
| ~ ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(5764,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i,SV256: $i,SV285: $i] :
( ( ! [SY1020: $i] :
( ~ ( c_Typedef_Otype__definition @ SY1020 @ SV285 @ SV256 @ SV217 @ SV166 )
| ~ ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5765,plain,
! [SV39: $i,SV108: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
= $true )
| ( ( SV108 = SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5710]) ).
thf(5766,plain,
! [SV39: $i,SV108: $i] :
( ( ( SV108 != SV39 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5711]) ).
thf(5767,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i,SV257: $i,SV286: $i] :
( ( ~ ( ( SV286 != SV257 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV286 ) @ SV109 ) ) @ SV257 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV257 ) @ SV40 ) ) @ SV286 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5712]) ).
thf(5768,plain,
! [SV41: $i,SV110: $i,SV168: $i,SV219: $i,SV258: $i,SV287: $i] :
( ( ~ ( c_Natural_Oevaln @ SV287 @ SV258 @ SV219 @ SV168 )
| ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV287 @ SV110 ) @ SV258 @ SV219 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(5769,plain,
! [SV42: $i,SV111: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
!= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $true )
| ( ( SV111 = SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(5770,plain,
! [SV42: $i,SV111: $i] :
( ( ( SV111 != SV42 )
= $true )
| ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5715]) ).
thf(5771,plain,
! [SV43: $i,SV112: $i,SV169: $i,SV220: $i,SV259: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
| ~ ( ( SV220 != SV112 )
| ( SV169 != SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(5772,plain,
! [SV44: $i,SV113: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
!= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true )
| ( ( SV113 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5717]) ).
thf(5773,plain,
! [SV44: $i,SV113: $i] :
( ( ( SV113 != SV44 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5718]) ).
thf(5774,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ~ ( ~ ( ( SV289 != SV260 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 ) )
| ~ ( ~ ( ( SV289 != SV260 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5719]) ).
thf(5775,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i,SV290: $i] :
( ( ! [SY1021: $i,SY1022: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1022 @ SY1021 @ SV290 @ SV261 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SY1021 @ SV290 @ SV118 ) @ SV49 ) )
| ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5721]) ).
thf(5776,plain,
! [SV50: $i,SV119: $i,SV174: $i,SV223: $i] :
( ( ( c_Natural_Oevaln @ SV223 @ SV174 @ SV119 @ SV50 )
= $false )
| ( ( c_Natural_Oevaln @ SV223 @ SV174 @ ( hAPP @ c_Nat_OSuc @ SV119 ) @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(5777,plain,
! [SV51: $i,SV120: $i,SV175: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm__idem @ SV262 @ SV224 @ SV175 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5723]) ).
thf(5778,plain,
! [SV52: $i,SV121: $i,SV176: $i,SV225: $i,SV263: $i,SV291: $i] :
( ( ( SV291 != SV263 )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV291 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5724]) ).
thf(5779,plain,
! [SV53: $i,SV122: $i,SV177: $i,SV226: $i,SV264: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV226 )
!= SV177 )
| ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV226 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV177 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(5780,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i,SV265: $i,SV293: $i] :
( ( ! [SY1024: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1024 @ SV293 @ SV265 @ SV227 ) @ SV179 )
!= SV124 )
| ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5727]) ).
thf(5781,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
| ~ ( ~ ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5728]) ).
thf(5782,plain,
! [SV57: $i,SV126: $i,SV181: $i,SV229: $i,SV267: $i,SV294: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV294 @ SV267 @ SV229 @ SV181 @ SV126 )
| ( ( hAPP @ SV181 @ ( hAPP @ SV229 @ SV57 ) )
= SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5729]) ).
thf(5783,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
| ( SV182 = SV58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5730]) ).
thf(5784,plain,
! [SV127: $i,SV230: $i,SV58: $i,SV182: $i] :
( ( ~ ( ( SV182 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5730]) ).
thf(5785,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ~ ( ~ ( ( SV295 != SV268 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 ) )
| ~ ( ~ ( ( SV295 != SV268 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5731]) ).
thf(5786,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
| ( SV129 = SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5732]) ).
thf(5787,plain,
! [SV184: $i,SV60: $i,SV129: $i] :
( ( ( SV129 != SV60 )
| ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5733]) ).
thf(5788,plain,
! [SV61: $i,SV130: $i,SV185: $i,SV232: $i,SV269: $i] :
( ( ( ~ ! [SY1004: $i] :
( ( hAPP @ SV269 @ SY1004 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV232 @ SV185 @ SV130 ) @ SY1004 ) ) )
= $true )
| ( ( ( hAPP @ SV269 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SV269 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(5789,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
| ~ ( ~ ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5735]) ).
thf(5790,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
| ( SV132 = SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5736]) ).
thf(5791,plain,
! [SV187: $i,SV234: $i,SV63: $i,SV132: $i] :
( ( ~ ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5736]) ).
thf(5792,plain,
! [SV65: $i,SV134: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
!= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
= $true )
| ( ( SV134 = SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5793,plain,
! [SV65: $i,SV134: $i] :
( ( ( SV134 != SV65 )
= $true )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5794,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
!= SV66 )
| ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5739]) ).
thf(5795,plain,
! [SV66: $i,SV188: $i,SV135: $i] :
( ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
| ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5740]) ).
thf(5796,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i,SV271: $i,SV296: $i] :
( ( ~ ( ( SV296 != SV271 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SV271 @ SV67 ) @ SV296 )
= ( hAPP @ SV136 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5741]) ).
thf(5797,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
| ~ ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5742]) ).
thf(5798,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i,SV273: $i,SV297: $i] :
( ( ! [SY1025: $i] :
( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SY1025 @ SV297 @ SV273 @ SV237 @ SV191 @ SV138 )
| ( ( hAPP @ ( hAPP @ SV273 @ SV69 ) @ SV69 )
= SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(5799,plain,
! [SV13: $i,SV83: $i,SV146: $i,SV198: $i,SV240: $i,SV274: $i,SV298: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV298 @ SV274 @ SV240 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV298 @ SV198 @ SV274 ) @ SV146 ) @ SV83 ) ) @ SV13 )
= ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV298 @ SV198 @ SV240 ) @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_Relation_Orel__comp @ SV198 @ SV274 @ SV240 ) @ SV83 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5744]) ).
thf(5800,plain,
! [SV14: $i,SV84: $i,SV147: $i,SV199: $i,SV241: $i,SV275: $i,SV299: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV299 @ SV275 @ SV241 @ SV199 ) @ ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SV299 @ SV241 @ SV84 ) @ SV14 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV147 @ SV275 @ SV241 @ ( hAPP @ ( c_Fun_Ocomp @ SV299 @ SV275 @ SV147 @ SV199 ) @ SV84 ) ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5745]) ).
thf(5801,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i] :
( ( ! [SY1026: $i,SY1027: $i,SY1028: $i,SY1029: $i] :
( ( ( hAPP @ SY1029 @ ( hAPP @ SY1028 @ SY1027 ) )
!= ( hAPP @ SY1026 @ ( hAPP @ SV300 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY1029 ) @ SY1028 ) @ SY1027 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SY1026 ) @ SV300 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(5802,plain,
! [SV28: $i,SV98: $i,SV159: $i,SV210: $i,SV249: $i] :
( ( ( ( hAPP @ SV249 @ SV210 )
= SV159 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV98 @ SV28 @ SV249 @ SV210 @ SV159 )
= SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(5803,plain,
! [SV29: $i,SV99: $i,SV160: $i,SV211: $i,SV250: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false )
| ( ( ~ ! [SY979: $i] :
( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ SY979 )
| ~ ( c_Natural_Oevaln @ SV211 @ SY979 @ SV99 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5804,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i,SV301: $i] :
( ( ! [SY1030: $i,SY1031: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1031 @ SY1030 @ SV301 @ SV282 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SY1030 @ SV301 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(5805,plain,
! [SV31: $i,SV101: $i,SV162: $i,SV213: $i,SV252: $i,SV283: $i] :
( ( ( ~ ( c_Finite__Set_Ofun__left__comm @ SV283 @ SV252 @ SV213 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5755]) ).
thf(5806,plain,
! [SV33: $i,SV253: $i,SV102: $i] :
( ( ( c_Natural_Oevaln @ v_com @ SV102 @ ( hAPP @ c_Nat_OSuc @ v_n ) @ SV253 )
= $false )
| ( ( v_fun2 @ SV33 @ SV253 )
= $true )
| ( ( v_fun1 @ SV33 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(5807,plain,
! [SV34: $i,SV103: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
= $false )
| ( ( SV103 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5808,plain,
! [SV34: $i,SV103: $i] :
( ( ( SV103 = SV34 )
= $false )
| ( ( ( hAPP @ c_Int_ORep__Integ @ SV103 )
= ( hAPP @ c_Int_ORep__Integ @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5758]) ).
thf(5809,plain,
( ( c_Natural_Oevaln @ v_com @ sK2_SY656 @ v_n @ sK3_SY814 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5760]) ).
thf(5810,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ~ ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5762]) ).
thf(5811,plain,
! [SV215: $i,SV254: $i,SV36: $i,SV105: $i,SV164: $i] :
( ( ~ ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5762]) ).
thf(5812,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
| ~ ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(5813,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i,SV256: $i,SV285: $i,SV302: $i] :
( ( ~ ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
| ~ ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(5814,plain,
! [SV39: $i,SV108: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
= $false )
| ( ( SV108 = SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(5815,plain,
! [SV39: $i,SV108: $i] :
( ( ( SV108 = SV39 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV108 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5816,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i,SV257: $i,SV286: $i] :
( ( ( ~ ( ( SV286 != SV257 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV286 ) @ SV109 ) ) @ SV257 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV257 ) @ SV40 ) ) @ SV286 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(5817,plain,
! [SV41: $i,SV110: $i,SV168: $i,SV219: $i,SV258: $i,SV287: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV287 @ SV258 @ SV219 @ SV168 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV287 @ SV110 ) @ SV258 @ SV219 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5768]) ).
thf(5818,plain,
! [SV42: $i,SV111: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $false )
| ( ( SV111 = SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(5819,plain,
! [SV42: $i,SV111: $i] :
( ( ( SV111 = SV42 )
= $false )
| ( ( ( hAPP @ c_Nat_OSuc @ SV111 )
= ( hAPP @ c_Nat_OSuc @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(5820,plain,
! [SV43: $i,SV112: $i,SV169: $i,SV220: $i,SV259: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $true )
| ( ( ~ ( ( SV220 != SV112 )
| ( SV169 != SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5771]) ).
thf(5821,plain,
! [SV44: $i,SV113: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $false )
| ( ( SV113 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(5822,plain,
! [SV44: $i,SV113: $i] :
( ( ( SV113 = SV44 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Onat__of @ SV113 )
= ( hAPP @ c_Code__Numeral_Onat__of @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(5823,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ~ ( ( SV289 != SV260 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 ) )
| ~ ( ~ ( ( SV289 != SV260 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(5824,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i,SV290: $i,SV303: $i] :
( ( ! [SY1032: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1032 @ SV303 @ SV290 @ SV261 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SV303 @ SV290 @ SV118 ) @ SV49 ) )
| ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(5825,plain,
! [SV51: $i,SV120: $i,SV175: $i,SV224: $i,SV262: $i] :
( ( ( c_Finite__Set_Ofun__left__comm__idem @ SV262 @ SV224 @ SV175 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= ( hAPP @ ( hAPP @ SV175 @ SV120 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(5826,plain,
! [SV52: $i,SV121: $i,SV176: $i,SV225: $i,SV263: $i,SV291: $i] :
( ( ( SV291 != SV263 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV291 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5778]) ).
thf(5827,plain,
! [SV53: $i,SV122: $i,SV177: $i,SV226: $i,SV264: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV226 )
!= SV177 )
= $true )
| ( ( ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV226 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV177 ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5779]) ).
thf(5828,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i,SV265: $i,SV293: $i,SV304: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV304 @ SV293 @ SV265 @ SV227 ) @ SV179 )
!= SV124 )
| ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(5829,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5781]) ).
thf(5830,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ~ ( ~ ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5781]) ).
thf(5831,plain,
! [SV57: $i,SV126: $i,SV181: $i,SV229: $i,SV267: $i,SV294: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV294 @ SV267 @ SV229 @ SV181 @ SV126 ) )
= $true )
| ( ( ( hAPP @ SV181 @ ( hAPP @ SV229 @ SV57 ) )
= SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5782]) ).
thf(5832,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
| ( SV182 = SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5783]) ).
thf(5833,plain,
! [SV127: $i,SV230: $i,SV58: $i,SV182: $i] :
( ( ( SV182 != SV58 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5784]) ).
thf(5834,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ~ ( ( SV295 != SV268 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 ) )
| ~ ( ~ ( ( SV295 != SV268 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(5835,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
!= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
= $true )
| ( ( SV129 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(5836,plain,
! [SV184: $i,SV60: $i,SV129: $i] :
( ( ( SV129 != SV60 )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5787]) ).
thf(5837,plain,
! [SV61: $i,SV130: $i,SV185: $i,SV232: $i,SV269: $i] :
( ( ( ! [SY1004: $i] :
( ( hAPP @ SV269 @ SY1004 )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV232 @ SV185 @ SV130 ) @ SY1004 ) ) )
= $false )
| ( ( ( hAPP @ SV269 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SV269 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5838,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ~ ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5789]) ).
thf(5839,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ~ ( ~ ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5789]) ).
thf(5840,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
| ( SV132 = SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5790]) ).
thf(5841,plain,
! [SV187: $i,SV234: $i,SV63: $i,SV132: $i] :
( ( ( SV132 != SV63 )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5791]) ).
thf(5842,plain,
! [SV65: $i,SV134: $i] :
( ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
= $false )
| ( ( SV134 = SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(5843,plain,
! [SV65: $i,SV134: $i] :
( ( ( SV134 = SV65 )
= $false )
| ( ( ( hAPP @ c_Code__Numeral_Oof__nat @ SV134 )
= ( hAPP @ c_Code__Numeral_Oof__nat @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(5844,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
!= SV66 )
= $true )
| ( ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5794]) ).
thf(5845,plain,
! [SV66: $i,SV188: $i,SV135: $i] :
( ( ( SV135
!= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
= $true )
| ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(5846,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i,SV271: $i,SV296: $i] :
( ( ( ~ ( ( SV296 != SV271 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SV271 @ SV67 ) @ SV296 )
= ( hAPP @ SV136 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(5847,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5797]) ).
thf(5848,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ~ ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5797]) ).
thf(5849,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i,SV273: $i,SV297: $i,SV305: $i] :
( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV305 @ SV297 @ SV273 @ SV237 @ SV191 @ SV138 )
| ( ( hAPP @ ( hAPP @ SV273 @ SV69 ) @ SV69 )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(5850,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i] :
( ( ! [SY1034: $i,SY1035: $i,SY1036: $i] :
( ( ( hAPP @ SY1036 @ ( hAPP @ SY1035 @ SY1034 ) )
!= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY1036 ) @ SY1035 ) @ SY1034 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5801]) ).
thf(5851,plain,
! [SV29: $i,SV211: $i,SV99: $i,SV160: $i,SV250: $i] :
( ( ( ! [SY979: $i] :
( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ SY979 )
| ~ ( c_Natural_Oevaln @ SV211 @ SY979 @ SV99 @ SV29 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(5852,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i,SV301: $i,SV307: $i] :
( ( ! [SY1037: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SY1037 @ SV307 @ SV301 @ SV282 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SV307 @ SV301 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(5853,plain,
! [SV31: $i,SV101: $i,SV162: $i,SV213: $i,SV252: $i,SV283: $i] :
( ( ( c_Finite__Set_Ofun__left__comm @ SV283 @ SV252 @ SV213 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ SV31 ) )
= ( hAPP @ ( hAPP @ SV213 @ SV101 ) @ ( hAPP @ ( hAPP @ SV213 @ SV162 ) @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(5854,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
| ( ( hAPP @ SV164 @ SV105 )
= SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5810]) ).
thf(5855,plain,
! [SV215: $i,SV254: $i,SV36: $i,SV105: $i,SV164: $i] :
( ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
| ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5811]) ).
thf(5856,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5812]) ).
thf(5857,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ~ ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5812]) ).
thf(5858,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i,SV256: $i,SV285: $i,SV302: $i] :
( ( ( ~ ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5813]) ).
thf(5859,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i,SV257: $i,SV286: $i] :
( ( ( SV286 != SV257 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV286 ) @ SV109 ) ) @ SV257 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV257 ) @ SV40 ) ) @ SV286 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(5860,plain,
! [SV41: $i,SV110: $i,SV168: $i,SV219: $i,SV258: $i,SV287: $i] :
( ( ( c_Natural_Oevaln @ SV287 @ SV258 @ SV219 @ SV168 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV287 @ SV110 ) @ SV258 @ SV219 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5817]) ).
thf(5861,plain,
! [SV43: $i,SV112: $i,SV169: $i,SV220: $i,SV259: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false )
| ( ( ~ ( ( SV220 != SV112 )
| ( SV169 != SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5862,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ~ ( ( SV289 != SV260 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5823]) ).
thf(5863,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ~ ( ~ ( ( SV289 != SV260 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5823]) ).
thf(5864,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i,SV290: $i,SV303: $i,SV308: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV308 @ SV303 @ SV290 @ SV261 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SV303 @ SV290 @ SV118 ) @ SV49 ) )
| ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(5865,plain,
! [SV52: $i,SV121: $i,SV176: $i,SV225: $i,SV263: $i,SV291: $i] :
( ( ( SV291 = SV263 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV291 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_Oprod_Oprod__case @ SV225 @ SV176 @ SV121 ) @ SV52 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5866,plain,
! [SV53: $i,SV122: $i,SV177: $i,SV226: $i,SV264: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV226 )
= SV177 )
= $false )
| ( ( ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV226 ) @ SV53 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV177 ) @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(5867,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i,SV265: $i,SV293: $i,SV304: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV304 @ SV293 @ SV265 @ SV227 ) @ SV179 )
!= SV124 )
= $true )
| ( ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(5868,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
| ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5829]) ).
thf(5869,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ~ ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5830]) ).
thf(5870,plain,
! [SV57: $i,SV126: $i,SV181: $i,SV229: $i,SV267: $i,SV294: $i] :
( ( ( c_Typedef_Otype__definition @ SV294 @ SV267 @ SV229 @ SV181 @ SV126 )
= $false )
| ( ( ( hAPP @ SV181 @ ( hAPP @ SV229 @ SV57 ) )
= SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(5871,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
= $true )
| ( ( SV182 = SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5832]) ).
thf(5872,plain,
! [SV127: $i,SV230: $i,SV58: $i,SV182: $i] :
( ( ( SV182 != SV58 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5833]) ).
thf(5873,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ~ ( ( SV295 != SV268 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5834]) ).
thf(5874,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ~ ( ~ ( ( SV295 != SV268 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5834]) ).
thf(5875,plain,
! [SV60: $i,SV129: $i,SV184: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
= $false )
| ( ( SV129 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(5876,plain,
! [SV184: $i,SV60: $i,SV129: $i] :
( ( ( SV129 = SV60 )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV184 ) @ SV129 )
= ( hAPP @ ( c_List_Orev @ SV184 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(5877,plain,
! [SV232: $i,SV185: $i,SV130: $i,SV61: $i,SV269: $i] :
( ( ( ( hAPP @ SV269 @ ( sK5_SY1004 @ SV61 @ SV130 @ SV185 @ SV232 @ SV269 ) )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ SV232 @ SV185 @ SV130 ) @ ( sK5_SY1004 @ SV61 @ SV130 @ SV185 @ SV232 @ SV269 ) ) )
= $false )
| ( ( ( hAPP @ SV269 @ ( hAPP @ c_Nat_OSuc @ SV61 ) )
= ( hAPP @ ( hAPP @ SV130 @ SV61 ) @ ( hAPP @ SV269 @ SV61 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5837]) ).
thf(5878,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
| ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5838]) ).
thf(5879,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ~ ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) )
| ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5839]) ).
thf(5880,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
= $true )
| ( ( SV132 = SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5840]) ).
thf(5881,plain,
! [SV187: $i,SV234: $i,SV63: $i,SV132: $i] :
( ( ( SV132 != SV63 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5841]) ).
thf(5882,plain,
! [SV66: $i,SV135: $i,SV188: $i] :
( ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 )
= $false )
| ( ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5844]) ).
thf(5883,plain,
! [SV66: $i,SV188: $i,SV135: $i] :
( ( ( SV135
= ( hAPP @ ( c_List_Orev @ SV188 ) @ SV66 ) )
= $false )
| ( ( ( hAPP @ ( c_List_Orev @ SV188 ) @ SV135 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5845]) ).
thf(5884,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i,SV271: $i,SV296: $i] :
( ( ( SV296 != SV271 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SV271 @ SV67 ) @ SV296 )
= ( hAPP @ SV136 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5885,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
| ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5847]) ).
thf(5886,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5848]) ).
thf(5887,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i,SV273: $i,SV297: $i,SV305: $i] :
( ( ( ~ ( c_Finite__Set_Ofolding__image__simple__idem @ SV305 @ SV297 @ SV273 @ SV237 @ SV191 @ SV138 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV273 @ SV69 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5849]) ).
thf(5888,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i,SV309: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ( ( hAPP @ SY1040 @ ( hAPP @ SY1039 @ SV309 ) )
!= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY1040 ) @ SY1039 ) @ SV309 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5850]) ).
thf(5889,plain,
! [SV211: $i,SV29: $i,SV99: $i,SV160: $i,SV250: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) )
| ~ ( c_Natural_Oevaln @ SV211 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) @ SV99 @ SV29 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5851]) ).
thf(5890,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i,SV301: $i,SV307: $i,SV310: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV310 @ SV307 @ SV301 @ SV282 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SV307 @ SV301 @ SV161 ) @ SV100 ) )
| ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5852]) ).
thf(5891,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
!= SV164 )
= $true )
| ( ( ( hAPP @ SV164 @ SV105 )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5854]) ).
thf(5892,plain,
! [SV215: $i,SV254: $i,SV36: $i,SV105: $i,SV164: $i] :
( ( ( ( hAPP @ SV164 @ SV105 )
!= SV36 )
= $true )
| ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5855]) ).
thf(5893,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
| ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5856]) ).
thf(5894,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
| ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5857]) ).
thf(5895,plain,
! [SV38: $i,SV107: $i,SV166: $i,SV217: $i,SV256: $i,SV285: $i,SV302: $i] :
( ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(5896,plain,
! [SV40: $i,SV109: $i,SV167: $i,SV218: $i,SV257: $i,SV286: $i] :
( ( ( SV286 = SV257 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV286 ) @ SV109 ) ) @ SV257 ) @ SV40 )
= ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ ( hAPP @ ( hAPP @ ( c_List_Olist__update @ SV218 @ SV167 ) @ SV257 ) @ SV40 ) ) @ SV286 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5859]) ).
thf(5897,plain,
! [SV258: $i,SV287: $i,SV41: $i,SV219: $i,SV168: $i,SV110: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV287 @ SV110 ) @ SV258 @ SV219 @ SV41 )
= $true )
| ( ( c_Natural_Oevaln @ SV287 @ SV258 @ SV219 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5860]) ).
thf(5898,plain,
! [SV259: $i,SV288: $i,SV43: $i,SV169: $i,SV112: $i,SV220: $i] :
( ( ( ( SV220 != SV112 )
| ( SV169 != SV43 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5861]) ).
thf(5899,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( SV289 != SV260 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5862]) ).
thf(5900,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ~ ( ( SV289 != SV260 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5863]) ).
thf(5901,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i,SV290: $i,SV303: $i,SV308: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV308 @ SV303 @ SV290 @ SV261 ) @ SV222 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SV303 @ SV290 @ SV118 ) @ SV49 ) )
= $true )
| ( ( ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5864]) ).
thf(5902,plain,
! [SV177: $i,SV264: $i,SV53: $i,SV226: $i,SV292: $i,SV122: $i] :
( ( ( SV122
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV226 ) @ SV53 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV177 ) @ SV53 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV226 )
= SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5866]) ).
thf(5903,plain,
! [SV55: $i,SV124: $i,SV179: $i,SV227: $i,SV265: $i,SV293: $i,SV304: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV304 @ SV293 @ SV265 @ SV227 ) @ SV179 )
= SV124 )
= $false )
| ( ( ( hAPP @ SV227 @ ( hAPP @ SV179 @ SV55 ) )
= ( hAPP @ SV124 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5867]) ).
thf(5904,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true )
| ( ( ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5868]) ).
thf(5905,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5869]) ).
thf(5906,plain,
! [SV58: $i,SV127: $i,SV182: $i,SV230: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
= $false )
| ( ( SV182 = SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5907,plain,
! [SV127: $i,SV230: $i,SV58: $i,SV182: $i] :
( ( ( SV182 = SV58 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV182 ) @ SV127 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV230 ) @ SV58 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5872]) ).
thf(5908,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( SV295 != SV268 )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5873]) ).
thf(5909,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ~ ( ( SV295 != SV268 ) )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5874]) ).
thf(5910,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 ) )
= $true )
| ( ( ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5878]) ).
thf(5911,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5879]) ).
thf(5912,plain,
! [SV63: $i,SV132: $i,SV187: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
= $false )
| ( ( SV132 = SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5880]) ).
thf(5913,plain,
! [SV187: $i,SV234: $i,SV63: $i,SV132: $i] :
( ( ( SV132 = SV63 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV132 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV234 ) @ SV187 ) @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5881]) ).
thf(5914,plain,
! [SV67: $i,SV136: $i,SV189: $i,SV235: $i,SV271: $i,SV296: $i] :
( ( ( SV296 = SV271 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV235 @ SV189 @ SV136 @ SV271 @ SV67 ) @ SV296 )
= ( hAPP @ SV136 @ SV296 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5884]) ).
thf(5915,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
!= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true )
| ( ( ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5885]) ).
thf(5916,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( ~ ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5886]) ).
thf(5917,plain,
! [SV69: $i,SV138: $i,SV191: $i,SV237: $i,SV273: $i,SV297: $i,SV305: $i] :
( ( ( c_Finite__Set_Ofolding__image__simple__idem @ SV305 @ SV297 @ SV273 @ SV237 @ SV191 @ SV138 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV273 @ SV69 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(5918,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i,SV309: $i,SV311: $i] :
( ( ! [SY1041: $i] :
( ( ( hAPP @ SY1041 @ ( hAPP @ SV311 @ SV309 ) )
!= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SY1041 ) @ SV311 ) @ SV309 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5888]) ).
thf(5919,plain,
! [SV211: $i,SV29: $i,SV99: $i,SV160: $i,SV250: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5889]) ).
thf(5920,plain,
! [SV250: $i,SV160: $i,SV99: $i,SV29: $i,SV211: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV211 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) @ SV99 @ SV29 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5889]) ).
thf(5921,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i,SV301: $i,SV307: $i,SV310: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV310 @ SV307 @ SV301 @ SV282 ) @ SV251 )
!= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SV307 @ SV301 @ SV161 ) @ SV100 ) )
= $true )
| ( ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5890]) ).
thf(5922,plain,
! [SV36: $i,SV105: $i,SV164: $i,SV215: $i,SV254: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 )
= $false )
| ( ( ( hAPP @ SV164 @ SV105 )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(5923,plain,
! [SV215: $i,SV254: $i,SV36: $i,SV105: $i,SV164: $i] :
( ( ( ( hAPP @ SV164 @ SV105 )
= SV36 )
= $false )
| ( ( ( c_Fun_Ofun__upd @ SV254 @ SV215 @ SV164 @ SV105 @ SV36 )
= SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(5924,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true )
| ( ( ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5893]) ).
thf(5925,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( ~ ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5894]) ).
thf(5926,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV38: $i,SV107: $i,SV256: $i] :
( ( ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
| ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5895]) ).
thf(5927,plain,
! [SV258: $i,SV287: $i,SV41: $i,SV219: $i,SV168: $i,SV110: $i] :
( ( ( c_Natural_Oevaln @ SV110 @ SV168 @ SV219 @ SV41 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV287 @ SV110 ) @ SV258 @ SV219 @ SV41 )
= $true )
| ( ( c_Natural_Oevaln @ SV287 @ SV258 @ SV219 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5897]) ).
thf(5928,plain,
! [SV43: $i,SV169: $i,SV259: $i,SV288: $i,SV112: $i,SV220: $i] :
( ( ( SV220 != SV112 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5898]) ).
thf(5929,plain,
! [SV112: $i,SV220: $i,SV259: $i,SV288: $i,SV43: $i,SV169: $i] :
( ( ( SV169 != SV43 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5898]) ).
thf(5930,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( SV289 != SV260 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5899]) ).
thf(5931,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( ~ ( ( SV289 != SV260 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5900]) ).
thf(5932,plain,
! [SV49: $i,SV118: $i,SV173: $i,SV222: $i,SV261: $i,SV290: $i,SV303: $i,SV308: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV308 @ SV303 @ SV290 @ SV261 ) @ SV222 )
= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SV303 @ SV290 @ SV118 ) @ SV49 ) )
= $false )
| ( ( ! [SY995: $i] :
( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SY995 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SY995 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5901]) ).
thf(5933,plain,
! [SV177: $i,SV264: $i,SV53: $i,SV226: $i,SV292: $i,SV122: $i] :
( ( ( SV122
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV226 ) @ SV53 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV122 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV177 ) @ SV53 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV292 ) @ SV264 ) @ SV226 )
= SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(5934,plain,
! [SV56: $i,SV125: $i,SV180: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false )
| ( ( ~ ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5904]) ).
thf(5935,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(5936,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( SV295 != SV268 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5908]) ).
thf(5937,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( ~ ( ( SV295 != SV268 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5909]) ).
thf(5938,plain,
! [SV62: $i,SV131: $i,SV186: $i,SV233: $i,SV270: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false )
| ( ( ~ ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(5939,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(5940,plain,
! [SV68: $i,SV137: $i,SV190: $i,SV236: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false )
| ( ( ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(5941,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( ~ ( ( SV236 != SV137 )
| ( SV190 != SV68 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5916]) ).
thf(5942,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i,SV309: $i,SV311: $i,SV312: $i] :
( ( ( ( hAPP @ SV312 @ ( hAPP @ SV311 @ SV309 ) )
!= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SV312 ) @ SV311 ) @ SV309 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5918]) ).
thf(5943,plain,
! [SV211: $i,SV29: $i,SV99: $i,SV160: $i,SV250: $i] :
( ( ( c_Natural_Oevaln @ SV250 @ SV160 @ SV99 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5919]) ).
thf(5944,plain,
! [SV250: $i,SV160: $i,SV99: $i,SV29: $i,SV211: $i] :
( ( ( c_Natural_Oevaln @ SV211 @ ( sK6_SY979 @ SV29 @ SV211 @ SV99 @ SV160 @ SV250 ) @ SV99 @ SV29 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV250 @ SV211 ) @ SV160 @ SV99 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5920]) ).
thf(5945,plain,
! [SV30: $i,SV100: $i,SV161: $i,SV212: $i,SV251: $i,SV282: $i,SV301: $i,SV307: $i,SV310: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV310 @ SV307 @ SV301 @ SV282 ) @ SV251 )
= ( hAPP @ ( c_Fun_Ocomp @ SV212 @ SV307 @ SV301 @ SV161 ) @ SV100 ) )
= $false )
| ( ( ( hAPP @ SV282 @ ( hAPP @ SV251 @ SV30 ) )
= ( hAPP @ SV161 @ ( hAPP @ SV100 @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(5946,plain,
! [SV37: $i,SV106: $i,SV165: $i,SV216: $i,SV255: $i,SV284: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false )
| ( ( ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(5947,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( ~ ( ( SV216 != SV106 )
| ( SV165 != SV37 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5925]) ).
thf(5948,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV38: $i,SV107: $i,SV256: $i] :
( ( ( ~ ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5926]) ).
thf(5949,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV256: $i,SV38: $i,SV107: $i] :
( ( ( ~ ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) ) )
= $false )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5926]) ).
thf(5950,plain,
! [SV43: $i,SV169: $i,SV259: $i,SV288: $i,SV112: $i,SV220: $i] :
( ( ( SV220 = SV112 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5928]) ).
thf(5951,plain,
! [SV112: $i,SV220: $i,SV259: $i,SV288: $i,SV43: $i,SV169: $i] :
( ( ( SV169 = SV43 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV220 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV288 @ SV259 ) @ SV112 ) @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5929]) ).
thf(5952,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( SV289 = SV260 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(5953,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( SV289 != SV260 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(5954,plain,
! [SV173: $i,SV290: $i,SV303: $i,SV308: $i,SV49: $i,SV118: $i,SV313: $i,SV222: $i,SV261: $i] :
( ( ( ( hAPP @ SV261 @ ( hAPP @ SV222 @ SV313 ) )
= ( hAPP @ SV118 @ ( hAPP @ SV49 @ SV313 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV308 @ SV303 @ SV290 @ SV261 ) @ SV222 )
= ( hAPP @ ( c_Fun_Ocomp @ SV173 @ SV303 @ SV290 @ SV118 ) @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5932]) ).
thf(5955,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ! [SY1000: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1000 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1000 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1000 ) @ SV56 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(5956,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ! [SY1001: $i] :
~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SY1001 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SY1001 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SY1001 ) @ SV56 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5935]) ).
thf(5957,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( SV295 = SV268 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(5958,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( SV295 != SV268 )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(5959,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ! [SY1005: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1005 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1005 @ SV131 @ SV62 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5938]) ).
thf(5960,plain,
! [SV62: $i,SV233: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ! [SY1006: $i] :
~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SY1006 )
| ~ ( c_Natural_Oevaln @ SV233 @ SY1006 @ SV131 @ SV62 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5939]) ).
thf(5961,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5940]) ).
thf(5962,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( ( SV236 != SV137 )
| ( SV190 != SV68 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5941]) ).
thf(5963,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i,SV309: $i,SV311: $i,SV312: $i] :
( ( ( ( hAPP @ SV312 @ ( hAPP @ SV311 @ SV309 ) )
!= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SV312 ) @ SV311 ) @ SV309 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(5964,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5946]) ).
thf(5965,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( ( SV216 != SV106 )
| ( SV165 != SV37 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5947]) ).
thf(5966,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV38: $i,SV107: $i,SV256: $i] :
( ( ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
| ( SV107 = SV38 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5948]) ).
thf(5967,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV256: $i,SV38: $i,SV107: $i] :
( ( ( ( SV107 != SV38 )
| ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5949]) ).
thf(5968,plain,
! [SV46: $i,SV115: $i,SV171: $i,SV221: $i,SV260: $i,SV289: $i] :
( ( ( SV289 = SV260 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV221 @ SV171 @ SV115 @ SV260 @ SV46 ) @ SV289 )
= ( hAPP @ SV115 @ SV289 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5953]) ).
thf(5969,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5955]) ).
thf(5970,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5956]) ).
thf(5971,plain,
! [SV59: $i,SV128: $i,SV183: $i,SV231: $i,SV268: $i,SV295: $i] :
( ( ( SV295 = SV268 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV231 @ SV183 @ SV128 @ SV268 @ SV59 ) @ SV295 )
= ( hAPP @ SV128 @ SV295 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5958]) ).
thf(5972,plain,
! [SV233: $i,SV62: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) )
| ~ ( c_Natural_Oevaln @ SV233 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) @ SV131 @ SV62 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5959]) ).
thf(5973,plain,
! [SV62: $i,SV233: $i,SV315: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 )
| ~ ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5960]) ).
thf(5974,plain,
! [SV68: $i,SV190: $i,SV272: $i,SV137: $i,SV236: $i] :
( ( ( SV236 != SV137 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5961]) ).
thf(5975,plain,
! [SV137: $i,SV236: $i,SV272: $i,SV68: $i,SV190: $i] :
( ( ( SV190 != SV68 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5961]) ).
thf(5976,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( SV236 != SV137 )
= $true )
| ( ( SV190 != SV68 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5962]) ).
thf(5977,plain,
! [SV27: $i,SV97: $i,SV158: $i,SV209: $i,SV248: $i,SV281: $i,SV300: $i,SV306: $i,SV309: $i,SV311: $i,SV312: $i] :
( ( ( ( hAPP @ SV312 @ ( hAPP @ SV311 @ SV309 ) )
= ( hAPP @ SV306 @ ( hAPP @ SV300 @ SV281 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV248 @ SV209 @ SV158 @ SV312 ) @ SV311 ) @ SV309 )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ SV97 @ SV209 @ SV27 @ SV306 ) @ SV300 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5963]) ).
thf(5978,plain,
! [SV37: $i,SV165: $i,SV255: $i,SV284: $i,SV106: $i,SV216: $i] :
( ( ( SV216 != SV106 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5964]) ).
thf(5979,plain,
! [SV106: $i,SV216: $i,SV255: $i,SV284: $i,SV37: $i,SV165: $i] :
( ( ( SV165 != SV37 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5964]) ).
thf(5980,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( SV216 != SV106 )
= $true )
| ( ( SV165 != SV37 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5965]) ).
thf(5981,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV38: $i,SV107: $i,SV256: $i] :
( ( ( ( hAPP @ SV256 @ SV107 )
!= ( hAPP @ SV256 @ SV38 ) )
= $true )
| ( ( SV107 = SV38 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5966]) ).
thf(5982,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV256: $i,SV38: $i,SV107: $i] :
( ( ( SV107 != SV38 )
= $true )
| ( ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5967]) ).
thf(5983,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5969]) ).
thf(5984,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 ) )
| ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(5985,plain,
! [SV233: $i,SV62: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) )
| ~ ( c_Natural_Oevaln @ SV233 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) @ SV131 @ SV62 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5972]) ).
thf(5986,plain,
! [SV62: $i,SV233: $i,SV315: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 )
| ~ ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(5987,plain,
! [SV68: $i,SV190: $i,SV272: $i,SV137: $i,SV236: $i] :
( ( ( SV236 = SV137 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5974]) ).
thf(5988,plain,
! [SV137: $i,SV236: $i,SV272: $i,SV68: $i,SV190: $i] :
( ( ( SV190 = SV68 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5975]) ).
thf(5989,plain,
! [SV272: $i,SV68: $i,SV190: $i,SV137: $i,SV236: $i] :
( ( ( SV236 = SV137 )
= $false )
| ( ( SV190 != SV68 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5976]) ).
thf(5990,plain,
! [SV37: $i,SV165: $i,SV255: $i,SV284: $i,SV106: $i,SV216: $i] :
( ( ( SV216 = SV106 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5978]) ).
thf(5991,plain,
! [SV106: $i,SV216: $i,SV255: $i,SV284: $i,SV37: $i,SV165: $i] :
( ( ( SV165 = SV37 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5979]) ).
thf(5992,plain,
! [SV255: $i,SV284: $i,SV37: $i,SV165: $i,SV106: $i,SV216: $i] :
( ( ( SV216 = SV106 )
= $false )
| ( ( SV165 != SV37 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(5993,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV38: $i,SV107: $i,SV256: $i] :
( ( ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) )
= $false )
| ( ( SV107 = SV38 )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5981]) ).
thf(5994,plain,
! [SV166: $i,SV217: $i,SV285: $i,SV302: $i,SV256: $i,SV38: $i,SV107: $i] :
( ( ( SV107 = SV38 )
= $false )
| ( ( ( hAPP @ SV256 @ SV107 )
= ( hAPP @ SV256 @ SV38 ) )
= $true )
| ( ( c_Typedef_Otype__definition @ SV302 @ SV285 @ SV256 @ SV217 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5982]) ).
thf(5995,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
!= SV56 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5983]) ).
thf(5996,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ~ ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5984]) ).
thf(5997,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV314: $i,SV228: $i,SV266: $i] :
( ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5984]) ).
thf(5998,plain,
! [SV233: $i,SV62: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) )
| ~ ( c_Natural_Oevaln @ SV233 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) @ SV131 @ SV62 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(5999,plain,
! [SV62: $i,SV233: $i,SV315: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 )
| ~ ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5986]) ).
thf(6000,plain,
! [SV272: $i,SV137: $i,SV236: $i,SV68: $i,SV190: $i] :
( ( ( SV190 = SV68 )
= $false )
| ( ( SV236 = SV137 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV236 ) @ SV190 )
= ( hAPP @ ( hAPP @ ( c_List_Olist_OCons @ SV272 ) @ SV137 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5989]) ).
thf(6001,plain,
! [SV255: $i,SV284: $i,SV106: $i,SV216: $i,SV37: $i,SV165: $i] :
( ( ( SV165 = SV37 )
= $false )
| ( ( SV216 = SV106 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV216 ) @ SV165 )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ SV284 @ SV255 ) @ SV106 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5992]) ).
thf(6002,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
!= SV56 ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5995]) ).
thf(6003,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
| ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5996]) ).
thf(6004,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV314: $i,SV228: $i,SV266: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5997]) ).
thf(6005,plain,
! [SV233: $i,SV62: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5998]) ).
thf(6006,plain,
! [SV270: $i,SV186: $i,SV131: $i,SV62: $i,SV233: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV233 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) @ SV131 @ SV62 ) )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5998]) ).
thf(6007,plain,
! [SV62: $i,SV233: $i,SV315: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5999]) ).
thf(6008,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6002]) ).
thf(6009,plain,
! [SV228: $i,SV125: $i,SV180: $i,SV56: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
!= SV56 )
= $false )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6002]) ).
thf(6010,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( SV228
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6003]) ).
thf(6011,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV314: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
!= SV125 )
= $true )
| ( ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6004]) ).
thf(6012,plain,
! [SV233: $i,SV62: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6005]) ).
thf(6013,plain,
! [SV270: $i,SV186: $i,SV131: $i,SV62: $i,SV233: $i] :
( ( ( c_Natural_Oevaln @ SV233 @ ( sK8_SY1005 @ SV62 @ SV233 @ SV131 @ SV186 @ SV270 ) @ SV131 @ SV62 )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6006]) ).
thf(6014,plain,
! [SV62: $i,SV233: $i,SV315: $i,SV131: $i,SV186: $i,SV270: $i] :
( ( ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6007]) ).
thf(6015,plain,
! [SV180: $i,SV56: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6008]) ).
thf(6016,plain,
! [SV228: $i,SV125: $i,SV180: $i,SV56: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ~ ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6009]) ).
thf(6017,plain,
! [SV56: $i,SV180: $i,SV314: $i,SV125: $i,SV266: $i,SV228: $i] :
( ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
!= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6010]) ).
thf(6018,plain,
! [SV56: $i,SV180: $i,SV125: $i,SV314: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
= SV125 )
= $false )
| ( ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6019,plain,
! [SV186: $i,SV270: $i,SV62: $i,SV131: $i,SV315: $i,SV233: $i] :
( ( ( c_Natural_Oevaln @ SV233 @ SV315 @ SV131 @ SV62 )
= $false )
| ( ( c_Natural_Oevaln @ SV270 @ SV186 @ SV131 @ SV315 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV270 @ SV233 ) @ SV186 @ SV131 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6014]) ).
thf(6020,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) )
= $false )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6015]) ).
thf(6021,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
| ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6016]) ).
thf(6022,plain,
! [SV125: $i,SV228: $i,SV56: $i,SV180: $i,SV314: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV180 )
= SV56 )
= $false )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV314 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6023,plain,
! [SV125: $i,SV228: $i,SV56: $i,SV314: $i,SV266: $i,SV180: $i] :
( ( ( SV180
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV314 ) @ SV56 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV314 )
= SV125 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6024,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
= $false )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6020]) ).
thf(6025,plain,
! [SV228: $i,SV125: $i,SV56: $i,SV266: $i,SV180: $i] :
( ( ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) )
= $false )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6020]) ).
thf(6026,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
!= SV125 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6021]) ).
thf(6027,plain,
! [SV228: $i,SV125: $i,SV56: $i,SV266: $i,SV180: $i] :
( ( ( SV180
!= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6021]) ).
thf(6028,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
= SV125 )
= $true )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6024]) ).
thf(6029,plain,
! [SV228: $i,SV125: $i,SV56: $i,SV266: $i,SV180: $i] :
( ( ( SV180
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) )
= $true )
| ( ( SV228
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6025]) ).
thf(6030,plain,
! [SV125: $i,SV180: $i,SV56: $i,SV228: $i,SV266: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) )
= SV125 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6026]) ).
thf(6031,plain,
! [SV228: $i,SV125: $i,SV56: $i,SV266: $i,SV180: $i] :
( ( ( SV180
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ ( sK7_SY1000 @ SV56 @ SV180 @ SV125 @ SV266 @ SV228 ) ) @ SV180 )
= SV56 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV228 ) @ SV180 )
= ( hAPP @ ( hAPP @ ( c_List_Oappend @ SV266 ) @ SV125 ) @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6027]) ).
thf(6032,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[5489,6031,6030,6029,6028,6023,6022,6019,6013,6012,6001,6000,5994,5993,5991,5990,5988,5987,5977,5971,5968,5957,5954,5952,5951,5950,5945,5944,5943,5933,5927,5923,5922,5917,5914,5913,5912,5907,5906,5903,5896,5883,5882,5877,5876,5875,5870,5865,5853,5843,5842,5825,5822,5821,5819,5818,5815,5814,5809,5808,5807,5806,5802,5800,5799,5776,5761,5759,5750,5749,5748,5747,5746,5726,5720,5705,5692,5687,5686,5679,5663,5660,5633,5631,5630,5624,5623,5622,5621,5569,5562,5557,5518,5508,5507,5498,5497,5496,5490]) ).
thf(6033,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.24 % Computer : n003.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Oct 6 16:55:40 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.29/15.78 ....................................
% 77.29/15.78
% 77.29/15.78 No.of.Axioms: 69
% 77.29/15.78
% 77.29/15.78 Length.of.Defs: 0
% 77.29/15.78
% 77.29/15.78 Contains.Choice.Funs: false
% 77.29/15.78 .....................................................................................
% 77.29/15.78
% 77.29/15.78 ********************************
% 77.29/15.78 * All subproblems solved! *
% 77.29/15.78 ********************************
% 77.29/15.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:70,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:293,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6032,loop_count:0,foatp_calls:1,translation:fof_full)
% 77.29/15.78
% 77.29/15.78 %**** Beginning of derivation protocol ****
% 77.29/15.78 % SZS output start CNFRefutation
% See solution above
% 77.29/15.79
% 77.29/15.79 %**** End of derivation protocol ****
% 77.29/15.79 %**** no. of clauses in derivation: 878 ****
% 77.29/15.79 %**** clause counter: 6032 ****
% 77.29/15.79
% 77.29/15.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:70,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:293,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6032,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------